j. m. p. q. delgado a. g. barbosa de lima editors

Advanced Structured Materials

J. M. P. Q. DelgadoA. G. Barbosa de Lima Editors

Transport Processes and Separation Technologies

Advanced Structured Materials

Volume 133

Series Editors

Andreas Öchsner, Faculty of Mechanical Engineering, Esslingen University ofApplied Sciences, Esslingen, Germany

Lucas F. M. da Silva, Department of Mechanical Engineering, Faculty ofEngineering, University of Porto, Porto, Portugal

Holm Altenbach , Faculty of Mechanical Engineering,Otto von Guericke University Magdeburg, Magdeburg, Sachsen-Anhalt, Germany

https://orcid.org/0000-0003-3502-9324

Common engineering materials reach in many applications their limits and newdevelopments are required to fulfil increasing demands on engineering materials.The performance of materials can be increased by combining different materials toachieve better properties than a single constituent or by shaping the material orconstituents in a specific structure. The interaction between material and structuremay arise on different length scales, such as micro-, meso- or macroscale, and offerspossible applications in quite diverse fields.

This book series addresses the fundamental relationship between materials and theirstructure on the overall properties (e.g. mechanical, thermal, chemical or magneticetc.) and applications.

The topics of Advanced Structured Materials include but are not limited to

• classical fibre-reinforced composites (e.g. glass, carbon or Aramid reinforcedplastics)

• metal matrix composites (MMCs)• micro porous composites• micro channel materials• multilayered materials• cellular materials (e.g., metallic or polymer foams, sponges, hollow sphere

structures)• porous materials• truss structures• nanocomposite materials• biomaterials• nanoporous metals• concrete• coated materials• smart materials

Advanced Structured Materials is indexed in Google Scholar and Scopus.

More information about this series at http://www.springer.com/series/8611

http://www.springer.com/series/8611

J. M. P. Q. Delgado • A. G. Barbosa de LimaEditors

Transport Processesand Separation Technologies

123

EditorsJ. M. P. Q. DelgadoCONSTRUCT-LFC, Department of CivilEngineeringUniversity of PortoPorto, Portugal

A. G. Barbosa de LimaDepartment of Mechanical EngineeringFederal University of Campina GrandeCampina Grande, Paraíba, Brazil

ISSN 1869-8433 ISSN 1869-8441 (electronic)Advanced Structured MaterialsISBN 978-3-030-47855-1 ISBN 978-3-030-47856-8 (eBook)https://doi.org/10.1007/978-3-030-47856-8

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer NatureSwitzerland AG 2021This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whetherthe whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse ofillustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, andtransmission or information storage and retrieval, electronic adaptation, computer software, or by similaror dissimilar methodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exempt fromthe relevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information in thisbook are believed to be true and accurate at the date of publication. Neither the publisher nor theauthors or the editors give a warranty, expressed or implied, with respect to the material containedherein or for any errors or omissions that may have been made. The publisher remains neutral with regardto jurisdictional claims in published maps and institutional affiliations.

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https://doi.org/10.1007/978-3-030-47856-8

Contents

1 Clay Ceramic Materials: From Fundamentals and Manufacturingto Drying Process Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1A. G. Barbosa de Lima, J. M. P. Q. Delgado, L. P. C. Nascimento,E. S. de Lima, V. A. B. de Oliveira, A. M. V. Silva, and J. V. Silva1.1 Ceramic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.2 Fundamental Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1.3 The Ceramic Industry and Clay Products . . . . . . . . . . . . . 31.1.4 Red Ceramic Product Manufacturing Process . . . . . . . . . . 5

1.2 The Drying Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2.1 General Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2.2 The Mathematical Modeling of the Drying

Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.3 Lumped Model Application: Drying of Clay Ceramic Brick . . . . . 13

1.3.1 The Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . 141.3.2 Phenomenological Mathematical Modeling . . . . . . . . . . . . 151.3.3 Results Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

1.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2 Vegetable Fiber Drying: Theory, Advanced Modelingand Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31J. F. Brito Diniz, A. R. C. de Lima, I. R. de Oliveira, R. P. de Farias,F. A. Batista, A. G. Barbosa de Lima, and R. O. de Andrade2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.2 Drying of Sisal Fibers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.2.1 Experimental Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.2.2 Theoretical Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

2.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

v

3 Foam-Mat Drying Process: Theory andApplications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61E. R. Mangueira, A. G. Barbosa de Lima, J. de Assis Cavalcante,N. A. Costa, C. C. de Souza, A. K. F. de Abreu, and A. P. T. Rocha3.1 Drying Theory of Porous Materials . . . . . . . . . . . . . . . . . . . . . . . 62

3.1.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.1.2 Mathematical Modeling in Drying . . . . . . . . . . . . . . . . . . 64

3.2 Foam-Mat Drying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663.2.1 General Foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663.2.2 Different Methods for Foam Formation . . . . . . . . . . . . . . . 683.2.3 Foaming Agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.3 Applications: Drying of Egg White and Yolk of Duck Egg . . . . . . 703.3.1 Material Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703.3.2 Experimental Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . 703.3.3 Experiment of Foam-Mat Drying . . . . . . . . . . . . . . . . . . . 723.3.4 Analysis of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

3.4 Final Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

4 Drying Process of Jackfruit Seeds . . . . . . . . . . . . . . . . . . . . . . . . . . . 89T. M. Q. de Oliveira, R. A. de Medeiros, V. S. O. Farias,W. P. da Silva, C. M. R. Franco, and A. F. da Silva Júnior4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 904.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4.2.1 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 914.2.2 Mathematical Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 92

4.3 Results Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 984.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

5 Spouted Bed Drying of Fruit Pulps: A Case Study on Dryingof Graviola (Annona muricata) Pulp . . . . . . . . . . . . . . . . . . . . . . . . . 105F. G. M. de Medeiros, I. P. Machado, T. N. P. Dantas, S. C. M. Dantas,O. L. S. de Alsina, and M. F. D. de Medeiros5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1065.2 Fundamentals of Spouted Bed Drying . . . . . . . . . . . . . . . . . . . . . 1075.3 Spouted Bed Drying of Fruit Pulps . . . . . . . . . . . . . . . . . . . . . . . 1095.4 Phytochemicals on Spouted Bed Dried Fruit

Powders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1115.4.1 Impact of Spouted Bed Drying on the Phytochemicals

Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1125.4.2 Use of Drying Carriers . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

5.5 Spouted Bed Drying of Graviola (Annona muricata) Pulp:A Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1165.5.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1175.5.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

vi Contents

5.5.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 1225.5.4 Final Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

6 Osmo-convective Dehydration of Fresh Foods: Theoryand Applications to Cassava Cubes . . . . . . . . . . . . . . . . . . . . . . . . . 151T. R. Bezerra Pessoa, A. G. Barbosa de Lima, P. C. Martins,V. C. Pereira, T. C. O. Alves, E. S. da Silva, and E. S. de Lima6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

6.1.1 Drying Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1526.1.2 The Focus of This Work . . . . . . . . . . . . . . . . . . . . . . . . . 153

6.2 Application: Hybrid Drying of Cassava Cubes . . . . . . . . . . . . . . . 1536.2.1 The Raw Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1536.2.2 Osmotic Dehydration Tests . . . . . . . . . . . . . . . . . . . . . . . 1546.2.3 Convective Drying Tests . . . . . . . . . . . . . . . . . . . . . . . . . 1586.2.4 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

6.3 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

7 Heat Transfer in a Packed-Bed Elliptic Cylindrical Reactor:Theory, Heterogeneous Transient Modeling, andApplications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185A. S. Pereira, R. M. da Silva, R. S. Santos, A. G. Barbosa de Lima,R. O. de Andrade, W. M. P. B. de Lima, and G. S. de Lima7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1867.2 Porous Media and Packed-Bed Reactors . . . . . . . . . . . . . . . . . . . 186

7.2.1 Porous Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1867.2.2 Chemical Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

7.3 Heat Transfer in Fixed-Bed Elliptical Reactor via Two-PhaseModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1917.3.1 Physical Problem and Geometry . . . . . . . . . . . . . . . . . . . . 1917.3.2 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1947.3.3 Numerical Treatment of Heat Transport

Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2007.4 Application: Heat Transfer in an Elliptic Cylindrical Reactor

Filled with Spheroidal Particles . . . . . . . . . . . . . . . . . . . . . . . . . . 2057.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

Contents vii

Chapter 1Clay Ceramic Materials: FromFundamentals and Manufacturingto Drying Process Predictions

A. G. Barbosa de Lima, J. M. P. Q. Delgado, L. P. C. Nascimento,E. S. de Lima, V. A. B. de Oliveira, A. M. V. Silva, and J. V. Silva

Abstract This chapter is devoted to study heat and mass transfer and dimensionvariations of arbitrary-shaped porous materials. The focus is on the drying processof clay ceramic materials. Here, different topics related to history, manufacturing,drying process, phenomenological lumped modeling, and parameters estimation arepresent and discussed. Emphasis is given to industrial clay bricks, with theoreticaland experimental approaches.

Keywords Drying · Brick · Experimental · Simulation · Lumped model

A. G. B. de Lima (B) · L. P. C. Nascimento · E. S. de Lima · A. M. V. Silva · J. V. SilvaDepartment of Mechanical Engineering, Federal University of Campina Grande, Av. AprígioVeloso, 882, Bodocongó, Campina Grande, PB 58429-900, Brazile-mail: [email protected]

L. P. C. Nascimentoe-mail: [email protected]

E. S. de Limae-mail: [email protected]

A. M. V. Silvae-mail: [email protected]

J. V. Silvae-mail: [email protected]

J. M. P. Q. DelgadoCONSTRUCT-LFC, Civil Engineering Department, Faculty of Engineering, University of Porto,Porto, Portugale-mail: [email protected]

V. A. B. de OliveiraState University of Paraiba, Rodovia PB 075, S/N, km 1, Guarabira, PB 58200-000, Brazile-mail: [email protected]

© The Editor(s) (if applicable) and The Author(s), under exclusive licenseto Springer Nature Switzerland AG 2021J. M. P. Q. Delgado and A. G. Barbosa de Lima (eds.), Transport Processesand Separation Technologies, Advanced Structured Materials 133,https://doi.org/10.1007/978-3-030-47856-8_1

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1.1 Ceramic Materials

1.1.1 History

The art of pottery is one of the oldest in the world due mainly to the abundance ofclay and the ease of extraction and fabrication. There is evidence of activity of thisart in almost all peoples of antiquity and to improve their quality of life, man hasalways been seeking to perfect the various uses of ceramic materials.

Pottery was invented in the Neolithic (polished stone age) in 25000 BC and duringthis period prehistoric man-made wicker baskets with clay, that is, the first objectswere intended to store grain and liquids and were just simple objects. Later, theplasticity of clays was discovered, where it was noted that by adding water the claycould be molded, dried in the sun, and hardened when exposed to high temperatures.Following, ceramics were widely used for various purposes, such as pieces withnozzles and handles made with relief images, or with living paintings that wereconsidered decorative objects (Cavalcanti 2010).

Each civilization and each culture have developed its own forms and characteris-tics in the use of clay, so that pottery is one of the greatest auxiliaries in historicalresearch. One of the greatest ancient peoples who have strong ties to ceramics is theGreeks, who for a long time produced the finest pieces in the Mediterranean world.It was common at that time to sell these products at fairs and there was a continuousexport of generally ovoid and handled vessels (Phoenician amphora), which couldoften be used to serve water, wine, and olive oil (Silva 2009).

In addition to the Greeks and Romans, other ancient peoples such as the Byzan-tines and Arabs were responsible for transmitting their practices throughout Europe,which consequently have varied styles of construction in their territories. It wasprecisely with the growth of civil construction that themanufacture of ceramic piecesevolved from a more artisanal activity to an industrial one. Initially, around 1850,the first bricks were made on animal-powered molding machines, only later that themanufacturing would go through a major leap.

Production systems were stagnant until the nineteenth century, i.e., drying wasstill done in the sun, burning in trapezoidal ovens and production was still mostly byhand. Only with the emergence of the first steam-powered machines, it was possibleto increase production as raw material extraction, preparation, and forming opera-tions became mechanized. Thus, in the modern era countries like Spain, France andGermany stood out in the market as producers of red ceramics and as equipmentmanufacturers. It is important to highlight that Italy was one of the great pioneers inthe production of bricks in series with good quality (Silva 2016).

Later, in the mid-twentieth century, the technological development of the ceramicindustry boosted the manufacture of high strength and low weight cast structuralblocks, a major evolution compared to previously manufactured solid bricks. At thistime, including Brazil, there was a resurgence of structural masonry with ceramicproducts, competing economically with conventional reinforced concrete structuresin medium-sized buildings (up to about 8–10 floors) (Silva 2009).

1 Clay Ceramic Materials: From Fundamentals … 3

Following, the ceramic industry underwent major developments, now based onresearch, technology, and studies by specialized laboratories. Along with the studyof ceramics, the study of ovens, better glazing, molding apparatus, dry molding, highstrength porcelain was developed and it was possible that the field of use of ceramicsgrew a lot, enabling aerospace and technology applications, such as space shuttlethermal shielding, nanofilm production, sensors to detect toxic gases, and amongothers.

With regard to Brazil, construction ceramics currently occupies a prominent placein the national economy. Great growth came in the industry when the Government’sGrowth Acceleration Programs (PAC) andMyHouseMy Life (MCMV)were imple-mented. Therefore, because it represents a sector of great importance in job creationand income distribution, it has received the attention of government sectors, researchinstitutes, universities, and various entities (Rodrigues Neto and Mota 2016).

1.1.2 Fundamental Concepts

Ceramic or ceramic material can be defined as any non-metallic and inorganic mate-rial whose structure, after heat treatment at high temperatures, is wholly or partiallycrystallized. They are composed of total or predominantly ionic interatomic bonds,but having some covalent character. Ceramics are known to have different raw mate-rials in their composition, but the main one is clay, which can be defined as an earthy,thin, and natural material that, by adding water, acquires a certain plasticity and canbe easily molded (Callister 2007; Callister and Rethwisch 2008).

Ceramic materials have a wide range of structural arrangement types. The exis-tence of several ceramic phases makes possible the combinations of metallic andnon-metallic atoms (which formmany structural arrangements) making themwidelyapplicable in various sectors besides construction. It is noteworthy that the structureof the ceramic material defines its properties (Silva 2009; Callister 2007; Callisterand Rethwisch 2008).

1.1.3 The Ceramic Industry and Clay Products

The ceramic industry sector plays a very important role in Brazil’s economy, with ashare of approximately 1% of GDP. Gaining prominence, the evolution of Braziliancompanies has been very fast, mainly due to the abundance of natural raw material,alternative sources of energy, and the availability of practical technologies. Amongthe regions of the country, the ones that stand out and have a large concentration ofindustries are the Southeast and the South; this is because they have higher demo-graphic density, greater industrial and agricultural activity, better infrastructure, andbetter income distribution. It is noteworthy that the other regions of the country haveshown a certain degree of development, especially in the northeast due to the large


occurrence of mineral resources, abundance of natural gas, expanding market, andgreat export potential (Silva 2009).

Despite the greatness of the Brazilian ceramics industry and its great potential,it is quite heterogeneous. In addition to the red ceramics industries, several miningcompanies, ceramic tiles, sanitary ware, thermal ceramics, enamels, and others havealready been installed or are in phase of deployment. However, within the currentscenario of globalization, it can be said that the segments that are best adapted andstructured are the covering, refractory, and sanitary ware. In the other segments, thereare some modern companies that stand out from the others, but this contingent is notso expressive.

One of the most important areas in the industry is related to red ceramic products.According to data from SEBRAE/Brazil (SEBRAE 2019), there is a range of 8500–11,000 companies in the country, generating around 300,000 direct jobs and 1.5million indirect jobs. Despite having good numbers, the production activity of thesector has a great technological backwardness, since most of the companies are ofsmall ormedium size and family order. It is alsoworth noting that this large number ofjobs that the sector generates is caused by the low level of knowledge and investmentrequired to start activities.

In the northeast region, and especially in the State of Paraíba (Brazil), there isa marked industrial activity in this area. There are around 60 active red ceramicfactories throughout the state, distributed in at least 30 towns, offering about 3000direct jobs. Research carried out in the state of Paraíba shows, as to geographicregions and watersheds, that studies in the area are concentrated in some specificregions of the state, especially in the coast and in the Agreste. On the other hand,in the Sertão and Cariri regions there is a large concentration of potentially usabledeposits, but, to date, there is no systematic study regarding their exploitation anduse.

Red ceramics encompass various products such as blocks, tiles, solid bricks,plumbing pipes, slabs, castings, and also expanded clay, which are often used inconstruction. It is also present in household items such as filters, decorative vases,and clay pots. This type of ceramics has the nomenclature “red” due to the presenceof ferrous compounds that develop reddish coloration.

The basic raw material of structural ceramics is common clay, which is used ina single dough to shape products, unlike other segments of the ceramics industrythat mix clay with other substances such as talc, kaolin, and others (Callister 2007;Callister and Rethwisch 2008; Cabral et al. 2008). Natural clay seeks an ideal compo-sition of plasticity and fusibility so that it provides good workability and mechanicalresistance during firing.

Red ceramic products are classified according to the manufacturing process usedand can be pressed or extruded. In summary, red or structural ceramics can be groupedgenerically according to Table 1.1, as follows.

The clay used for the production of red ceramics is composed of a large amountof amorphous material, in other words, those that do not have long-distance spatialordering; however, the crystalline material predominates, which is grouped in well-defined mineralogical species. From the physicochemical point of view, clays can be


Table 1.1 Types and characterization of red ceramics (Silva 2009)

Types Description

Porous Solid bricks, pressed solid bricks, laminated bricks, hollow bricks,prefabricated panels, tiles, components for slabs, tiles, conductors for electricalcables, and others (sills, cladding plates, etc.)

Glazed Tiles, glazed glazes, laminated bricks, pipes, glazed internally, glazed internallyand externally, and unglazed

Expanded clay Obtained from thermo-expansion of some types of clays (illite). In theproduction process, mineral oil is added to the ceramic mass. They are launchedin an inclined rotary kiln with a burner at the bottom

considered as dispersed mineral systems in which particles below 2 µm in diameterpredominate (Silva 2016).

A great advantage of the clay used in red ceramics is that it has great plasticitywhile wet, allowing the manufacture of pieces of various shapes using simple equip-ment. Another important point is that when cooked at more than 800 °C it has a goodmechanical resistance, making the final product suitable for various applications(Brito 2016).

To produce bricks and tiles the clay used is generally quaternary and sometimestertiary. One of the main characteristics is to present, in large quantities, iron, andalkalis in their composition. They are fine-grained and have a considerable organicmatter content, factors that are responsible for their high plasticity.

It is recommended that the clays used have easy molding, flexural strength beforeand after sintering, have a reddish color after sintering, with a minimum of cracksand warping. It is noteworthy that high levels of bivalent iron and alkaline elementsmay reduce the range of vitrification and cause undesirable coloration (Silva 2009).

1.1.4 Red Ceramic Product Manufacturing Process

Red ceramics can generate a wide variety of products and for this it goes througha specific production process, which is sometimes still poorly evolved compared toother segments of the ceramic industry. However, due to the increasing emergenceof technological innovations in some companies, we can find good quality produc-tion processes with high production rates. Most of these technological advances arerelated to equipment automation and, consequently, the reduction of labor costs.

The production process, exemplified in Fig. 1.1, is common to all red ceramiccompanies in general, with slight variations depending on the particular charac-teristics of each raw material or end product. For example, some companies userudimentary equipment and others have more modern equipment, or some have amuch higher degree of production, among other differences.

The production process of pieces with red ceramic comprises several steps thatcan be divided into four major stages, namely, extraction and preparation of raw


Fig. 1.1 Manufacturing flowchart of red ceramic pieces

materials, mechanical forming, thermal processing, and shipping. The followingbest describes these steps:

1.1.4.1 Extraction and Preparation of Raw Materials

Themanufacturing process begins with the extraction of clay, which is removed fromthe deposits with the aid of backhoes and then transported to storage sheds, whichmay be owned by companies or third parties. At this stage, the material goes througha “rest”, thus undergoing chemical changes and being unpacked. Shed storage alsoensures continued production in rainy seasons. After this phase, we have the dosage,in which the clays are proportionally dosed in a feeder coffin obeying their ceramiccharacteristics.

Following the manufacturing process is disintegration, which is the step respon-sible for bringing the hardest and most compacted clays to a disintegrator that willcrush the larger clumps of clay to facilitate subsequent operations. Then, the rawmaterial goes to the mixer, where it will be homogenized, thus allowing the additionof water in the mixture to obtain adequate moisture and plasticity for extrusion.


The last step of this first major stage is lamination, which is responsible for athickening of the mixture, eliminating air bubbles or clumps that may have remainedso far. With the end of this stage, the raw material already prepared can be directedto the extruders, which may even have a rolling mill attached to them.

1.1.4.2 Mechanical Forming

The mechanical conformation stage is responsible for transforming the clay plasticmass into products with different shapes and sizes. Thus, according to the type ofproduct to be obtained and also depending on the plasticity characteristics of theavailable raw material, it will be possible to choose the appropriate forming system.

The main systems of this stage are extrusion and cutting. Firstly, the clay masswill take the desired shape upon entering the extruder, which contains a steel plateperforated in a vacuum chamber. Then, through the manual or automatic cutter, theextruded block is cut to standard sizes, thus obtaining products such as bricks, tiles,ceramic tubes, and among others (Oliveira and Bernils 2006).

1.1.4.3 Thermal Processing

This stage consists of the drying and burning steps of the already formed parts. Thisis where the composition and structure transformations will occur, generating thefinal properties of the product, such as color, gloss, porosity, flexural strength, hightemperatures, and among others (Silva 2009).

During drying, a large amount of thermal energy is used to slowly and evenlyevaporate the water added during the molding process. This step usually takes placeinside drying chambers and aims to reduce the moisture content of the products from20–25% to 3–10% after the process.

An important property of any clay is that it has water in the constitution of itscrystal lattice. Thus, during the drying process, the water that has been added iseasily removed, with the temperature starting from room temperature and reachingapproximately 110 °C. However, water that is in the clay crystal lattice will only beremoved at temperatures above 400 °C andmay vary to even higher values dependingon the type of clay.

During the drying process, the clay may contract as the spaces that were occupiedby water inside the material become empty after evaporation. This shrinkage isproportional to the degree of moisture removed. Thus, it is important to controlthe process well, as a possible consequence of this shrinkage is that it can causedeformation or cracking in the material.

Following is the firing step, in which the product is taken to a kiln and, as wellas drying, will receive an even greater amount of thermal energy. Once these stepsare completed, the product will have lower porosity and greater mechanical strengthand will also be ready for commercialization and use.


1.1.4.4 Expedition

Shipment is the final stage of the production process, where finished product isinspected to identify excessively cracked, broken, chipped, or burned products. Then,the parts are stored in a covered area until they leave for delivery to the customer. InBrazil, transportation of the parts is usually made by trucks on the highways of thecountry.

The thermal processing stage must be performed correctly, otherwise the partscould present a series of defects and thus, the products will not be able to performtheir respective functions. Given this, the most common defects are as follows (Silva2009; Silva et al. 2011):

(a) Commitments—This defect is a deformation of the part usually caused byresidual shrinkage stresses, which arisewhen one side of thematerial dries fasterthan the other, i.e., it is important that the drying is done evenly. Commitmentsmay also arise due to poor positioning of the product on the drying support.

(b) Cracks—It is important that during the drying process the air velocity andtemperature are controlled, because when we have a very fast drying, it iscommon the appearance of cracks, which are nothing more than small fissuresthat start at the edges and spread until the center of the piece. Cracks may alsoappear in the firing step, which may be by heating or cooling. The heating onesare characterized by being open, little winding, and with jagged edges, while thecooling ones are characterized by being closed and very thin, usually S-shapededges. It is important to point out that all drying starts must be done with theplastic-covered part, to prevent a very fast outflow of water that is closer to thesurface, causing a localized shrinkage that can cause cracks.

(c) Blackheart—This type of defect is black or gray spots that can be seen along thecross section of the part and appear after the firing process. The existence of the“black heart” is associated with the presence of carbon-containing compounds,which are formed due to the small amount of oxygen, preventing the completeoxidation of carbon compounds and organic matter.

(d) Efflorescence—Efflorescence occurs on the outer surface of the product andis a salt deposit accumulated in some regions, which may cause undesirablestains and colors. This defect appears as the water interferes with salts. If thepiece, after burning, absorbs moisture, the salts will be dissolved; however, ifthe external environment becomes dry, the opposite process occurs, the surfacewater is evaporated and the crystallization of the salts occurs.

(e) Defects related to steps before or after drying—It is common for small cracksto occur when the clay paste is improperly mixed in the mixing step. This defectis most pronounced in areas with higher moisture content and is quite commonin manual manufacturing processes. Finally, it is worth mentioning the problemof moisture absorption. Depending on the type of clay, if the time elapsed fromthe clay leaves the dryer to when it is introduced into the kiln is large and theambient absolute humidity is very high, a rehydration (reabsorption) processmay occur, which may cause breakage and/or explosion when material entersthe kiln.


1.2 The Drying Process

1.2.1 General Principles

Drying can be explained as a thermodynamic process responsible for the partialremoval of a liquid, usually water, from the porous material by providing energy to itand providing water loss by evaporation. In this process, there is a simultaneous heatand mass transfer, and the transport of moisture from the interior to the surface of thematerial may occur in the form of liquid and/or vapor, depending on the percentageof moisture present and the type of product (Brooker et al. 1992; Strumillo andKudra1986).

The drying process has become, amongmanyother uses, one of themost importantsteps in the manufacture of ceramic parts. In the case of red ceramic, this step is ofrelevant importance, since if the moisture is not removed properly, severe stressesoccur inside the part, causing deformations, cracks, and reducing the quality of theproduct post-drying process. Thus, it is noteworthy that the in-depth study relatedto drying of ceramic materials increases the overall efficiency of the ceramic sectorby reducing losses and increasing material quality and provides an environmentconducive to progress and sustainable development.

There are three ways to classify drying: natural, artificial, or mixed. Whatever thetype of drying, it has to fulfill four basic functions: the transport of the heat necessaryfor water evaporation, the removal of the produced water vapor, the reduction of thesaturated vapor layer formed on the product surface and the movement of liquid,and/or vapor inside the part.

The process time depends on the special conditions of the drying environment,such as temperature, relative humidity, and air velocity, and may reach periods of upto six weeks (natural drying). Artificial drying is carried out in drying chambers ordryers, usually taking advantage of the residual heat of the kiln, which significantlyreduces the drying time. In addition, the artificial drying period also depends on thecharacteristics of the raw material, the shape of the parts, and the type of dryer.

Convective drying technique differs from other separation techniques such asosmotic dehydration, evaporation, and decantation by the waywater is removed fromthe solid. In convective drying, there is a difference between the partial pressure ofthe water vapor at the surface of the product and the surrounding air, which allowsthe migration of the liquid from the inside and consequently the removal of the watermolecules from it. In osmotic dehydration, for example, this moisture removal mayoccur due to a pressure difference between the product and a hypertonic solution,due to a density difference, or due to temperature increase (Silva 2016; Brooker et al.1992; Strumillo and Kudra 1986).

In order, to perform a thermodynamic analysis of drying it is necessary to under-stand the influence of velocity, relative humidity, and temperature of the drying air onthe process. Relative humidity can be defined as the ratio of the vapor partial pressurein the air to the vapor saturation pressure, which varies with temperature. The abilityof air to absorb water vapor will be higher when the saturation pressure of water


vapor is greater than the partial pressure of water vapor. Therefore, the ability of airto absorb water vapor increases with temperature, so that the higher the air temper-ature, the greater its drying capacity, in fixed conditions of the air relative humidity.In addition, if the air is warmer, the volume of air needed for drying decreases and,as a result, the powers of the hoods and air circulators are reduced, reducing dryingcosts.

The speed with which the product is dried can be affected by many factors, suchas moisture movement mechanism, product shape, external environment conditions,and green product porosity. Thus, it is of great importance to verify the influenceof the shape and volume of the pores in the part, because it is inside them thatis the moisture, that even under favorable conditions can be retained inside thesepores. This occurs when the surface of the part is dried very quickly, as the pores,being very narrow, reduce moisture migration for a rate less than the evaporationrate. Another important point is that with a higher drying air temperature and lowerrelative humidity there will be an increase in drying rate.

The drying process is generally divided into four distinct phases: adaptation,colloidal water outlet, void formation, and interstitial moisture expulsion. In the firstphase occurs the adaptation of the product to environmental conditions (tempera-ture, relative humidity, and pressure), in which drying will be performed. In thesecond phase, there is evaporation of the colloidal water, and sensible variations inthe dimensions of the part occur due to the approximation of the particles of itsmicrostructure. Even at this stage water continually migrates to the surface of thepart, constantly forming an evaporating saturated wet film. In the third phase occursthe disappearance of the water film on the surface of the piece, which provokeschanges in color. The last drying phase, which is not always reached in the dryersand is often performed in the kilns, is the expulsion of the last amounts of moisturefrom interstitial origin, in which the moisture removal rate decreases to near zero(Silva 2009).

Given the importance and complexity of the drying process, a large number ofresearchers have been working intensively on its analysis. Some focus on external airconditions, such as temperature, relative humidity, and velocity, correlated with theproduct’s drying rate, while others consider the internal conditions of the product,with emphasis on the mechanisms of moisture movement and their effects on it. Inthis regard, several drying theories have been proposed to describe heat and masstransport in capillary porous media, namely,

(a) Liquid diffusion theory;(b) Vaporization–condensation theory;(c) Cappilary theory;(d) Kricher’s theory;(e) Luikov’s theory;(f) Philip and De Vrie’s theory;(g) Berger and Pei’s theory;(h) Fortes and Okos theory.


A more detailed discussion of drying theories can be found in the literature(Brooker et al. 1992; Strumillo and Kudra 1986; Lima et al. 2014). According tothe drying theories listed before, the following mechanisms of moisture transport inporous material have been cited in the literature:

(a) Transport of liquid by diffusion due to moisture concentration gradients;(b) Transport of vapor by diffusion due to moisture concentration gradients and

vapor partial pressure (caused by temperature gradients);(c) Transport by effusion (Knudsen flow) that occurs when the average free path

of vapor molecules is of the same order as the pore diameter. It is important forhigh vacuum conditions such as freeze drying;

(d) Transport of vapor by thermofusion due to temperature gradients;(e) Transport of liquids by capillary forces due to capillarity phenomena;(f) Transport of fluid by osmotic pressure due to osmotic force;(g) Transport of liquid due to gravity;(h) Transport of liquid and vapor due to total pressure difference caused by external

pressure, shrinkage, high temperature, and capillarity;(i) Transport of liquid and vapor by surface diffusion due to the migration of these

phases through the pores of the product surface.

Then, based on the drying theories and moisture migration mechanisms, severaldrying models have been reported in the literature. This topic will be discussedfollowing.

1.2.2 The Mathematical Modeling of the Drying Process

Themain objective of an appropriated dryingmodeling is tomathematically describethe physical phenomena, so that it is possible to choose appropriate operating condi-tions, themost appropriatemethod of drying and also to control and know the processdeeply. Thus, we can optimize the steps of drying and eliminate or minimize existingirregularities.

The development of mathematical models to describe the drying process isincreasingly recurrent and has been studied for several decades. This is because theprocess has great importance in the production of different products and also involvescomplex phenomena of heat and mass transfer, linear momentum, and dimensionvariations of the product.

The principle of modeling is based on having a system of mathematical equationsthat completely characterizes the system to be modeled. In particular, the solutionof these equations makes it possible to predict process parameters as a function ofdrying time based only on initial and boundary conditions, and some simplifications.The starting point in mathematical modeling is the definition of the process to bemodeled, in particular the description of the input data that influence the process, aswell as the variables that depend on the process behavior.


The complexity of the drying process depends on the geometric and thermophys-ical parameters of the material and thickness of the material layer in study. Theycan then be classified in thin-layer drying models (particle level models) and thick-layer models (dryer models). The dryer mathematical models (thick-layer model)most used by the researchers take into account the thermophysical properties, dryingkinetics, and mass and energy balance in the device. Some researchers have applieddryer model to predict drying process of clay ceramic materials with particular refer-ence to industrial clay bricks (Almeida et al. 2013; Tavares et al. 2014; Almeida et al.2016; Silva 2018). From a practical point of view, thin-layer drying is very limited.But to have a good understanding of the thick-layer drying process it is necessary tohave thin-layer equations for the drying kinetics of a particular material under certainpredetermined operating conditions (Macedo 2016).

Several thin-layer mathematical models have been proposed to describe the rateof moisture loss during drying and can be divided into two large groups: lumpedand distributed models. Distributed models express heat and mass transfer rates asa function of position within the part and drying time, taking into account externaland internal resistances. Lumped models, on the other hand, express the same ratesonly as a function of process time and ignoring the existing internal resistance forheat end mass transfer.

The following general balance equation (distributed model) has been applied topredict drying process (by diffusion only) of irregularly-shaped porous body:

d(λΦ)

dt= ∇ · (Γ Φ∇Φ) + Φ ′′ (1.1)

where λ and Γ Φ are transport properties. Φ is the unknow, Φ ′′ is the source term,and t is the time.

Distributed models based on the liquid diffusion theory have been applied topredict drying of ceramic porous materials. For example, clay plates (Silva et al.2009), clay pipes (Santos 2018), roof tiles (Farias et al. 2013; Silva et al. 2012;Farias et al. 2012), and bricks (Araújo et al. 2019a, b, 2017; Brito et al. 2017; Araújoet al. 2017; Silva et al. 2011; Lima et al. 2015; Santos et al. 2020).

This chapter addresses the use of the lumpedmodel to describe the drying process.The equations of the lumped model can be classified as empirical, semi-empirical,and theoretical. It is noteworthy that in this analysis the effects of temperature andmoisture variation inside the material are neglected during the process.

When it comes to empirical equations, they have a direct link between mois-ture content and drying time, while semi-empirical ones are analogous to Newton’slaw of cooling, assuming that the drying rate is proportional to the differencebetween moisture content of the product and its equilibrium moisture content forthe specified drying conditions. Theoretical equations generally use heat and massbalances between the product and air surrounding it, taking account different phys-ical phenomena during the process. Some researchers have applied lumped modelsto describe drying process of clay porous materials. For example, clay pipes (Silvaet al. 2016), bricks (Silva 2009; Almeida et al. 2013; Tavares et al. 2014; Silva 2018;


Fig. 1.2 Representative scheme of the drying process of an arbitrarily-shaped solid based on alumped analysis

Silva et al. 2011; Lima et al. 2015), and others geometries (Silva et al. 2016; Limaet al. 2018; Lima 2017).

For a better understanding of the lumped analysis method (theoretical model),consider the solid with arbitrary geometry, illustrated in Fig. 1.2.

In this scheme, the arbitrary solid will receive on its surface a flux per unit areaof the potential of interest Φ and has uniformly distributed internal generation perunit volume. According to what has already been mentioned, when applying thelumped analysis method, the effects of the potential variation within the material areneglected. Thus, all flux ofΦ received and generatedwill diffuse instantly through thesolid. In order for this condition to be physically possible and well approximated, theflux resistance within the solid must be much lower than the flux resistance betweenthe solid and its vicinity.

Thus, the balance of Φ (potential of interest) can be obtained as follows:

Vd(λ∧

Φ)

dt= Φ ′′S + Φ ′′′V (1.2)

inwhichΦ ′′ andΦ ′′′ are flux ofΦ per unit area and source term, respectively. Further,λ∧

includes transport parameters and S and V are the surface area and volume of theporous material, respectively.

1.3 Lumped Model Application: Drying of Clay CeramicBrick

As an application, in this topic will be developing new research methods and tech-niques, particularly process modeling and simulation involving heat and mass trans-port in solid–liquid systems, with particular reference to drying of clayey ceramicmaterials, via lumped models.


The focus is to develop a phenomenologicalmathematicalmodeling and its analyt-ical solution via method of separation of variables to predict heat and mass transferin clayey, cast, and arbitrary-shaped ceramic materials (industrial ceramic bricks).

1.3.1 The Experimental Data

Thematerials used for drying in ovenwere parallelepiped-shaped ceramic brickswith8 rectangular holes (industrial ceramic bricks). Figure 1.3 illustrates the test bodymodel used, as well as the positions where the measurements of length (R1), width(R2), height (R3), and dimensions that characterize the brick holes, a1, a2, a3, anda4, were obtained. Initially, dimensions were measured with a digital caliper, masswith a digital scale, brick temperature (vertex) with infrared thermometer, and roomtemperature and relative humidity with thermohygrometer. Then, the samples weretaken inside the forced-air oven where drying was performed. In this process, theinternal temperature of the ovenwas set as desiredwith the temperature controller. Atpredefined intervals, the brickwas taken from the oven andmeasured its temperature,mass, and dimensions.

Table 1.2 summarizes, for each experimental condition, the product, and air data.Table 1.3 presents, for each operating condition, the dimensions, volume, and surfacearea of the sample before the drying process begins.

During the process, measurements were taken every 10 min until the mass hadminimal variation. Then, the measurements were changed every 30 min, and the nextmeasurements were taken every 60min until it reached constant mass. Soon after, the

Fig. 1.3 Hollow brick with dimensions


Table 1.2 Experimental air and brick parameters for each drying test (Silva 2009)

T (°C) Air Brick Time, t (h)

UR (%) V(m/s) Mo (db) Mf (db) Me (db) θo (°C) θ f (°C)

50 80 0.05 0.13969 0.0 0.00011 20.6 41.0 18.5

60 79 0.06 0.14795 0.0 0.00268 20.5 50.2 13.7

70 69 0.07 0.15414 0.0 0.00076 26.0 64.5 17.8

80 66 0.08 0.15248 0.0 0.00039 21.4 69.2 15.0

90 68 0.09 0.15921 0.0 0.00151 21.0 78.5 11.5

100 52 0.10 0.16903 0.0 0.00038 26.1 93.2 12.3

sample was dried for 24 h at the same drying temperature to obtain the equilibriummass and then, for another 24 h at 105 °C to obtain the mass of the dried product.

All experiment was performed by Silva (2009). This author also performed anadjustment of experimental data related tomass transfer (moisture content) during theprocess and proposed an exponential equation with two terms and four parameters.The equation has the form:

M = A1 exp(k1t) + A2 exp(k2t) (1.3)

where t is given in minutes. The A1, A2, k1, and k2 parameters were estimated usingthe Statistica® Software, the Rosembrock andQuasi-Newton numerical method, anda convergence criterion of 0.001. After fitting, Silva (2009) presented the parametersreported in Table 1.4.

The experimental data of the brick vertex temperature was fitted to an equationwith four parameters. The equation has the form:

θ = B1 + B2 log10(t K1 + B3

)(1.4)

where t is given in minutes. Parameters B1, B2, K1, and B3 were estimated usingStatistica® Software, the Quasi-Newton numerical method, and with a convergencecriterion of 0.0001.

Table 1.5 summarizes the coefficients of Eq. 1.4 obtained after fitting to theexperimental data.

1.3.2 Phenomenological Mathematical Modeling

To predict the drying process was developed an advanced and phenomenologicalmathematic model. It is based on the following hypotheses:


Table1.3

Brick

dimension

sbefore

thedrying

processbegins

(Silv

a2009)

T (°C)

R1(m

m)

R2(m

m)

R3(m

m)

a 1(m

m)

a 2(m

m)

a 3(m

m)

a 4(m

m)

Vo(m

m3)

S o(m

m2)

5093.36

197.00

200.00

9.04

7.10

7.88

6.30

141,56

43.80

371,100.44

6092.75

195.00

200.00

8.34

7.32

7.11

6.45

1,36

7,26

9.30

369,020.69

7093.16

197.00

203.00

8.54

9.87

7.99

6.96

1,62

1,58

0.85

162,158.85

8092.76

197.00

201.00

8.16

7.20

7.84

6.66

1,40

8,07

4.95

37,214.46

9093.10

197.00

201.00

8.88

7.95

6.57

6.78

1428

,426

.08

37,233.87

100

92.80

198.00

202.00

1.70

9.41

8.74

8.00

1,73

4,02

6.10

36,116.49


Table 1.4 Parameters of Eq. 1.3 obtained after fitting to experimental data of average moisturecontent

T (°C) Parameter R (–) Explainedvariance (%)A1 (–) k1 (mm−1) A2 (–) k2 (mm−1)

50 0.576178 −0.004711 0.482232 −0.004711 0.997676745 0.995358888

60 0.547740 −0.005945 0.513349 −0.005945 0.997968284 0.995940696

70 0.000000 −0.006781 1.045050 −0.0070948 0.999112861 0.998226509

80 0.535201 −0.009190 0.527668 −0.009190 0.998502641 0.997007523

90 10.63554 −0.014298 −9.613313 −0.015018 0.998876724 0.997754709

100 4.875507 −0.008383 −3.827964 −0.007881 0.998297496 0.996597890

Table 1.5 Parameters of Eq. 1.4 obtained after fitting to experimental data of the vertex temperature

T (°C) Parameter R (–) Explainedvariance (%)B1 (°C) B2 (°C/min) k1 (–) B3 (min)

50 −546.0430 283.1605 0.42554 101.18296 0.960840804 0.923215051

60 −48.7454 39.22594 0.86804 66.362934 0.981233190 0.962818573

70 −18.4408 40.19277 0.698315 11.943974 0.953411275 0.908993060

80 −21.3661 37.35810 0.871389 14.410538 0.970896765 0.942640529

90 −30.7995 33.11958 1.222654 47.338410 0.981074082 0.962506354

100 −2.86969 15.41788 2.234665 118.38213 0.984632771 0.969501694

(a) Brick is composed of liquid water and solid matter;(b) Water migrates from the interior of the brick in liquid form and evaporates on

the surface;(c) On the solid surface there is thermal convection, evaporation, and heating of

produced vapor;(d) Dimensional variations were considered during drying process;(e) Heat and mass generation were neglected;(f) Constant mechanical and thermophysical properties.

1.3.2.1 Geometric and Dimensional Analysis

From the various measurements of the brick dimensions, made during the dryingprocess, mathematical equations were proposed to calculate the volume and surfacearea of the brick (Fig. 1.3). The brick volume at any time t was calculated as follows:

Vf = aVaHR3(brick holes volume) (1.5)

V = (R1R2R3) − (8Vf)(brick volume) (1.6)


The brick surface area at any time t was determined by using the followingequation:

S = (2R1R3) + (2R2R3) + 2[(R1R2) − (8aHaV)] + 8[(2aHR3) + (2aVR3)](1.7)

where in Eqs. 1.5, 1.6, and 1.7:

aV = (R2 − 2a1 − 3a3)/4 (height of a hole) (1.8)

aH = (R1 − 2a2 − a4)/2 (width of a hole) (1.9)

After determination of the volume and surface area at differentmoments of drying,it was possible to adjust them to mathematical models that describe the volumetricvariation and surface area of the brick during the drying process. This procedure wasrealized by using Statistica® software (Simplex numerical method and convergencecriterion of 0.00001). For this, a third-degree polynomial model was proposed forboth volume and surface area, as follows:

V (t) = C1t3 + C2t

2 + C3t + C4 (1.10)

S(t) = D1t3 + D2t

2 + D3t + D4 (1.11)

1.3.2.2 Mass Transfer Analysis

The complexity of the drying process depends, among other parameters, on theanalysis taken into account. Distributed models express heat and mass transfer ratesas a function of position within the part and drying time, taking into account externaland internal resistances. Already the lumped models express the same rates only asa function of the process time and ignoring the existing internal resistance for thistransfer. This study makes use of the lumped model analysis to describe the dryingprocess of ceramic brick. Thus, from Eq. 1.2, we have the following mass balance:

VdM

dt= −hmS(M − Me) + V M (1.12)

where S and V represent the surface area and volume of the solid at any time t, hmis the convective mass transfer coefficient,M is the average moisture content,Me isthe equilibrium moisture content of the brick, and t is the time.

Considering M ′ = M − Me, it is valid dM ′ = dM. Therefore, it is possible towrite:


VdM ′

dt= −hmSM

′ + V M (1.13)

Separating the variables and rearranging the terms, Eq. 1.13 results in:

dM ′[(M ′) − V M

hmS

] = −hmS

Vdt (1.14)

Since thatM =M0 at t = 0, and that there are no reactions that can generate waterinside the product, it was considered M = 0. So, Eq. 1.14 can be integrated from theinitial condition. Thus, it is possible to write:

M−Me∫

M0−Me

dM ′

(M ′)= −

t∫

0

(hmS

V

)dt (1.15)

PuttingEqs. 1.10 and11.11 intoEq. 1.15 and integrating it,weobtain the followingequation, which defines the mass transfer, considering dimensional variations duringthe process:

M =⎧⎨⎩(M0 − Me) exp

⎡⎣−hm

⎧⎨⎩a∧

1t + a∧

2 arctan[a∧

3(a∧

4 + 2t)] + a

∧

5 log[a∧

6 − t]

+ a∧

7 log[a∧

8 + a∧

9t + t2]

− a∧

10

⎫⎬⎭

⎤⎦

⎫⎬⎭ + Me (1.16)

where the coefficients a∧

k are specified according to drying conditions.

1.3.2.3 Heat Transfer Analysis

Similarly, to mass transfer, for heat transfer analysis, considering constant the heatflux per area unit, the following energy balance is given:

ρVCpdθ

dt= [hcS(θ∞ − θ)] + qV (1.17)

where ρ and Cp represent the density and specific heat of the brick, respectively,hc is the convective heat transfer coefficient, θ and θ ∞ represent, respectively, theaverage product temperature at any time t and the equilibrium temperature (whichis equal to the drying air temperature).

Considering T ′ = θ∞ − θ , it turns out that dT ′ = −dθ. Then, putting this resultinto Eq. 1.17, separating the variables, this equation can be rewritten as follows:

dT ′[T ′ + qV

(hcS)

] = − hcS

ρVCpdt (1.18)


Since that θ = θ0 at t = 0, and that there are no chemical reactions that cangenerate heat inside the product, it is possible to consider q = 0. So, Eq. 1.18 can beintegrated from the initial condition. Thus, we have that:

θ∞−θ∫

θ∞−θo

dT ′

[T ′]= −

t∫

0

hcS

ρVCpdt (1.19)

Now, puttingEqs. 1.10 and1.11 intoEq. 1.19 and integrating it,weobtain as resultsthe following equation, which defines the heat transfer, considering dimensionalvariations during the process:

θ = θ∞ −

⎧⎪⎨⎪⎩

(θ∞ − θo) exp

⎡⎢⎣− hc

ρCp

⎧⎪⎨⎪⎩b∧

1t + b∧

2arc tan[b∧

3

(b∧

4 + 2t)]

+ b∧

5log[b∧

6 − t]

+ b∧

7 log[b∧

8 + b∧

9t + t2]

− b∧

10

⎫⎪⎬⎪⎭

⎤⎥⎦

⎫⎪⎬⎪⎭(1.20)

where the coefficients b∧

k are specified according to drying conditions.Equations 1.16 and 1.20 were fitted to the experimental data of the average mois-

ture content (Eq. 1.3) and surface temperature (Eq. 1.4) of the ceramic brick using theStatistica® software (Quasi-Newton numerical method and convergence criterion of0.0001). From the non-linear regression, it was possible to estimate the convectivemass transfer (hm) and heat transfer (hc) coefficients.

1.3.3 Results Analysis

1.3.3.1 Dimensional Variations

Tables 1.6 and 1.7 summarize the parameters obtained for Eqs. 1.10 and 1.11,respectively.

Table 1.6 Parameters of Eq. 1.10 that describe the volumetric behavior of the brick during dryingprocess

T (°C) Parameter R (–) Explainedvariance (%)C1 (m3/min3) C2 (m3/min2) C3 (m3/min) C4 (m3)

50 −0.000862 1.76499 −1099.66 1,381,400 0.98227288 96.486

60 −0.001538 2.46177 −1213.49 1,356,500 0.98812668 97.639

70 −0.000678 1.36975 −911.113 1,546,700 0.94004504 88.368

80 −0.001273 2.02475 −977.457 1,374,700 0.94563064 89.422

90 −0.003695 4.40681 −1596.91 1,392,300 0.9535488 90.926

100 −0.003480 5.278373 −2066.011 1,551,571 0.81039933 65.675


Table 1.7 Parameters of Eq. 1.11 that describe the surface area behavior of the brick during dryingprocess

T (°C) Parameter R (–) Explainedvariance (%)D1 (m2/min3) D2 (m2/min2) D3 (m2/min) D4 (m2)

50 −0.000126 0.259821 −163.671 371,912 0.99130038 98.268

60 −0.000315 0.45662 −202.289 368,692 0.98169467 96.372

70 −0.000200 0.366684 −192.89 366,801 0.93426766 87.286

80 −0.000267 0.41566 −190.31 370,685 0.9335808 87.157

90 −0.000628 0.761024 −271.251 373,572 0.95696019 91.577

100 −0.000226 0.322700 −134.0546 355,682 0.82398847 67.896

Statistica® software also provides graphs of the estimated functions compared tothe collected experimental points. Thus, Figs. 1.4 and 1.5 show the transient volumeand surface area variations under operating conditions from 50 to 100 °C.

After analysis of Figs. 1.4 and 1.5, it is possible to notice that the volume andsurface area have a decreasing behavior over time. This is because thewater inside thebrick is being evaporated during drying (shrinkage) and it is being heated during theprocess (volumetric expansion). Since that, drying at higher temperatures provokesincreases in the drying and heating rates, these phenomena are more intensive.

It is also possible to see that the experimental data found at 100 °C have a lessaccurate adjustment for both volume and surface area variation. This is due to possiblemeasurement errors with brick drying and large temperature variations due to thefact that the brick was removed from the oven so that measurements could be made.

It can be verified that at 50 °C, the brick volume decreased by 17.88% and at100 °C a reduction of 20.57% occurred. At 100 °C, the amount of evaporated wateris greater. With regard to surface area at temperature 50 °C the brick was reducedin surface area by 8.46% and at 100 °C by 5.83%. Thus, we can see that the areareduction was much smaller than the volume, which shows that the drying was doneproperly and the brick did not suffer large deformations, maintaining its originalshape, but in a smaller size.

1.3.3.2 Drying Process

Table 1.8 summarizes the coefficients of Eqs. 1.16 and 1.20.With this, it was possibleto adjust these equations to the experimental data of moisture content (Eq. 1.3) andsurface temperature (Eq. 1.4) and to estimate the convective heat transfer and masstransfer coefficients.

Figures 1.6 and1.7 illustrate a comparison between the predicted and experimentalbrick average moisture content as a function of time for drying at 50 and 100 °C,respectively.


Fig. 1.4 Predicted (---) and experimental (ooo) volumevariations of the brick during drying. a 50 °Cand b 100 °C


Fig. 1.5 Predicted (---) and experimental (ooo) surface area variations of the brick during drying.a 50 °C and b 100 °C


Table 1.8 Parameters of Eqs. 1.16 and 1.20 that describe mass transfer and heat transfer of thebrick during drying process

Parameter T (°C)

50 60 70 80 90 100

a∧

1 = b∧

1 0.15 0.20 0.29 0.21 0.17 0.06

a∧

2 = b∧

2 95.11 48.35 47.31 39.10 44.57 88.20

a∧

3 = b∧

3 0.0005 0.0006 0.0005 0.0006 0.0008 0.0009

a∧

4 = b∧

4 −218.45 −128.91 −85.22 −44.78 −83.38 −194.00

a∧

5 = b∧

5 −51.82 −14.11 −25.59 −21.74 −27.83 −34.53

a∧

6 = b∧

6 1829.10 1471.72 1935.06 1545.75 1109.26 1322.77

a∧

7 = b∧

7 24.85 22.52 14.76 14.41 12.28 20.15

a∧

8 = b∧

8 876141.16 599290.09 1.18 × 106 698617.29 339691.29 337060.33

a∧

9 = b∧

9 −218.45 −128.91 −85.22 −44.78 −83.38 −194.00

a∧

10 = b∧

10 −60.3635 192.68 401.945 33.22 −41.86 −6.50

Fig. 1.6 Predicted and experimental average moisture content of ceramic brick as a function ofdrying time (T = 50 °C)

From the analyzes of the figures, we can state that the drying of brick occurred inthe falling drying rate period, for two reasons: the drying rate isn’t constant and thebrick temperature arises during the drying process.

Further, the drying rate increases with increasing drying temperature. For alldrying temperatures, it can be considered that after the first 1000 min of process,the average moisture content varies slightly. Thus, we can state that the equilibriummoisture content was reached at this time.


Fig. 1.7 Predicted and experimental average moisture content of ceramic brick as a function ofdrying time (T = 100 °C)

Analyzing the graphs, it is noted that there is an agreement between the exper-imental values and the predicted values by the model used, confirming that themodeling used to find the average moisture content, as a function of drying time, iseffective.

1.3.3.3 Heating Process

Similar to the procedure adopted for the moisture content, to find the convective heattransfer coefficients, at the different drying temperatures, a comparison between thepredicted and experimental brick vertex temperature (Eq. 1.4) was made, until itreached a minimum error.

Figures 1.8 and 1.9 illustrate the brick temperature adjustment curves as a functionof time for drying at 50 and 100 °C, respectively.

Through analysis, it can be proved that, for drying at higher temperatures, thebrick reaches its equilibrium temperature in a shorter process time.

When evaluating the graphs, it is noted that there was a good agreement betweenthe experimental values and the values determined through the proposed model. Theadjustment efficiency was not as good as in mass transfer, but this was due to thefact that the analytical model developed took into account only the heat transfer,disregarding the simultaneous mass transfer effect and the energy to be used in thephase change of water.

Therefore, even with a not so refined agreement between the experimental andpredicted brick temperatures, it can be said that the modeling used to estimate theprocess parameters is effective.


Fig. 1.8 Predicted and experimental brick surface temperature as a function of drying time (T =50 °C)

Fig. 1.9 Predicted and experimental brick surface temperature as a function of drying time (T =100 °C)

1.3.3.4 Estimation of Transport Parameters

After gravimetric and thermal analysis, the process parameters were found for thedifferent drying conditions. After fitting of Eqs. 1.16 and 1.20 to experimental dataof average moisture content and temperature, the heat and mass transfer coefficientswere estimated. Table 1.9 summarizes the estimated values of convective heat andmass transfer coefficients, with the respective errors obtained with Eqs. 1.21 and1.22. In these equations, the number of experimental points is n = 110.


Table 1.9 Convective heat and mass transfer coefficients estimated from fitting of Eqs. 1.16 and1.20 to experimental data

T (°C) hm (m/s) ERM (kg/kg)2 hc (W/m2 °C) ERT (–)

50 2.6500 × 10−7 0.000293 0.36985 0.823922

60 3.3266 × 10−7 0.000307 0.50538 0.375189

70 4.7300 × 10−7 0.000176 0.75000 0.525849

80 5.2783 × 10−7 0.000276 0.88250 0.792176

90 5.7216 × 10−7 0.000462 1.00000 0.539377

100 6.9816 × 10−7 0.000263 1.33333 0.689403

ERM =n∑

i=1

(Mpred − Mexp

)2(1.21)

ERT =n∑

i=1

[θpred − θexp

θpred

]2

(1.22)

Analyzing the convective heat and mass transfer coefficients as a function ofdrying temperatures, it is noted that there is an increase in the value of these coef-ficients with increasing drying temperature. Increasing the temperature implies anincrease in the drying and heating rates of the brick, which makes it possible to reachits thermal and hygroscopic equilibrium conditions faster. The small values of theheat transfer coefficient are equivalent to the free convection heat transfer condition.

1.4 Concluding Remarks

From the studies performed, it can be concluded that:

(a) The drying process at high temperatures takes place in a shorter process time.(b) Parameters for third-degree polynomial functions describe well the behavior of

volume and surface area during the drying process.(c) At high temperatures, the volumetric variation was 20.57% while the surface

area varied by 5.83%. This point explains that the drying process was donecorrectly as the integrity of the brick shape was maintained. It is important toevaluate the behavior of the brick shape during drying, as this can make processcontrol and therefore avoid possible defects in the parts.

(d) The mathematical modeling developed taking into account the dimensionalvariations during the drying process was considered satisfactory.

(e) The convective heat and mass transfer coefficients increased with the evolutionof the drying temperature.


Acknowledgments The authors thank CNPq, CAPES, FINEP (Brazilian Research Agencies), andPIBIC/CNPq-UFCG scientific initiation undergraduate program for the financial support, and theresearchers cited in the text, who helped in the improvement of the investigation made.

References

Almeida, G.S., Silva, J.B., Silva, C.J., Swarnakar, R., Neves, G.A., Lima, A.G.B.: Heat and masstransport in an industrial tunnel dryer: modeling and simulation applied to hollow bricks. Appl.Thermal Eng. 55, 78–86 (2013)

Almeida, G.S., Tavares, F.V.S., Lima, W.M.P.B., Lima, A.G.B.: Energetic and exergetic analysis ofthe clay bricks drying in an industrial tunnel dryer. Def. Diff. Forum 369, 104–109 (2016)

Araújo, M.V., Pereira, A.S., Oliveira, J.L., Brandão, V.A.A., Brasileiro Filho, F.A., Silva, R.M.,Lima, A.G.B.: Industrial ceramic brick drying in oven byCFD.Mater 12(10), 1612–1634 (2019a)

Araújo, M.V., Santos, R.S., Silva, R.M., Nascimento, J.B.S., Santos, W.R.G., Lima, A.G.B.: Dryingof industrial hollow ceramic brick: a numerical analysis using CFD. Def. Diff. Forum 391, 48–53(2019b)

Araújo, M.V., Santos, R.S., Silva, R.M., Lima, A.G.B.: Drying of industrial hollow ceramic brick:analysis of themoisture content and temperature parameters. Def.Diff. Forum 380, 72–78 (2017a)

Araújo, M.V., Delgado, J.M.P.Q., Lima, A.G.B.: On the use of CFD in thermal analysis of industrialhollow ceramic brick. Diff. Found. 10, 70–82 (2017b)

Brito, M.K.T.: Theoretical study of heat and mass transfer in the drying of ceramic bricks withparallelepiped shape. Master’s dissertation in Mechanical Engineering, Federal University ofCampina Grande, Campina Grande, Brazil (2016). (In Portuguese)

Brito, M.K.T., Almeida, D.B.T., Lima, A.G.L., Rocha, L.A., Lima, E.S., Oliveira, V.A.B.: Heat andmass transfer during drying of clay ceramic materials: a three-dimensional analytical study. Diff.Found. 10, 93–106 (2017)

Brooker, D.B., Bakker-Arkema, F.W., Hall, C.W.: Drying and Storage of Grains and Oilseeds. AVIBook, New York (1992)

Cabral Jr., M., Motta, J.F.M., Almeida, A.S., Tanno, L.C.: Clay for red ceramics. Industrial rocksand minerals. CETEM 2(1), 747–770 (2008). (In Portuguese)

Callister Jr.,W.D.:Materials Science andEngineering: An Introduction, 7th edn.Wiley, USA (2007)Callister Jr., W.D., Rethwisch, D.G.: Fundamentals of Materials Science and Engineering: AnIntegrated Approach, 3rd edn. Wiley, USA (2008)

Cavalcanti, M.S.L.: Development of ceramic masses for sanitary stoneware using flat glass residueas a flux in partial replacement to feldspar, Doctoral Thesis in Process Engineering, FederalUniversity of Campina Grande, Campina Grande, Brazil (2010). (In Portuguese)

Farias, V.S.O., Silva, W.P., Silva, C.M.D.P.S., Delgado, J.M.P.Q., Farias Neto, S.R., Lima, A.G.B.:Transient diffusion in arbitrary shape porous bodies: numerical analysis using boundary-fittedcoordinates. In: Delgado, J.M.P.Q., Barbosa de Lima,A.G., Silva,M.V. (eds.) Numerical Analysisof Heat and Mass Transfer in Porous Media, vol. 27, pp. 85–119. Springer, Heidelberg, Germany(2012)

Farias, V.S.O., Silva, W.P., Silva, C.M.D.P.S., Rocha, V.P.T., Lima, A.G.B.: Drying of solids withirregular geometry: numerical study and application using a three-dimensional model. Heat MassTransfer 49(5), 695–709 (2013)

Lima,A.G.B.,Delgado, J.M.P.Q., Santos, I.B., Santos, J.P.S.,Barbosa,E.S., Silva,C.J.:GBImethod:A powerful technique to study drying of complex shape solids. In: Delgado, J.M.P.Q., Barbosade Lima, A.G. (eds.) Transport Phenomena and Drying of Solids and Particulate Materials, vol.48, pp. 25–431, Springer International Publishing, Heidelberg, Germany (2014)


Lima, A.G.B., Silva, J.B., Almeida, G.S., Nascimento, J.J.S., Tavares, F.V.S., Silva, V.S.: Clayproducts convective drying: foundations, modeling and applications. In: Drying and EnergyTechnologies, vol. 63, pp. 43–70. Springer, Heidelberg, Germany (2015)

Lima, E.S., Lima, W. M.P.B., Lima, A.G.B., Farias Neto, S.R., Silva, E.G., Oliveira, V.A.B.:Advanced study to heat and mass transfer in arbitrary shape porous materials: Foundations,phenomenological lumpedmodeling and applications In: Delgado, J.M.P.Q., Lima, A.G.B. (eds.)Transport Phenomena inMultiphase Systems, 93, pp. 181–217. Springer International Publishing,Heidelberg, Germany (2018)

Lima, W.M.P.B.: Heat and mass transfer in porous solids with complex geometry via concentratedanalysis: modeling and simulation. Master,s dissertation in Mechanical Engineering, FederalUniversity of Campina Grande, Campina Grande, Brazil (2017)

Macedo, R.F.: Continuous drying of bentonite clay in an industrial rotary dryer: modeling, simu-lation and experimentation. Master’s dissertation in Mechanical Engineering, Federal Universityof Campina Grande, Campina Grande, Brazil (2016)

Oliveira, M.C., Bernils, M.F.: Environmental technical guide for the white ceramics and coatingsindustry. In: CETESB—Companhia de Tecnologia de Saneamento Ambiental, São Paulo (2006).(In Portuguese)

Rodrigues Neto, A., Mota, J.A.: Local productive arrangements in the red ceramic industry: a casestudy in Brazil Northeastern. Rev. Econ. NE. 47(1), 127–142 (2016). (In Portuguese)

Santos, J.P.S.: Drying of ceramic materials with complex shape: a theoretical study via CFX.DoctoralThesis inProcessEngineering, FederalUniversity ofCampinaGrande,CampinaGrande,Brazil (2018)

Santos, R.S., Farias Neto, S.R., Lima, A.G.B., Silva Jr., J.B., Silva, A.M.V.: Drying of ceramicbricks: thermal and mass analysis via CFD. Diff. Found. 25, 133–153 (2020)

SEBRAE (Serviço Brasileiro deApoio àsMicro e Pequenas Empresas). RedCeramics: Overview ofthe market in Brazil. http://www.bibliotecas.sebrae.com.br/chronus/ARQUIVOS_CHRONUS/bds/bds.nsf/b877f9b38e787b32594c8b6e5c39b244/$File/5846.pdf. Accessed 13 Jan 2019

Silva, A.A., Nascimento, J.J.S., Lima, A.G.B: Analytical study of ceramic tiles drying using theGalerkin-based integral method andDirichlet boundary condition Rev. EletrônicaMater. Process.(UFCG) 4(2), 48–55 (2009). (In Portuguese)

Silva, A.M.V.: Drying of industrial ceramic blocks: Modeling, simulation and experimentation.Doctoral thesis in Process Engineering, Federal University of CampinaGrande, CampinaGrande,Brazil (2018)

Silva, J.B.: Simulation and experimentation of the drying of holed ceramic bricks. Doctoral Thesisin Process Engineering, Federal University of Campina Grande, Campina Grande, Brazil (2009).(In Portuguese)

Silva, V.S.: Heat and mass transfer in complex shaped materials via the lumped analysis method.Case study: drying of ceramic materials. Doctoral Thesis in Process Engineering, FederalUniversity of Campina Grande, Campina Grande, Brazil (2016). (In Portuguese)

Silva, J.B., Almeida, G.S., Lima, W.C.P.B., Neves, G.A., Lima, A.G.B.: Heat and mass diffusionincluding shrinkage and hygrothermal stress during drying of holed ceramics bricks. Def. Diff.Forum 312–315, 971–976 (2011)

Silva, W.P., Farias, V.S.O., Neves, G.A., Lima, A.G.B.: Modeling of water transport in roof tiles byremoval of moisture at isothermal conditions. Heat Mass Transfer 48(5), 809–821 (2012)

Silva, V.S., Delgado, J.M.P.Q., Lima, W.M.P.B., Lima, A.G.B.: Heat and mass transfer in holedceramic material using lumped model. Diff. Found. 7, 30–52 (2016)

Strumillo, C., Kudra, T.: Drying: Principles, Science and Design. Gordon and Breach SciencePublishers, New York (1986)

Tavares, F.V.S., Farias Neto, S.R., Barbosa, E.S., Lima, A.G.B., Silva, C.J.: Drying of ceramichollow bricks in an industrial tunnel dryer: a finite volume analysis. Int. J. Multiphys. 8(3),297–312 (2014)

http://www.bibliotecas.sebrae.com.br/chronus/ARQUIVOS_CHRONUS/bds/bds.nsf/b877f9b38e787b32594c8b6e5c39b244/%24File/5846.pdf

Chapter 2Vegetable Fiber Drying: Theory,Advanced Modeling and Application

J. F. Brito Diniz, A. R. C. de Lima, I. R. de Oliveira, R. P. de Farias,F. A. Batista, A. G. Barbosa de Lima, and R. O. de Andrade

Abstract This chapter aims to study the dryingof sisal fibers. The interest in this typeof material is related to its high mechanical performance. Several important topicssuch as theory, experiments, lumped and distributed mathematical modeling, andtechnological applications of fibers are presented and discussed. Emphasis is givento advanced distributed modeling that describes the heat and mass transfer in a wetfiber bed during drying. The model includes different effects such as bed porosity,fiber and bed moisture, coupling between heat and mass transport, and conduc-tion, convection, and evaporation heat transfer. Results of fiber drying and heatingkinetics, temperature distribution, and water vapor concentration in the fibrous bedare presented, compared with experimental data and analyzed.

J. F. Brito DinizDepartment of Mathematics, Federal University of Campina Grande, Av. Aprígio Veloso 882,Bodocongó, 58429-900 Campina Grande, PB, Brazile-mail: [email protected]

A. R. C. de Lima · I. R. de Oliveira · A. G. B. de Lima (B) · R. O. de AndradeDepartment of Mechanical Engineering, Federal University of Campina Grande, Av. AprígioVeloso 882, Bodocongó, 58429-900 Campina Grande, PB, Brazile-mail: [email protected]

I. R. de Oliveirae-mail: [email protected]

R. O. de Andradee-mail: [email protected]

R. P. de FariasDepartment of Agriculture Science, State University of Paraiba, Catolé do Rocha, PB 58884-000,Brazile-mail: [email protected]

F. A. BatistaDepartment of Physics, State University of Paraiba, R. das Baraúnas, 351, Campina Grande, PB58429-500, Brazile-mail: [email protected]


31








https://doi.org/10.1007/978-3-030-47856-8_2

32 J. F. Brito Diniz et al.

Keywords Drying · Sisal fiber · Experimental · Simulation · Finite-Volume

2.1 Introduction

Vegetable fibers are structural tissues of plants. It is a body consisting of fibers (solid)and pores (filled with fluid) as illustrated in Fig. 2.1.

The main chemical components of vegetable fibers are polar substances such ascellulose, hemicellulose (or polyoses), and lignin, with lower percentages of othercomponents such as pectin, proteins, wax, inorganic salts, and other water-solublesubstances. Its chemical composition varies slightly according to cultivation region,soil type, and climatic conditions (Silva 2003).

Vegetable fiber is made up of several elemental fibers strongly bonded together bya resinous material consisting primarily of lignin. Each elemental fiber is essentiallya composite in which rigid cellulose microfibrils are encased in an amorphous matrixof lignin and hemicellulose. Lignin acts as a resinous material, uniting microfibrils,

Fig. 2.1 Longitudinalmicrographs of untreatedsisal fiber obtained byScanning ElectronMicroscope (SEM): a 100×magnification and b 200×magnification

2 Vegetable Fiber Drying: Theory, … 33

while hemicellulose acts as an interface between cellulose microfibril and lignin(Silva 2003). The structure of an elemental plant fiber consists of a thick wall formedby several microfibril spirals along the fiber axis, having a lumen in the center.

There are several types of vegetable fibers such as caroá, curauá, pineapple leaf,juta, and sisal. Sisal is a plant of the cactaceae family with the scientific name AgaveSisalana Perrine, being cultivated in semi-arid regions, being resistant to aridity andintense sun. The main and best-known product of sisal is biodegradable yarn.

The cycle of transformation of sisal into natural yarn begins at 3 years of plant lifeor when its leaves reach about 150 cm in length. Plant growth depends, among otherfactors, on water availability: The plant stores water in the rainy season (winter) toconsume it in the dry season (summer). Its useful life is 6–7 years, and the leaves arecut every 6 months. Sisal can produce between 200 and 250 leaves before flowering,each leaf measuring 6–10 cmwide, 150–200 cm long, and containing approximately700–1400 bundles of fiber ranging in length from 0.5 to 1.0 m. The leaf of sisalconsists of a structure composed of approximately 4%fiber, 1%film (cuticle), 8%drymatter, and 87%water. Except fiber, thesematerials are considered processing waste,being used as organic fertilizer, animal feed, and by the pharmaceutical industry(Martin et al. 2009; Wei and Meyer 2014).

The sisal fiber extraction process, which consists in the elimination of the pulpfrom the fibers, can be done manually, by maceration or by a mechanical processcalled decorticating (Silva 2008). In the decorticating process, the sisal leaves arecrushed by passing between two blunt-bladed wheels (defibrillator), so that only thefibers remain (Silva 2008). In the Brazilian northeastern, the defibration is performedthrough a machine called “agave engine”.

Benefited or industrialized, the sisal fiber generates more than half a milliondirect or indirect jobs through its service chain, which begins with the activitiesof crop maintenance, harvesting, leaf cutting, fiber shredding and processing, andfinally with industrialization and varied use (Martin et al. 2009). It has been usedin handicrafts, baling fodder, and ropes of various uses. Sisal is also used in theproduction of upholstery, paste for the cellulose industry, the production of tequila,decorative rugs, medicines, biofertilizers, animal feed, organic fertilizer, and sacks.Fibers can also be used in the automotive industry, replacing fiberglass.

In recent years, with increasing awareness of environmental preservation andpollution control, interest in the use of natural fibers in polymer composite mate-rials has increased significantly. In this context, the use of vegetable fibers as rein-forcement in polymer composites, with the objective of totally or partially replacingsynthetic fibers, has received attention from the researchers. This is because vegetablefibers have important advantages such as low cost, low density, high specific strengthand stiffness, and low abrasiveness to process equipment are biodegradable, non-toxic, non-polluting, which reduces environmental problems. They also come fromrenewable sources and are available worldwide (Cruz et al. 2011; Melo Filho et al.2013; Nóbrega et al. 2010; Zhou et al. 2014). However, plant fibers are very suscep-tible to humidity and temperature, which strongly affect their mechanical properties,especially when used as reinforcement in polymeric materials.


Because it is a lignocellulosic fiber, light and non-toxic, with high modulus andspecific resistance, costing about ten times lower than fiberglass (inorganic fiber),causing less abrasion damage to equipment and molds, sisal can have its commercialvalue multiplied if used as reinforcement in polymer composites (Angrizani et al.2006; Barreto et al. 2011).

The use of sisal fiber in high performance composites requires study of themechanical behavior of the fibers. There is a large discrepancy between the valuesreported in the literature for tensile strength and elastic modulus of sisal fiber. Thevariability in the properties of these fibers can be attributed to three main factors: testparameters and conditions, plant characteristics, and the cross-sectionalmeasurementmethod. Among the parameters or test conditions that may influence the mechanicalproperties of the fibers, we can mention the precision of the instruments, the fiberlength, the test speed, the types of claws used, and the sensitivity of the equipmentitself. The characteristics of the plants themselves include the origin of the plant, age,type of processing (extraction process) as well as its microstructure. The measure-ment of the cross-section may also cause variation in the measurement of mechanicalproperties due to the indefinite shape of the section and the variation itself along thefiber (Silva 2008).

2.2 Drying of Sisal Fibers

Sisal fibers when extracted from plants are moist, which requires drying them forlater use in different applications.

Drying is a thermodynamic process whereby a body’s moisture is reduced and itstemperature increased by supplying energy. It involves complex phenomena of heatand mass transfer, momentum, and dimensional variations (Lima et al. 2016). Thecontrol of the drying process is of fundamental importance to determine the idealdrying conditions, minimizing product losses, and energy consumption.

According to Ferreira et al. (2012), the cellulose polysaccharide chains are moretightly arranged with the removal of water during drying and thus the microfibrilscome together in the dry state as a result of increased packaging. Fiber voids areprogressively closed with drying and cannot be completely reopened with rehu-midification. A direct consequence of reduced absorption is the decrease in fiberdimensional variation between the dry and saturated state. Thus, we have a greaterdimensional stability of the fiber.

Moisture transport from the interior to the material surface may occur as a liquidand/or vapor, depending on the type of product and the percentage of moisturepresent. The diffusion process should occur in a controlled way, avoiding high mois-ture and temperature gradients within the material that may affect material prop-erties. Thus, understanding the mechanisms involved in diffusion is a fundamentalrequirement in the study of solutions that minimize such problems.


2.2.1 Experimental Study

In this work, the phenomena of heat andmass transport in fibrous bodies (sisal fibers)were investigated. Agave sisalana variety sisal fibers with average moisture contentof 11.2% (db) were used. The fibers were submitted to oven drying with forced aircirculation at 70 °C. Figure 2.2 illustrates the sisal fibers used in the experiment.Table 2.1 contains the fiber and drying air information.

During the drying process, moisture loss was measured by taking the samplefrom the oven and periodicallyweighing (predefined intervals) using a 0.1 g precisiondigital electronic device, and the surface temperature wasmeasured using an infraredthermometer. In the experiment, measurements were taken every 5min until themasshad minimal variation (about 30 min), after 10, 15, 20, 25, and 30 min. Then, themeasurements were changed every 60 min until the constant mass was reached.

Fig. 2.2 Sisal fibers used inthe experiments


Table2.1

Experim

entalp

aram

etersof

airandfib

rous

medium

Air

Fibrou

smedium

Processtim

e

RH(%

)T(°C)

v(m

/s)

2R1(m

)2R

1(m

)2R

1(m

)M

o(db)

Meq

(db)

To(oC)

Tf(oC)

t(h)

6.89

700.07

0.1

0.05

0.1

0.11

148

0.02

015

31.5

67.3

5.7


Following, the sample was dried for 24 h to obtain the equilibrium mass and then fora further 24 h at 105 °C to obtain the dry mass.

2.2.2 Theoretical Study

To describe (theoretically) the moisture and heat transfer within a fibrous mediumand to analyze the effects of certain parameters on their mechanical properties, itis necessary that these transport phenomena within the fibrous medium be wellrepresented by a mathematical model. Therefore, it is important to fully insert alleffectswithinmathematicalmodels so that the physical phenomenoncanbedescribedwith great realism, and to increase the reliability of the results obtained.

Analytical and numerical solutions to the transient diffusion problem for variousgeometries have been reported in the literature; however, there are few studies relatedto transient and three-dimensional problems, particularly those related to plant fibersand incorporating the effect of porosity inside the fibrous medium.

2.2.2.1 Lumped Modeling

To describe the drying behavior of the fibrous media (sisal fibers) and to predict itunder different operating conditions, it is necessary to model the drying process. Forthis, mathematical models are used in an attempt to predict the drying and heatingkinetics, which, as a rule, predominantly follow a falling rate period.

Several empirical, semi-empirical, and theoretical models have been proposedto describe the drying process. Theoretical models take into account only internalresistance, while semi-empirical and empirical models (thin-layer drying models)take into account only external resistance to heat and moisture transfer betweenmaterial and air (internal resistance is insignificant). Currently, there are few modelsthat represent the drying of fibrous bodies, for this, the following models have beenproposed:

(a) Drying model

M = c1 exp(−k1t) + c2 exp(−k2t) + c3 exp(−k3t) (2.1)

(b) Heating model

T = c1 log2[(k1t + k2)c2 · (k3t + k4)

c3] (2.2)


Fig. 2.3 Geometricconfiguration of the physicalproblem

where M is the average moisture content on dry basis, T is the temperature, andt corresponds to the process time. The ci and ki parameters of the proposed thin-layer models were obtained by nonlinear regression analysis by the Quasi-Newtonmethod using the STATISTICA 7.0 software. In addition, some statistical parameters(correlation coefficient and variance) were determined for each proposed model.

2.2.2.2 Advanced Distributed Modeling

Governing Equations

This section presents the mathematical models required for the development of heatandmoisture (vapor) transport simulations in porous solids, with particular referenceto plant fibers. The entiremathematical formulationwas developed in a fibrous regionin the form of a parallelepiped, according to Figs. 2.2 and 2.3.

(a) Vapor diffusion equation

The porous media consists of a series of rigid and inert fibers. Water vapor is free todiffuse between the voids of the fiber bed (interfiber) and to be sorbed or desorbedby the fiber (intrafiber). In addition, changes in fiber bed volume due to moistureabsorption/desorption may be neglected.

To describe the water vapor concentration in the fiber bed throughout the process,it was considered: (a) that the vapor diffusion through the voids and across the fibersis proportional to the concentration gradient in the usual way. The diffusion throughthe pores will in many cases be greater than through the fibers, but even so, bothprocesses can be represented by assuming that the vapor in the fiber is always inequilibrium with the surrounding air vapor and that the absorption isotherm has alinear behavior, given by Eq. (2.5); (b) that moisture absorption or desorption throughthe voids inside the fiber.

The mass and heat conservation equations will be expressed in terms of a unitvolume of the air-fiber mixture. Water vapor accumulates in the volume elementin both voids (interfiber) and fibers (intrafiber). Thus, the differential equation thatdescribes the phenomenon of vapor diffusion is as follows:

∇ · (εD′∇C

) = ε∂C

∂t+ (1 − ε)ρs

∂M

∂t(2.3)


where ε is the porosity of the fibrous medium, D′ is the diffusion coefficient, M isthe amount of moisture absorbed per unit mass of fiber, ρs is the fiber density, C isthe water vapor concentration in the voids (inter fibers), and t is the time.

(b) Heat conduction equation

Changes in heat flux in the element arise from various processes: heat conductioninto or out of the element, water phase change (sorption or desorption), changes intemperature of the solid and gaseous phases. The contribution due to the last causeis small and will be neglected.

To determine the change in the temperature of the fiber volume element, it wasconsidered: (a) heat conduction through air and fibers; (b) the heat released whenmoisture is absorbed by the fibers.

Thus, the differential equation that describes the heat diffusion phenomenon is asfollows:

ρ · cP ∂T

∂t= ∇ · (K∇T ) + hsρ

∂M

∂t(2.4)

where cp is the specific heat, K is the thermal conductivity of the material, hs is theenthalpy, and T is the temperature. In Eq. (2.4), the assumption that air energy isnegligible compared to fiber is used.

An important point to note is that both the vapor diffusion Eq. (2.3) and the energyEq. (2.4) involve M (fiber moisture). This shows that the two processes, moisturetransfer and heat transfer, are coupled, so in general, one process cannot be consideredwithout considering the other simultaneously.

(c) Equilibrium equation

According to Crank (1975), one can always consider that the fiber comes intobalance with its immediate surroundings. In addition, it is possible to assume lineardependence on temperature and moisture content and write:

M = α + σC − βT (2.5)

whereM is the amount ofmoisture absorbedper unitmass offiber in kgvapor/kgdry fiber,C is the concentration of water vapor in the voids (interfibers) expressed in kg/m3,T is the temperature in °C, and α, σ and β are constants. It is just a reasonableapproximation over small ranges of moisture and temperature.

The average value of the quantity of interest Φ can be obtained by a weightedaverage using the volume of each control volume as follows:

Φ = 1

V∫V

ΦdV (2.6)

where Φ = C, T, or even M (Eq. 2.5) and V is the volume of the fibrous medium.


Considering a three-dimensional solid with vapor distribution C = C (x, y, z),temperature T = T (x, y, z), and moisture M = M (x, y, z), the transient equationsof vapor diffusion (2.3) and heat conduction (2.4) in Cartesian coordinates are givenby:

[ε + (1 − ε)ρsσ ]∂C

∂t=

[∂

∂x

(D

∂C

∂x

)+ ∂

∂y

(D

∂C

∂y

)+ ∂

∂z

(D

∂C

∂z

)]+ SC

(2.7)

and

ρ(cP + hsβ)∂T

∂t=

[∂

∂x

(K

∂T

∂x

)+ ∂

∂y

(K

∂T

∂y

)+ ∂

∂z

(K

∂T

∂z

)]+ ST (2.8)

where

∂M

∂t= σ

∂C

∂t− β

∂T

∂t(2.9)

D = εD′ (2.10)

SC = (1 − ε)ρsβ∂T

∂t(2.11)

and

ST = hsρσ∂C

∂t(2.12)

In the models, the following initial and boundary conditions were used:

• Initial condition:

C(x, y, z, t = 0) = Co; (Mass transfer) (2.13)

T (x, y, z, t = 0) = To. (Heat transfer) (2.14)

• Boundary conditions for mass transfer:

−D∂C

∂x

∣∣∣∣x=R1

= hm(C − Ceq

), ∀(x = R1, y, z, t > 0); (2.15)


−D∂C

∂y

∣∣∣∣y=R2

= hm(C − Ceq

), ∀(x, y = R2, z, t > 0); (2.16)

−D∂C

∂z

∣∣∣∣z=R3

= hm(C − Ceq

),∀(x, y, z = R3, t > 0). (2.17)

• Boundary conditions for heat transfer:

−K∂T

∂x

∣∣∣∣x=R1

= hc(T − Teq

), ∀(x = R1, y, z, t > 0); (2.18)

−K∂T

∂y

∣∣∣∣y=R2

= hc(T − Teq

), ∀(x, y = R2, z, t > 0); (2.19)

−K∂T

∂z

∣∣∣∣z=R3

= hc(T − Teq

), ∀(x, y, z = R3, t > 0). (2.20)

Numerical Procedure

Often a diffusive problem is so complex and contains intense nonlinear equations thatit cannot be solved by analytical solutions. However, it can be solved by numericalmethods. The numerical method consists of replacing a continuous domain by adiscrete domain and the partial differential equation is replaced by several algebraicequations, one for each control volume of the discrete domain. One of the mainadvantages of this method is the possibility of finding numerical solutions for thediffusion equation for the most diverse situations, such as non-homogeneous andnon-isotropic medium, variable volume and diffusivity, and any geometry and shapeof the body (Maliska 2004). There are several numerical methods reported in theliterature.

The Finite-Volume Method (FVM) does not present problems of instability orconvergence, ensuring that in each discretized volume, the property under studyobeys the conservation law, giving a conservative characteristic. It is one of the mostused in the discretization of partial differential equations. This method works withcontrol volumes, thus preserving the finite-volume level. Therefore, FVM is widelyused in solving problems involving heat and/or mass transfer, and fluid flow (Maliska2004).

In the finite-volume method, any continuous quantity can be approximated bya discrete model composed of a set of continuous step or linear functions, definedunder a finite number of subdomains. Subdomains are called the control volumesand the nodal points are well known as centroid of the control volume. In thismethod, the partial differential equation that governs the phenomenon is numeri-cally discretized by integrating it into elementary volumes and time, thus obtaining


Fig. 2.4 Scheme used to exploit the inherent symmetry condition of the parallelepiped: a domain,b highlight to 1/8 of the parallelepiped, and c new domain

a system of algebraic equations, which must be solved by specific mathematicaltechniques.

In order to obtain the numerical solution of the diffusion equation for aparallelepiped-shaped porous material, the diffusion process takes into account thefollowing assumptions:

• The thermophysical and mechanical properties are constant;• The diffusion coefficient is constant throughout the diffusion process;• The solid is homogeneous and isotropic;• There is symmetry in each central plane of the solid;• The only mechanism of water transport within the solid is diffusion;• Convective boundary conditions at the solid surface, with moisture content and

temperature depending on position and time;• The field of moisture content and temperature inside the body is uniform at the

beginning of the process;• Convective mass and heat transfer coefficients are constant for all faces of the

solid.

Because the geometric shape of the parallelepiped is regular, one can use thesymmetry condition and numerically solve the diffusive problem for only onesymmetrical part of the domain, such as studying only the region illustrated inFig. 2.4c.

Figure 2.5 illustrates the discretized domain used for discretization of thegoverning equation. The numerical solution of the diffusion equation for a paral-lelepiped was obtained considering a fully implicit formulation. This formulationwas chosen because it presents no instability or convergence problems.


Fig. 2.5 Discretizedthree-dimensional domainwith 27 types of controlvolumes

Considering Fig. 2.5, and integrating Eq. (2.7) into space and time, the followingresult is obtained for a control volume P:

[ε + (1 − ε)ρsσ ]

(CP − C0

P

)

txyz =

(DCe

∂C

∂x

∣∣∣∣e

− DCw

∂C

∂x

∣∣∣∣w

)yz +

(DCn

∂C

∂y

∣∣∣∣n

− DCs

∂C

∂y

∣∣∣∣s

)xz

+(DCf

∂C

∂z

∣∣∣∣f− DC

b∂C

∂z

∣∣∣∣b

)xy + SCxyz (2.21)

where superscript zero means that the term must be evaluated at time t prior tothe time of interest, whereas terms without superscript are evaluated at the time ofinterest. The subscripts “e”, “w”, “n”, “s”, “f”, and “b” mean the east, west, south,north, front, and back boundaries, respectively, of a considered control volume, P isthe nodal point, centered on this control volume, and N, S, E, W, F, and B refer tothe neighbors to the north, south, east, west, front, and back, respectively (Figs. 2.5and 2.6).

From the analysis of Figs. 2.5 and 2.6, the following derivatives for Eq. (2.21) areobtained:

∂C

∂x

∣∣∣∣e

= CE − CP

δxe(2.22)

∂C

∂x

∣∣∣∣w

= CP − CW

δxw(2.23)


Fig. 2.6 Internal controlvolume of nodal point P andits neighbors

∂C

∂y

∣∣∣∣n

= CN − CP

δyn(2.24)

∂C

∂y

∣∣∣∣s

= CP − CS

δys(2.25)

∂C

∂z

∣∣∣∣b

= CP − CB

δzb(2.26)

∂C

∂z

∣∣∣∣f

= CF − CP

δzf(2.27)

Substituting Eqs. (2.22)–(2.27) in Eq. (2.21) and arranging terms, we have for theinternal control volumes the following algebraic equation:

ApCP = AeCE + AwCW + AnCN + AsCS + AfCF + AbCB + B (2.28)

where

Ap = [ε + (1 − ε)ρsσ ]xyz

t+ DC

eyz

δxe+ DC

wyz

δxw+ DC

nxz

δyn

+ DCs

xz

δys+ DC

fxy

δzf+ DC

bxy

δzb(2.29)

Ae = DCe

yz

δxe(2.30)

Aw = DCw

yz

δxw(2.31)

An = DCn

xz

δyn(2.32)

As = DCs

xz

δys(2.33)


Fig. 2.7 Scheme used to identify the symmetry condition in the parallelepiped (new domain)

Af = DCf

xy

δzf(2.34)

Ab = DCb

xy

δzb(2.35)

B = [ε + (1 − ε)ρsσ ]xyz

tC0P + SCxyz (2.36)

Equation (2.28) has important physical significance. The coefficients Ae, Aw, An,As, Af, and Ab represent the conductance between point P and its neighbors. Theterm C0

P represents the influence of the value of variable C at the previous time onits value at the present time. In this equation, V = xyz is the volume of theinfinitesimal element considered in Fig. 2.6.

Equation (2.28) is applied to all points within the computational domain exceptboundary points, where boundary conditions must be incorporated into the formu-lation. In this case, volumes adjacent to the body surface, called boundary controlvolumes, are used. For such volumes, the integration of the conservation equationis preceded, as described above, considering the existing boundary conditions. Forexample, in the newdomain under study (Fig. 2.4c), considering the symmetry condi-tion, it is found that the mass flux in the west, back, and south boundaries is zero, inother words, C

′′w = 0,C

′′b = 0, and C

′′s = 0 (Fig. 2.7).

Consequently, for the proposed discretization, with boundary conditionof the third type, it is sufficient to impose hmw = hmb = hms =0, (where hmw = hmb = hms = hm).

Similarly, to what was obtained for the vapor diffusion equation as applied to theinternal control volumes, the following algebraic equation for the heat transfer isobtained:

ApTP = AeTE + AwTW + AnTN + AsTS + AfTF + AbTB + B (2.37)

where


Fig. 2.8 Two control volumes with transport coefficients DCP e DC

E

Ap = ρ(cP + hsβ)xyz

t+ K T

eyz

δxe+ K T

wyz

δxw+ K T

nxz

δyn+ K T

bxz

δys

+ K Tf

xy

δzf+ K T

bxy

δzb(2.38)

Ae = K Te

yz

δxe(2.39)

Aw = K Tw

yz

δxw(2.40)

An = K Tn

xz

δyn(2.41)

As = K Ts

xz

δys(2.42)

Af = K Tf

xy

δzf(2.43)

Ab = K Tb

xy

δzb(2.44)

B = ρ(cP + hsβ)xyz

tT 0P + STxyz (2.45)

The discretization of the diffusion equation requires knowledge of the DC valuesnot only at the nodal point, but at the east, west, north, south, front and back facesof each control volume, as illustrated in Fig. 2.8.

The value of DCe is the value of the property at the interface of the nodal points.

So, it is the value of DC on the common face between P and E. Such value is givenby:


DCe = DC

E DCP

(1 − fd)DCP + fdDC

E

(2.46)

where

fd = dPdP + dE

(2.47)

where dPe dE are the distances from the interface “e” to the nodal points P and E,respectively.

Considering a uniform mesh, we have that fd = 1/2, since in this case dP = dE.Thus, Eq. (2.46) results in:

DCe = 2DC

E DCP

DCE + DC

P

(2.48)

The average value of C can be obtained by a weighted average using each controlvolume as follows (Eq. 2.6):

C = 1

V

npx−1∑

i=2

npy−1∑

j=2

npz−1∑

k=2

Ci jkV′i jk (2.49)

with

V =npx−1∑

i=2

npy−1∑

j=2

npz−1∑

k=2

V′i jk (2.50)

where V is the volume of the solid, i, j, and k define the position nodal point, in thecontrol volume considered, V

′i jk is the volume value of this elemental volume, npx

− 2, npy − 2, and npz − 2 define the number of control volumes along the x, y, andz directions, respectively. In the case of a uniform mesh, it’s given:

one-dimensional approach is described as:

V′i jk = xyz (2.51)

To solve the systems of algebraic equations generated by Eqs. (2.7) and (2.8), acomputer code using Mathematica® software was developed. In it, the systems oflinear equations are iteratively solved using theGauss–Seidelmethod. Itwas assumedthat the numerical solution converged when, starting from an initial condition, thefollowing criterion was met at each nodal point in the computational domain at acertain time:

∣∣Φn+1 − Φn∣∣ ≤ 10−8 (2.52)


where Φ can be C or T, and n represents the nth iteration at each time point. Thiscriterion from the physical and numerical point of view is sufficiently precise toguarantee the physical realism of the obtained results. To obtain the results it wasconsidered a numerical mesh of 20 × 20 × 20 nodal points and a t = 20 s. Theseparameters were obtained after a mesh and time step refining was performed.

A program operation flowchart in block diagram form is shown in Fig. 2.9.

Estimation of Process Parameters

(a) Estimation of transport coefficients

With Eqs. (2.1) and (2.2) adjusted, “data capture” moments were establishedthroughout the process in which the average moisture content and temperature couldbe determined so that the distribution of these points was approximately uniform.Subsequently, these equations were used in the computer code to adjust the diffusiveand convective transport coefficients.

Transport coefficients were obtained by varying their values to minimize thesum of quadratic deviations between predicted and experimental results. Deviationsbetween experimental and calculated values and variance were obtained as follows:

ERMQ =n∑

i=1

(Φi,Num − Φi,Exp

)2(2.53)

S2 = ERMQ(n − n

∧) (2.54)

where n is the number of experimental points and n∧

number of adjusted parameters(number of degrees of freedom).

The initial value of the convective heat transfer coefficient used during the adjust-ment was obtained using the correlations for the Nusselt

(Nu

), Reynolds (Re), and

Prandtl numbers (Incropera and De Witt 2002), applied to a plane plate as follows:

h′c, j = Nuk

R j(2.55)

where R j can be R1 or R2 or R3 (Fig. 2.2), and

Nu j = 0.664Re1/ 2j

1/ 3Pr (2.56)


Fig. 2.9 Computational algorithm diagram


being

Re j = ρvR j

μ(2.57)

with validity range (5 × 105 < Re ≤ 1 × 108).The equation used to obtain the initial convective mass transfer coefficient calcu-

lated for air was obtained using the correlations for Sherwood numbers(Sh

)and

Schmidt (Sc), as follows (Incropera and De Witt 2002):

h′m, j = ShDAB

R j(2.58)

where DAB is the diffusivity of water vapor in the air, and the Sherwood numbergiven by:

Sh j = 0.664Re1/ 2j Sc1/ 3 (2.59)

To obtain the apparent density of the samples, we used the following equation:

ρsample = mfiber

Vsample(2.60)

The equations used to obtain the thermal conductivity and the specific heatcalculated for the sample are given as follows:

ksample = (1 − ε)k(fiber) + εk(air) (2.61)

and

cp,sample = (1 − ε)cp,(fiber) + εcp,(air) (2.62)

(b) Estimation of equilibrium equation parameters

Considering the equilibrium equation, Eq. (2.5) can also be written as follows:

M = a1 + a2T (2.63)

where a1 = α + σC e a2 = −β.With the values of T eq and Meq for each experimental condition, a linear fit of

Eq. (2.63) to the experimental datawas performed using theQuasi-Newton numericalmethod using the Statistica® Software, with a convergence criterion of 0.000099,from which we obtained the values of a1 and a2 parameters.


Table 2.2 Thermophysical and process parameters of the sample and fiber used in the simulationfor T = 70 °C

Co (kgvapor/m3) Ceq (kgvapor/m3) ρ(sample) (kg/m3) ρ(fiber) (kg/m3)

0.04125 0.01381 81.956 1450.00

cp,(sample) (J/kg K) cp,(fiber) (J/kg K) k(sample) (W/m K) k(fiber) (W/m K)

961.617968 149.65 0.03141034 0.067

On the other hand, the equation of state for an ideal gas is given by:

P = ρair · R · T (2.64)

where P is the atmospheric pressure, ρ is the density, R is the particular gas constant(atmospheric air), andT is the drying temperature. Thus, air densitywithin the fibrousmedium can be determined as follows:

ρair = P

R · T (2.65)

To calculate the equilibrium water vapor concentration in the fibrous medium(between the fibers), consider the following formula:

Ceq = ρair · UA (2.66)

where UA is the air absolute humidity in voids, obtained from the temperature andrelative humidity of the drying air. So, using the data fromCeq andMeq and the valueof β obtained from the adjustment (Eq. 2.63), there is a system of equations withtwo unknowns, which allows obtaining the α and σ parameters.

Thermophysical Properties of Materials

Table 2.2 presents some thermophysical properties and process parameters of thefibrous medium for the drying experiment. These data were used in the simulation.

Table 2.3 presents some thermophysical properties and process parameters of thedrying air at atmospheric pressure for the experiment. These data were used to obtainthe parameters of Table 2.4 and the transport coefficients reported in Table 2.7.

Table 2.4 presents some calculated transport parameters. These data were used todetermine the transport coefficients reported in Table 2.7.


Table 2.3 Thermophysical and process parameters of drying air at atmospheric pressure for T =70 °C

ρair (kg/m3) k (W/m K) μ (N s/m2) UA(kgvapor/kgdry air)

UAsat (kgvapor/kgdry air)

1.020411 0.028260 19.96557 × 10−6 0.01353746 0.2765

DAB(m2/s

)cp(kJ/kg K) hs (kJ/kg) Pr Sc

31.1693 ×10−6

1.033492 2333.26 0.73016 0.627739

Table 2.4 Transportparameters calculated for theexperimental test in T =70 °C

Dimensionless parameters

Rex Rey Rez

127.7713 63.8856 127.7713

Nux Nuy Nuz

6.75860 4.77905 6.75860

Shx Shy Shz

6.42655 4.54425 6.42655

2.2.3 Results

2.2.3.1 Lumped Analysis

From the analysis of the experimental data obtained, it was observed that themoisturecontent decreases with time. In general, the drying rate increases with higher dryingair temperature and lower air relative humidity. Therefore, increasing the drying airtemperature resulted in a shorter processing time.

The surface temperature of the fibrous medium varied during the drying processand reached thermal equilibrium faster at the highest drying temperature. Since thesurface temperature of the fiber rises during drying, the process occurs at a fallingdrying rate, i.e., the migration rate of water from the fiber to its surface is lessthan the water removal rate from the surface by the heated air. The fiber temperatureincreases as the drying rate decreases. Similar results have been reported for differentresearchers (Zhou et al. 2014; Santos et al. 2017).

It is noticed that at the end of the process, the drying rate tends to zero whenthe moisture content approaches the hygroscopic equilibrium condition and the fibertemperature stabilizes, that is, the fiber approaches its thermal equilibrium.

All details of the results and statistical parameters obtained with the modeladjustments to the experimental data are presented in Tables 2.5 and 2.6.

Figure 2.10 shows the fitted curves for the averagemoisture content of the samplesversus drying time.


Table 2.5 Parameters of Eq. (2.1) obtained after adjustment to experimental data of sisal fibermoisture content

T (°C) Parameters

c1 k1 (min−1) c2 k2 (min−1) c3 k3 (min−1)

70 0.779910 0.031757 0.022230 0.000215 0.011298 0.243766

R (kg/kg)2 Proportion ofvariance (kg/kg)2

Loss function(kg/kg)2

0.99995 0.99989 0.000001574

Table 2.6 Parameters of Eq. (2.2) obtained after adjustment to experimental data of sisal fibertemperature

T (°C) Parameters

c1 (°C) k1 (min−1) c2 (–) k2 (–) c3 (–) k3 (min−1) k4 (–)

70 0.536510 0.000406 −5.85983 0.006903 8.947182 13.39565 3.234171

R (°C)2 Proportion ofvariance(°C)2

Lossfunction(°C)2

0.99737 0.99474 6.887782641

__T = 70oC Model: M = c1 exp(-k1 t) + c2 exp(-k2 t) + c3 exp(-k3 t)

__M = (0.077991) exp[-(0.031757) t]+(0.02223) exp[-(0.000215) t]+(0.011298) exp[-(0.243766) t]

0 100 200 300 400 500t (min)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

M (k

g/kg

)

Fig. 2.10 Average moisture content of the sample during drying at 70 °C. Experimental (ooo) andpredicted (__)


Ts = 70oC Model: T = c1 log2[(k1 t + k2)c2 (k3 t + k4 )c3]T = (0.53651) log2{[(0.000406) t + (0.006903)] (-5.8598) [(13.3956) t + (3.23417)](8.94718)}

0 100 200 300 400 500t (min)

0

10

20

30

40

50

60

70T

(ºC)

Fig. 2.11 Sample surface temperature during drying at 70 °C. Experimental (ooo) and predicted(__)

Figure 2.11 shows the curves of the fiber surface temperature versus drying time.From the analysis of Tables 2.5 and 2.6 and Figs. 2.10 and 2.11, it can be seen thata good fit was obtained, with correlation coefficient R above 0.988, in all cases.

2.2.3.2 Equation Equilibrium Analysis

Based on the methodology presented before, we obtained the following equilibriumequation:

M = 0.044702 + 2.217337C − 0.000784T (2.67)

Equation (2.67) describes the linear dependence of temperature (T ), watervapor concentration (C), and moisture content (M), fundamental for the couplingbetween the vapor diffusion equation and the heat conduction equation. A correlationcoefficient of 0.99 was obtained in this regression.

2.2.3.3 Distributed Analysis

Drying and Heating Kinetics

In this topic will be presented the results of drying and heating kinetics, and distri-bution of moisture content and temperature inside the fibrous medium, for drying air


Table 2.7 Initial values of the transport coefficients used during the nonlinear regression (T =70 °C)

Parameters

h′mx (m/s) h

′my(m/s) h

′mz(m/s)

4.00622 × 10−3 5.66564 × 10−3 4.00622 × 10−3

h′cx

(W/m2 K

)h

′cy

(W/m2 K

)h

′cz

(W/m2 K

)

3.81996 5.40224 3.81996

Table 2.8 Parameters Estimated transport coefficients for the drying air temperature T = 70 °C

Parameters

hmx (m/s) hmy(m/s) hmz(m/s) hcx(W/m2 K

)hcy

(W/m2 K

)hcz

(W/m2 K

)

5.0622 ×10−4

21.6564 ×10−4

5.0622 × 10−4 5.538942 7.833248 5.538942

D′ (m2/s) α(m2/s

)ERMQM (kg/kg)2 S

2M (kg/kg)2 ERMQT (°C)2 S

2T (°C)2

1.612 ×10−6

3.9855592 ×10−7

0.0000722468 7.52571 ×10−7

967.74872 9.976791

Fig. 2.12 Comparison between numerical and experimental values of the average moisture contentof the fibrous medium as a function of time (T = 70 °C)

temperature of 70 °C. Later, on Tables 2.7 and 2.8 will be presented and discussed thevalues of the diffusive and convective transport coefficients obtained after comparingthe predicted data with the experimental data for the experiment performed.

Figure 2.12 presents the comparison of the numerical and experimental values ofthe average moisture content (on dry basis) of the fibrous medium as a function of


Fig. 2.13 Comparison between numerical and experimental values of the fibrous medium surfacetemperature as a function of time (T = 70 °C)

time for the air temperature of 70 °C. From the analysis of this figure, we can seethat data of there is a good agreement between the numerical and experimental theaverage moisture contents throughout the drying process.

The temperature behavior of sisal fibers during drying was described by Eq. (2.4).The properties of the fibrousmedium,which are thermal conductivity (k) and specificheat (cp) were obtained using Eqs. (2.61) and (2.62), respectively.

On the surface of the fibrous medium occurs both convective heat transport andheat transfer associated with moisture evaporation. Taking into account only theconvective heat transport on the surface of the fibrous medium, the boundary condi-tion of third kind was considered, in which the heat flux on the surface of thefibrous medium is proportional to the difference between the surface temperatureof the fibrous medium and the drying air temperature (equilibrium temperature).The proportionality constant hc (convective heat transfer coefficient) was obtainedapplying the best square error technique between the numerical and experimentaldata of fiber temperature during drying at 70 °C. The best value of hc corresponds tothe lowest value of S2.

Figure 2.13 shows the comparison of numerical and experimental values of thefibrous medium surface temperature as a function of time for the temperature of70 °C. From the analysis of this figure, we can note that there is good agreementbetween numerical and experimental surface temperature values in the first 4000 sof process.

Since the surface temperature of the fiber rises during drying, the process occurs ata falling drying rate. The fiber temperature increases as the rate of drying decreases.It can be seen in Fig. 2.13 that at the end of the process, the drying rate tends to


a) t = 200 s b) t = 700 s c) t = 8000 s

Fig. 2.14 Water vapor concentration distribution (kgvapor/m3) in the plane yz at x = 0.025 m (R1/2)to a drying air temperature of 70 °C

zero when the moisture approaches the equilibrium moisture content and the fibertemperature stabilizes, that is, the fiber approaches its equilibrium thermal.

Analyzing the result, it can be stated that the model used to describe the heatingkinetics of thefibrousmedium, considering constant volumeand transport parameterscan be considered satisfactory, even if a discrepancy between the simulated andexperimental data is perceived from t = 4000 s. This discrepancy may have beencaused by errors in the temperature measurement process during the experiments oreven by the measuring device itself.

These differences observed between the simulated results and the experimentaldata of the temperature after the process 4000 s may also indicate that the convectiveheat coefficient hc from this time should be lower than in the initial moments. Inthis case, the hypothesis of hc variable throughout the process would be a moreappropriate choice.

Water Vapor Concentration and Temperature Distributions

Figures 2.14 and 2.15 show the distribution of water vapor concentration and temper-ature inside the fibrous medium, analyzed in the planes x = 0.025 m (R1/2), for threetimes 200 s, 700 s, and 8000 s, respectively. It is important to remember that allresults are plotted to 1/8 of the fibrous body volume, due to the symmetry that existsin the physical problem and in the geometry of the sample.

By analyzing these figures, we can see that water vapor concentration presentedthe highest results in the central regions of the body at any time. The decrease invapor concentration over time at any position was also noted, tending toward itsequilibrium value for sufficiently long drying times (Fig. 2.12).


c) t = 8000 sb) t = 700 sa) t = 200 s

Fig. 2.15 Temperature distribution (°C) in the plane yz at x= 0.025m (R1/2) to a drying temperatureof 70 °C

Temperature has the lowest results in the central regions of the body at any time.The temperature also increases over time in any position, tending to its equilibriumvalue for sufficiently long drying times. This shows that heat flux occurs from thesurface to the center of the material, in contrast to the moisture flux that occurs fromthe center to the surface of the material.

Estimation of Transport Coefficients (D, hm and hc)

The mass diffusion coefficient measures the tendency of water molecules to migratefrom one region of high concentration to another of lower concentration. The higherthe diffusion coefficient, the faster the diffusion of one species relative to another.This coefficient is directly related to the temperature and moisture content.

The initial convective transport coefficients h′c and h

′m were obtained using

Eqs. (2.55) and (2.58), respectively. From these initial values, an optimization processwas performed to obtain the ideal values of the convective coefficients, as describedearlier. Table 2.7 gives the obtained values of these parameters.

Estimation of the transport coefficients hc, hm, and D was made by minimizingthe sum of the squares of the residues, as mentioned earlier. Table 2.8 summarizesthe obtained values of these coefficients as well as relative error and variance for theexperimental test.

In general, the numerical results showed a good agreement with the experimentaldata ofmoisture content and temperature of sisal fibers submitted to drying. The smallerrors and variances indicate that the methodology used to estimate the transportcoefficients is satisfactory.


Specifically, with respect to the mass diffusion coefficient (D), it can be said thatit is a multiplication of the vapor diffusion coefficient inside the fibrous medium bythe bed porosity that is, D = εD′. Since the porosity of the medium ε > 0.91, it canbe noted that the drying of the fibrous medium resembles the drying of individualfibers. This in fact is almost true and can be proved by the value of the D′ whichis smaller than the DAB (Table 2.3) for the experimental test. This indicates that thevapor flux inside the fibrous medium is more difficult than in the air outside thefibrous medium, as expected.

Comparison between the mass diffusivities of porous materials reported in theliterature becomes difficult due to the lack of specific studies of these materials.In general, it is important to note that differences in mass diffusion coefficient canbe attributed to the different factors, such as geometric considerations, calculationmethod, initial and equilibrium moisture contents, physical structure of the materialused, and porosity of the material and boundary conditions.

2.3 Conclusions

In this chapter, the physical problemof simultaneous heat andmass transfer in a paral-lelepiped porous bed has been studied. Due to the great importance of plant fibers,emphasis is given to drying of sisal fibers. A transient three-dimensional mathe-matical modeling, written in Cartesian coordinates was proposed, and its numericalsolution based on the finite-volume method is presented and discussed. Results ofthe drying and heating kinetics and the vapor concentration and temperature distri-butions inside the fiber bed at different times of the process are presented, comparedwith experimental data and discussed.

From the obtained results it can be concluded that: (a) The proposed lumpedmodels can satisfactorily be used to describe the drying process of sisal fibers,considering that they presented good agreement with the experimental data, withcorrelation coefficient greater than 0.988; (b) the finite-volume method proved tobe adequate to predict the phenomenon of heat and mass transfer within the fibrousmedium; (c) drying of sisal fibers occurred at a falling drying rate; (d) there is adifference in water vapor concentration and temperature between the central regionand the surface of the fibrous medium; (e) the largest water vapor concentration andtemperature gradients are located in the regions near the vertices of the fiber porousbed. Since these regions are in more intense contact with the drying air, fibers locatedin these regions are more susceptible to deformation and thermal effects.

Acknowledgments The authors thank CNPq, FINEP and CAPES (Brazilian Research Agencies),and the Federal University of Campina Grande (Brazil) for financial support.


References

Angrizani, C.A., Vieira, C. A.B., Zattera, A.J., Freire, E., Santana, R.M.C., Amico, S.C.: Influenceof sisal fiber length and its chemical treatment on the properties of polyester composites. In:17º CBECIMat—Brazilian Congress of Materials Science and Engineering, Foz do Iguaçu, PR,Brazil (2006). (In Portuguese)

Barreto, A.C.H., Rosa, D.S., Fechine, P.B.A., Mazetto, S.E.: Properties of sisal fibers treated byalkali solution and their application into cardanol-based biocomposites. Compos. Part A: Appl.Sci. Manufac. 42(5), 492–500 (2011)

Crank, J.: The Mathematics of Diffusion. Oxford University Press, London (1975)Cruz, V.C.A., Nóbrega, M.M.S., Silva, W.P., Carvalho, L.H., Lima, A.G.: B: An experimentalstudy of water absorption in polyester composites reinforced with macambira natural fiber.Materialwiss. Werkstofftech. 42(11), 979–984 (2011)

Ferreira, S.R., Lima, P.R.L., Silva, F.A., ToledoFilho,R.D.: Effect of sisal fiber humidification on theadhesion with portland cement matrices. Rev. Matéria 17(2), 1024–1034 (2012). (In Portuguese)

Incropera, F.P., De Witt, D.P.: Fundamentals of Heat and Mass Transfer. Wiley, New York, USA(2002)

Lima, A.G.B., Silva, J.B., Almeida, G.S., Nascimento, J.J.S., Tavares, F.V.S., Silva, V.S.: Clay prod-ucts convective drying: Foundations, modeling and applications. In: Delgado, J.M.P.Q., Barbosade Lima, A.G. (eds.) Drying and Energy Technologies. Series: Advanced Structured Materials,vol. 63, 63edn, pp. 43–70. Springer, Heidelberg (Germany) (2016

Maliska, C.R.: Computational Heat Transfer and Fluid Mechanics, p. 453. LTC, Rio de Janeiro,Brazil (2004)

Martin, A.R., Martins, M.A., Mattoso, L.H.C., Silva, O.R.R.F.: Chemical and structural characteri-zation of sisal fibers from Agave Sisalana variety. Polímeros: Ciência e Tecnologia 19(1), 40–46(2009). (In Portuguese)

Melo Filho, J.A., Silva, F.A., Toledo Filho, R.D.: Degradation kinetics and aging mechanisms onsisal fiber cement composite systems. Cem. Concr. Compos. 40, 30–39 (2013)

Nóbrega, M.M.S., Cavalcanti, W.S., Carvalho, L.H., Lima, A.G.B.:Water absorption in unsaturatedpolyester composites reinforced with caroá fiber fabrics: modeling and simulation. Materialwiss.Werkstofftech 41(5), 300–305 (2010)

Santos, D.G., Lima, A.G.B., Costa, P.S.: The effect of the drying temperature on the Moistureremoval and mechanical properties of sisal fibers. Def. Diff. Forum 380, 66–71 (2017)

Silva, J. S.: Drying and Storage of Agricultural Products. Aprenda Fácil, Viçosa,) 560 p. (2008).(In Portuguese)

Silva, R.V.: Polyurethane Resin Composite Derived from Castor Oil and Vegetable Fibers. DoctoralThesis in Science and Materials Engineering. University of São Paulo, São Carlos, SP, Brazil(2003) (In Portuguese)

Wei, J., Meyer, C: Improving degradation resistance of sisal fiber in concrete through fiber surfacetreatment. Appl. Surf. Sci. 289, 511–523 (2014)

Zhou, F., Cheng, G., Jiang, B.: Effect of silane treatment on microstructure of sisal fibers. Appl.Surf. Sci. 292, 806–812 (2014)

Chapter 3Foam-Mat Drying Process: Theoryand Applications

E. R. Mangueira, A. G. Barbosa de Lima, J. de Assis Cavalcante,N. A. Costa, C. C. de Souza, A. K. F. de Abreu, and A. P. T. Rocha

Abstract The duck egg is an ideal product to increase human nutrition becauseit has a large amount of protein and vitamins. This chapter focuses on the foam-mat drying technique applied to duck egg white and yolk. The aim is to obtainpowder of these materials after drying. Herein, different topics related to founda-tions, experiments, and lumped underling are presented and discussed. Drying exper-iments with and without emulsifiers to obtain stable foam were performed based onthe complete factorial experimental design. The idea is to assist researchers, engi-neers, and academics in the understanding of this important topic related to foodpreservations.

E. R. Mangueira · J. de Assis Cavalcante · N. A. Costa · C. C. de SouzaDepartment of Chemical Engineering, Federal University of Paraiba (UFPB), 58051-900 JoãoPessoa, PB, Brazile-mail: [email protected]

J. de Assis Cavalcantee-mail: [email protected]

N. A. Costae-mail: [email protected]

C. C. de Souzae-mail: [email protected]

A. G. B. de Lima (B)Department of Mechanical Engineering, Federal University of Campina Grande, Av. AprígioVeloso, 882, Bodocongó, Campina Grande 58429-900, PB, Brazile-mail: [email protected]

A. K. F. de AbreuDepartment of Technology and Development, Federal University of Campina Grande (UFCG),Sumé, PB 58540-000, Brazile-mail: [email protected]

A. P. T. RochaDepartment of Food Engineering, Federal University of Campina Grande (UFCG), CampinaGrande 58429-900, PB, Brazile-mail: [email protected]


61









https://doi.org/10.1007/978-3-030-47856-8_3

62 E. R. Mangueira et al.

Keywords Foam-mat drying · Egg white · Egg yolk · Experimental · Theoretical

3.1 Drying Theory of Porous Materials

3.1.1 Fundamentals

Drying is one of the oldest processes used by humans in food preservation. In general,it is a process in which water is removed from the product, involving simultaneousheat and mass transfer, and phase change of the water present in the food. In thisprocess, a large amount of water is eliminated, consequently reducing weight of theproduct and the water activity that affects microbial growth, enzymatic reactions,and other reactions of chemical and physical reactions (Gava 2008).

Two of the main factors governing drying are the removal of moisture from theproduct surface and themigration ofmoisture inside the product. The rate ofmoistureremoval from the surface of the product is a function of both the surface area of theproduct exposed to air and the ability of the air to remove water of the surface (dryingpotential). The larger the surface area of the product, the larger the heat and massexchange area with the airflow, facilitating the removal of water. In this step, thedriving force related to water removal is directly related to the difference betweenthe water vapor pressure at the material surface, the water vapor pressure in the airpassing through the dryer. When the moisture is removed from the concentrationgradient is created internally in the product, causing a migratory process of moisturefrom the center to the product surface (Fioreze 2004).

The migration of moisture from the interior to the surface of the product dependson the particle size, its internal structure, and the driving force for this migration(concentration gradient). The larger the particle, the greater the distance to be trav-eled by heat from surface to center and by moisture from center to surface of theproduct to be evaporated. Different products have different internal structures, facil-itating or hindering moisture migration, according to their porosity and the positiveand negative charges of the carbon chains of the product. Increased driving forcefor water migration can be observed by increasing temperature and/or decreasingrelative humidity of the drying air. This increases drying rate and the differences inconcentrations between the inner and surface of the product (Fioreze 2004).

In convective drying process, the water vapor present at the surface of the wetporous material is removed by air flow, either in natural or forced convection.

For successful drying of biological products, it is well known that several variablesmust be taken into account during the process. The main variables are: air relativehumidity; air temperature; air velocity; initial moisture of the product; final moistureof the product; product shape; and product type (Fioreze 2004).

Some products, when dried, keep their physical and nutritional characteristicsintact and return to their natural appearance or undergo few changes when rehumid-ified. This characteristic makes the drying process a viable way of preserving foodfor human consumption (Cornejo et al. 2003; Mayor and Sereno 2004).

3 Foam-Mat Drying Process: Theory and Applications 63

Fig. 3.1 Typical dryingcurve of a wet porousmaterial

The drying process has evolved from the use of solar energy to current techniques,including but not limited to tray drying, tunnel drying, spray drying, rotary drying,freeze drying, osmotic dehydration, extrusion, fluidized bed drying, and microwaveand radiofrequency use (Vega-Mercado et al. 2001). Therefore, there are severaltypes of dryers; however, the choice of an appropriated method depends on severalfactors, among which stand out: product type, dryer availability, drying cost, andpurpose of the dehydrated product (Sagar and Kumar 2010).

When a wet porous material is subjected to the drying process, it can lose water ata constant velocity throughout the process. As drying progresses under fixed condi-tions, the rate of water removal decreases (Meloni 2003). This can be seen in Fig. 3.1which shows the relationship of productmoisture contentwith time in a typical dryingcurve. The importance of studying the drying curves of a wet porous product is thatthey indicate the rate of water removal at any time measured from the beginning ofthe process. A higher or lower slope of the curve indicates the ease or difficulty ofremoving water during the drying process (Meloni 2003).

Drying curves can help in choosing a desirable drying time, with the aim ofobtaining the product with the required moisture, and thus increasing a good qualityproduct.

TheA–B section of the curve represents the initial stage of dryingwhen the solid isheated or cooled and goes from the initial temperature T0 to the wet-bulb temperatureT bu. This stretch is called the stabilization period, in which the surface conditions ofthe solid balance with those of the drying air. In general, this stage is described by ashort period and, in general, is negligible of the total drying cycle (Ordonéz 2005).During this time the drying rate may increase or decrease under the effect of dryingtemperature.

In B–C section, the drying rate and product temperature become constant. Fromthis point, the temperature increases and the drying rate drops rapidly. At this stage,liquid water evaporates at the surface of the product in the same rate as the liquidwater moves inside it. The surface of the solid remains wet and at a temperature closeto the wet-bulb temperature of the drying air. This stage is known as the constantdrying rate period and continues until it reaches the critical moisture that correspondsto the point C in Fig. 3.1 (Fellows 2000).


Fig. 3.2 Typical drying ratecurves

The C–D section is called the first falling drying rate period. It occurs whenthe velocity of water migration from the interior of the product to the surface isreduced, and therefore the partial pressure of water vapor at the surface of the productdecreases progressively, and it begins to dry. In this period, the drying rate is limitedmainly by the velocity of moisture movement within the solid, reducing the effectsof external factors, especially air velocity. At this stage, water is entrapped in thestructure of the moisture, and its movement through the dehydrated product is veryslow. Therefore, for the drying rate to be significant, it is necessary to increase thetemperature of the product to provide sufficient desorption heat and to raise the watervapor pressure inside of the material (Ordonéz 2005). The D–E stretch is well knownas the second-rate period, where the product dries to reach the equilibrium moisturecontent (hygroscopic equilibrium condition).

Variations in product moisture content overtime during the drying process giverise to the drying rate curve (Fig. 3.2). The drying curve is linked to heat and masstransfer phenomena (Strumillo and Kudra 1986).

In the initial drying period, the solid and its surface are covered by a liquid layer.The constant drying rate period considers themass transfer resistance and the limitingfactors of the drying rate are the external conditions and the gaseous boundary layerat the surface of the product. In the falling drying rate period, the amount of moisturethat reaches the surface of the material decreases gradually. As a result, the watervapor partial pressure on the material surface also decreases and the drying rateis controlled by the moisture transport that depends on the moisture concentrationgradient inside the material (Mangueira 2017). In general, the falling drying rateperiod is almost always the only one observed for the drying of agricultural and foodproducts.

3.1.2 Mathematical Modeling in Drying

The study of drying kinetics aims at understanding the behavior of the product duringthe process and the prediction of drying time.On the one hand, drying experiments are


of great importance, on the other hand, process modeling plays important role in thedevelopment and optimization of dryers, as well as enabling process standardizationand the reduction of exhaustive drying tests, and predicting the drying behavior ofvarious materials quickly.

Predicting the falling drying rate is more complex than the constant drying rateand encompasses not only external heat and mass transfer mechanisms but alsointernal mechanisms in the product. The complexity of phenomena during dryingleads researchers to propose numerous theories and multiple empirical formulasto predict the drying rate adequately. These theories can be summarized as beingderived from two other theories: diffusional theory and capillary (Park et al. 2007).Diffusional theory is based on Fick’s law, which expresses mass flow rate per unitarea as proportional to the water concentration gradient within the product. It isa model used for the falling drying rate period. However, the analytical solutionof Fick’s diffusional model requires that boundary conditions be known and thatthe effective means diffusivity be specified. These limitations, in addition to therequirement of knowing the material geometry, often lead searchers to use empiricalor semi-empirical models.

Semi-theoreticalmodels are generally derived from the simplification of a solutionin series of Fick’s second law (Doymaz 2005).

The empirical method is used for drying analysis using experimental data, whichcan be determined in laboratory and in the use of dimensionless analysis (Gouveiaet al. 2002). This method is generally based on drying external conditions such astemperature, relative humidity, and drying-air velocity (Carlesso et al. 2007), withoutproviding information on energy or mass transport within the product.

From the drying data, it is possible to study the drying kinetics, with the aid of thedrying characteristic curve of the product. In fact, to adequately product the drying,it is necessary to know the initial moisture content of the product to be drier, therelationship of water with the solid structure, and the mechanism of water migrationfrom inside the material to its surface (Park et al. 2001).

Some empirical and semi-empirical mathematical models are summarized inTable 3.1. These models can be fitted to experimental data by nonlinear regres-sion using appropriately statistical software (Doymaz 2005; Biazus 2006; Marques

Table 3.1 More commonempirical and semi-empiricalmodels used to describe thedrying process

Name Model References

Henderson andPabis

RU = a exp(−Kt) Park et al. (2002)

Midilli et al. RU = a exp(−Ktn) +bt

Midilli et al. (2002)

Page RU = exp(−Ktn) Zhang andLitchfield (1991)

Page (modified) RU = a exp(−Ktn) Mangueira (2017)

Newton RU = exp(−Kt) Liu et al. (1997)


2009). In Table 3.1, RU = X/Xo is the moisture content ratio of the product; t is thetime; K is the drying coefficient; and a, b, and n are constants.

3.2 Foam-Mat Drying

3.2.1 General Foundations

Foam-mat drying is a technique used to obtain powdered food products. In this tech-nique, liquid or semi-liquid foods are transformed into stable foams by the addition ornot of foaming agents (which is intended to keep the foam stable during the process)and incorporation of air, nitrogen, or other gases in blenders or other foam generationequipment (Brennan 1994).

Foam is a colloidal dispersion in which gas is dispersed in a continuous liquidphase. The dispersed phase is referred to as the internal phase and the continuousphase is called the external phase (Baniel et al. 1997). Based on the ratio of dispersedphase to continuous phase, the foams can be classified into polyhedral foam anddiluted bubbling foam. In polyhedral foams, the proportion is large, resulting in alarge number of bubbles. As the number of bubbles increases, they push themselvesto form a honeycomb structure. Egg white foam and beer foam are good examplesof polyhedral foam. In diluted foams, the proportion is small; therefore, individualbubbles retain their spherical shape. Chocolate mousse is a good example of dilutedbubbling foams (Prins 1988). The gas phase (usually air) is incorporated as evenlydistributed small particles. The idea is to the texture and appearance of the product(Narchi et al. 2009).

The foams have thin, flat, and liquid films or lamella between bubbles. The cover-slips meet at a point called the plateau border (Fig. 3.3). As described in Fig. 3.3, gasbubbles are confined to the structures formed by the foam and plateau border cover-slips. Other foam characteristics depend on the air interface that determines foam

Fig. 3.3 Schematic representation of a foam structure


stability. The use of viscous liquids for foaming results in stable foaming. The foamtexture is also influenced by proteins and surfactants as they help in the formation ofstable foam (Vernon-Carter et al. 2001).

The mechanical strength of the lamella determines the stability of the foam alongwith its air/water interface properties. If viscous liquids are used for foam production,they would produce more stable foams due to increased lamella elasticity (Dickinson1998).

Foam increases drying efficiency because it increases surface area and the heatand mass transfer. In addition, capillarity through the foam pores facilitates moistureloss. This makes drying in a foam mat approximately three times faster than dryingin a similar liquid layer (Muthukumaran et al. 2008; Rajkumar et al. 2007). Foamthickness directly influences drying time, but this effect is greater for foods that aredehydrated in solid form (Kadam et al. 2010).

After production, the foam is spread as a thin sheet or mat and exposed to hotairflow to be dried until the desiredmoisture content.Drying is performed at relativelylow temperatures to form a thin porous layer which is disintegrated to produce a free-flowing powder. The larger surface area exposed to the drying air is the main causeof accelerated moisture removal (Brygidyr et al. 1977). During drying, moisturecan be reduced to a level ranging from 1 to 5%, which prevents microbial andenzymatic deterioration. In addition to a substantial reduction inweight andvolume, itminimizes packaging, storage, and transportation costs (Falade and Solademi 2010).

Foam-mat drying is used in heat-sensitive foods as it requires lower dehydra-tion temperatures and drying time due to a larger surface area exposed to air, andconsequently, a faster drying rate, thus accelerating the water removal process andobtaining an easily rehydrated porous product (Karim andChee-Wai 1999; Rajkumaret al. 2007).

This technique has some advantages over other liquid drying techniques, such assimpler technique, lower operating cost and allows the use of lower temperatures,which better preserves the taste and nutritional value. According to Franco et al.(Franco 2015), the powder produced by thismethod is easily reconstituted, presentingcharacteristics of texture, color, taste, and nutritional composition very similar tothe original material. This consequently increases the commercial possibilities ofobtaining dehydrated products by the method, especially for heat-sensitive foods.

The main disadvantages of this technique are related to the need for a large dryingsurface area to meet high production rates, which increases the investment cost(Francis 2000). Furthermore, additives can modify the taste, aroma, and color char-acteristics of the food. In addition, a lack of foam stability may occur during heatingor drying processes (Karim 1999), thus some variables such as the chemical natureof the raw materials, soluble solids, type, and concentration of foaming agent haveinfluenced the foam stability (Hart et al. 1963).


3.2.2 Different Methods for Foam Formation

The quantity and quality of the foam produced is determined by the different foamingtechniques. Themost common foamingmethods arewhipping, shaking, andbubbling(Dehghannya et al. 2018).

3.2.2.1 Whipping or Beating

Whipping is a process that involves adding a large amount of air to a known amountof liquid to generate foam (Lomakina and Mikova 2006). This can be accomplishedusing various devices such as mixers and homogenizers. These devices can mix avariety of food materials including fruits, vegetables, and liquids. In this process,the stirring air gets entrapped in a liquid. The amount of air entrapped in a liquidincreaseswith increasing agitation. Incorporation of air into the liquid initially resultsin large bubbles, which upon further agitation are reduced to a smaller size, providinga homogeneous foamy structure to the food material. The final size of the air bubbledepends on the stirring speed, equipment design, and rheological properties of theliquid. This technique is widely applied in the food processing sector and also forthe basic study of foam (Dehghannya et al. 2018).

3.2.2.2 Shaking

In thismethod, the foam is generated by vigorous stirring of the liquid. The volume offoam produced by this method depends on the magnitude and frequency of agitation,and the shape and size of the container, temperature, type, and concentration offoaming agent (Arzhavitina and Steckel 2010). This method is slower compared tothe whipping or bubbling method, as under similar agitation conditions they produceless foam volume (Lomakina and Mikova 2006).

3.2.2.3 Bubbling or Sparging

In this method, gas is injected into a known amount of liquid through small openings(Arzhavitina and Steckel 2010), where bubbles of uniform size are produced. Thesize of the bubbles can be controlled by adjusting the size of the opening throughwhich air is injected. The volume of foam produced depends on the amount of liquidand foaming agent. In this method, the liquid can be completely foamed if a largeamount of air is injected (Mounir 2017).


3.2.3 Foaming Agents

Food foams are composed of air and liquid and sometimes it is necessary to usean active agent on the surface (Kinsella 1981). A foaming agent is a surfactant thatfacilitates foaming when present in small amounts. The foaming agent reduces thesurface tension between two liquid materials or between a solid and liquid materialthat results in foam generation.

A good foaming agent must be able to stabilize the foam adequately and rapidlyat low concentrations; effectively function over a wide range of pH values andability to perform effectively in the presence of foam inhibitors such as fat, flavoringsubstances, and alcohol (Zayas 1997). The most commonly used foaming agents areegg albumin, milk protein, soy protein, and gelatin.

3.2.3.1 Egg Albumin

Egg albumin is a natural protein found in eggs with good foaming properties(Sangamithra et al. 2015). By rapidly beating the egg albumin, the air/liquid inter-face is denatured and interact with each other to form a stable film (Lomakina andMikova 2006). Therefore, the whipping time required by egg albumin is compara-tively shorter compared to other foaming agents. This implies that egg white proteinscould be adsorbed faster at the air–liquid interface and more rapidly denatured thanother proteins (Townsend and Nakai 1983).

3.2.3.2 Whey Protein

Whey protein is obtained from the dairy industry as a byproduct during cheeseproduction (Tariq et al. 2003). This is one of the main sources of protein in industrialfoods because of its properties, which include its use as an emulsifier, its nutritionalcontent, and its ability to form gel and stable foam (Broch et al. 2014). Due to thehigher solubility of whey protein in water and on its surface, whey protein has theability to form a high-quality foam (Sangamithra et al. 2015).

Whey protein has the ability to retard oxidation reactions in dry food materials.Furthermore, whey protein has a greater ability to bind flavored compounds, makingit highly conducive toworkingwith vegetableswith sensitive andvolatile constituents(Zhang et al. 2017).

3.2.3.3 Soy Protein

Soy protein can be obtained by removing soy oil at a lower temperature. Isolated soyprotein is a highly purified form of protein, with a minimum protein content of 90%(Nishinari et al. 2014). Isolated soy protein has many functional properties such as


solubility, water and fat absorption, water retention capacity, viscosity, foaming orwhipping, emulsification, and gelling (Liu et al. 1958).

3.3 Applications: Drying of Egg White and Yolk of DuckEgg

3.3.1 Material Preparation

Duck eggs were purchased from the popular commerce of the city of João Pessoa,Paraíba, Brazil. Following, they were cleaned and sanitized with chlorinated water(50 ppm) according to the industrial and sanitary inspection of products regulationof animal origin (Mapa 2005). After washing, the duck eggs were broken, and theegg white and yolk were separated manually. Then, they were weighed and beatenin a food mixer to obtain the foam.

3.3.2 Experimental Planning

Experimental planning is used in basic and technological research, where manyfactors can be varied at the same time, and the analysis of variance (ANOVA) is usedto determine which factors are statistically significant. The analysis of the signifi-cance of the parameters can also be performed using the F-test values, which canbe obtained by the ratio between the quadratic means associated with the regressionand the residuals. The use of the central point allows to add a third level for eachfactor, thus enabling the factorial study using the response surface methodology, aswell as quantifying the significance of possible curvature and errors associated withindividual effects and interactions between them.

For the accomplishment of the experiments, a complete factorial experimentaldesign was carried out 23 + 3 central points, with the input variables for the eggwhite one: temperature (50, 60, and 70 °C), agitation rate (6, 7, and 8 levels), andstirring time (4, 5, and 6 min), and for the yolk, the input variables were temperature(50, 60, and 70 °C), emulsifier concentration (Emustab®) (7, 10, and 13%),. andstirring time (4, 5, and 6 min). The following output variables were considered: finalmoisture of the product and drying time (min) for both.

Tables 3.2 and 3.3 present the coded and actual values of the independent vari-ables and the matrix of the complete factorial experimental design for egg white,respectively. Tables 3.4 and 3.5 present the coded and actual values of the indepen-dent variables and the matrix of the complete factorial experimental design for theyolk, respectively.

The complete factorial experimental design methodology was used aiming theproposition of statistical models able to adequately predict the characteristics of the


Table 3.2 Coded and realvalues of the independentvariables for the egg white

Independent variables Levels

−1 0 1

vag (level) 6 7 8

tag (min) 4 5 6

T (°C) 50 60 70

vag—stirring rate; tag—stirring time; T—temperature

Table 3.3 Matrix ofcomplete factorialexperimental design 23 + 3central points for the eggwhite

Experiment Independent variables

vag (level) tag (min) T (°C)

1 (−1) 6 (−1) 4 (−1) 50

2 (1) 8 (−1) 4 (−1) 50

3 (−1) 6 (1) 6 (−1) 50

4 (1) 8 (1) 6 (−1) 50

5 (−1) 6 (−1) 4 (1) 70

6 (1) 8 (-1) 4 (1) 70

7 (−1) 6 (1) 6 (1) 70

8 (1) 8 (1) 6 (1) 70

9 (0) 7 (0) 5 (0) 60

10 (0) 7 (0) 5 (0) 60

11 (0) 7 (0) 5 (0) 60

Table 3.4 Coded and actualvalues of independentvariables for the yolk

Independent Levels

variables −1 0 1

tag (min) 4 5 6

C (%) 7 10 13

T (°C) 50 60 70

tag—stirring time; T—temperature; C—emulsifier concentration

powder obtained after the foam-mat drying of the egg white and the yolk. Statisticalanalysis was performed using the Statistica® 12 software, where the obtained datawere interpreted by analysis of variance (ANOVA), for the comparison of arithmeticmeans, calculating the main effects and interactions of the variables on the obtainedresponses.


Table 3.5 Matrix ofcomplete factorialexperimental design 23 + 3central points for the yolk

Experiment Independent variables

C (%) tag (min) T (°C)

1 (−1) 7 (−1) 4 (−1) 50

2 (1) 13 (−1) 4 (−1) 50

3 (−1) 7 (1) 6 (−1) 50

4 (1) 13 (1) 6 (−1) 50

5 (−1) 7 (−1) 4 (1) 70

6 (1) 13 (−1) 4 (1) 70

7 (−1) 7 (1) 6 (1) 70

8 (1) 13 (1) 6 (1) 70

9 (0) 10 (0) 5 (0) 60

10 (0) 10 (0) 5 (0) 60

11 (0) 10 (0) 5 (0) 60

3.3.3 Experiment of Foam-Mat Drying

The foam obtained after beating using the Arno Deluxe Planetary Mixer SX80 wasplaced in aluminum trays (Fig. 3.4) and set was placed in the oven at a constanttemperature of 50, 60, and 70 °C. At regular time intervals, the trays were weighed

Fig. 3.4 Foam of a eggwhite and b yolk of the duckegg arranged in a tray

a)

b)


on a semi-analytical digital scale, accurate to ±0.01 g until they reached constantweight. The driedmaterial was removed from the traywith the aid of spatulas, packedin polyethylene bags, and closed.

In this stage, we studied the drying kinetics of the egg white and yolk, wherethe experiments were performed according to the complete factorial design 23 + 3central points as described in Table 3.1. After completion of drying, some empiricalmodels were fitted to the experimental moisture content data.

3.3.4 Analysis of Results

3.3.4.1 Duck Egg White

Duck egg white has good air incorporation capacity where the addition of a foamingand/or stabilizing agent is not required to produce a stable foam. This is due to theaction of its proteins, which move through the aqueous phase and are spontaneouslyabsorbed by the liquid–gas interface where the viscoelastic film is subsequentlyformed. The result of protein adsorption is related to reduction in surface tension,which improves the foaming ability, as well as the ability to encapsulate and retainincorporated air (Davis and Foegeding 2007).

Table 3.6 shows the results of moisture content (X f) and drying time (tf) for theegg white of the duck at the end of foam-mat drying process.

Figures 3.5, 3.6, and 3.7 show the drying kinetics for the duck egg white foam attemperatures of 50, 60, and 70 °C, respectively. Figures 3.8, 3.9, and 3.10 illustrate

Table 3.6 Moisture content values on dry basis and drying time at the end of drying of the duckegg white

Experiment Independent variables Dependent variables

vag (level) tag (min) T (°C) Xf (db) tf (min)

1 (−1) 6 (−1) 4 (−1) 50 0.1475 250

2 (+1) 8 (−1) 4 (−1) 50 0.4559 250

3 (−1) 6 (+1) 6 (−1) 50 0.0596 250

4 (+1) 8 (+1) 6 (−1) 50 0.0689 250

5 (−1) 6 (−1) 4 (+1) 70 0.1182 150

6 (+1) 8 (−1) 4 (+1) 70 0.4158 110

7 (-1) 6 (+1) 6 (+1) 70 0.0623 110

8 (+1) 8 (+1) 6 (+1) 70 0.0461 180

9 (0) 7 (0) 5 (0) 60 0.0224 180

10 (0) 7 (0) 5 (0) 60 0.1810 210

11 (0) 7 (0) 5 (0) 60 0.1896 130


Fig. 3.5 Drying curves of duck egg white foam at a temperature of 50 °C


the specific water mass flowrate (m′′) as a function of drying time, obtained for eachexperiment performed.

After analysis of these figures, it can be observed that the drying curves presentedboth constant (approximately) and falling drying rate period. It can be observedthat there was a variation in the drying time for the different temperatures, beingthe drying at 50 °C the longest, not exceeding 250 min, and the fastest, using the



Fig. 3.8 Specific drying rate of duck egg white during foam-mat drying at temperature of 50 °C

temperature of 70 °C, drying approximately 180 min. This is due to the higherheat and mass transfer between air and foam layer, which proves that temperaturepositively influences the drying of egg white and that drying occurs with moderatevelocity even at low temperatures.

In addition, it was found that both levels and stirring time affect the moisturereduction of the product, especially at low temperatures. This implies that the domi-nant variable in the low-temperature foam-mat drying process is the heat and massexchange area available in the product. However, at high temperatures, it is the




temperature of the drying air that determines the phenomenon behavior. Obviously,in both cases, the drying-air potential is directly related to the relative humidity andthe drying-air velocity (in the constant drying rate period).

Pereira (Pereira 2015), in his studies on chicken egg white drying, reports valuesfor the drying time, of approximately 360 min at temperatures of 50, 60, and 70 °C.

From some mathematical models reported in Table 3.1, nonlinear regressionswere made to the experimental data. For each drying condition, Table 3.7 shows theresults of the statistical parameters obtained with this procedure. The best-fit model


Table 3.7 Statistic parameters of the modified Page’s model after fitting to the experimental datafor the drying of the duck egg white at 50, 60, and 70 °C

Experiment Parameters

X0 (db) K (min−1) a (–) n (–) R2 (–) S (–)

1 6.1017 0.0010 0.9878 1.4886 0.9988 0.0051

2 9.7615 0.0138 1.0394 1.0477 0.9945 0.0219

3 5.6573 0.0009 0.9599 1.4450 0.9965 0.0119

4 5.7980 0.0008 0.9678 1.5687 0.9984 0.0072

5 6.0155 0.0027 0.9766 1.5177 0.9988 0.0044

6 8.9434 0.0055 0.9872 1.3774 0.9994 0.0016

7 4.4871 0.0027 0.9681 1.5458 0.9981 0.0056

8 3.9617 0.0028 0.9684 1.5619 0.9983 0.0070

9 2.9781 0.0043 0.9822 1.3707 0.9976 0.0095

10 2.9775 0.0023 0.9774 1.4369 0.9969 0.0126

11 3.1212 0.0070 0.9955 1.2698 0.9979 0.0060

(modified model Page’s) was chosen taking into consideration the statistical analysis(coefficient of determination above 0.99 and estimation errors less than 0.01).

The graph showing the result predicted by the Modified Page’s model and theexperimental dimensionless moisture content at 50, 60, and 70 °C are illustrated inFigs. 3.11, 3.12, and 3.13, respectively.

Fig. 3.11 Comparison between predicted (modified Page’s model) and experimental results of themoisture content ratio during the foam-mat drying process of the duck egg white at 50 °C


3.3.4.2 Duck Egg Yolk

For the production of duck egg yolk foam, the Emustab® emulsifier (Sousa 2017)was required. In studies realized by Negreiros (Negreiros 2016) related to foam-matdrying chicken egg yolk, the egg white was used as emulsifier. In the duck egg yolk,it was not possible to produce the foam using the egg white because, despite theemulsifying characteristic of the duck egg yolk, this product has a high-fat content,which makes the formation of foam difficult.

Table 3.8 shows the results of moisture content (X f) and drying time (tf), for theduck egg yolk at the end of drying process.

Figures 3.14, 3.15, and 3.16 show the drying kinetics for the duck egg yolk foamat temperatures of 50, 60, and 70 °C, respectively. Figures 3.16, 3.17, and 3.18illustrate the specific water mass flowrate (m′′) as a function of time, obtained foreach experiment performed.

After analysis of these figures, it can be observed in Figs. 3.14, 3.15, and 3.16 thatthe drying curves present approximately constant and falling drying rate periods. Itcan also be observed that there was a variation in the drying time for the differenttemperatures, being the drying at 50 °C the longest, occurring in approximately450 min, and the fastest, using the temperature of 70 °C, in a drying time approxi-mately 250 min, almost half of drying realized at 50 ° C. With this, it was possibleto prove the influence of temperature on foam-mat drying process. Approximatedrying time values were found by Negreiros (Negreiros 2016) in their studies relatedto foam-mat drying of chicken egg yolk at the same temperatures. The experimentsshow a good reproducibility in the behavior of the drying curve to the center pointcited in Table 3.5 (Experiments 9–11).

Table 3.8 Moisture content values on dry basis and drying time at the end of drying for duck eggyolk

Experiment Independent variables Dependent Variables

C (%) tag (min) T (°C) Xf (db) tf (min)

1 (−1) 7 (−1) 4 (−1) 50 0.0144 450

2 (+1) 13 (−1) 4 (−1) 50 0.1406 450

3 (−1) 7 (+1) 6 (−1) 50 0.0058 450

4 (+1) 13 (+1) 6 (−1) 50 0.0024 390

5 (−1) 7 (−1) 4 (+1) 70 0.0008 210

6 (+1) 13 (−1) 4 (+1) 70 0.1400 180

7 (−1) 7 (+1) 6 (+1) 70 0.0124 250

8 (+1) 13 (+1) 6 (+1) 70 0.0065 210

9 (0) 10 (0) 5 (0) 60 0.0842 290

10 (0) 10 (0) 5 (0) 60 0.0223 290

11 (0) 10 (0) 5 (0) 60 0.0866 250


Fig. 3.14 Drying curves of duck egg yolk foam at a temperature of 50 °C


Figures 3.17, 3.18, and 3.19 show the specific drying rates for the duck egg yolkat temperatures of 50, 60, and 70 °C, respectively. From the analysis of these figures,we state the existence of both constant and falling drying rate periods.

Now, as reported for duck egg white, for some mathematical models reportedin Table 3.1, nonlinear regression was made to the experimental data. The results



Fig. 3.17 Specific drying rate of duck egg yolk during foam-mat drying at temperature of 50 °C

presented in Table 3.9 are only of the model with statistically significant fitting(modified Page’s model).

The graphs showing the result predicted by the Modified Page’s model and theexperimental dimensionless content at 50, 60, and 70 °C are shown in Figs. 3.20,3.21, and 3.22, respectively.




3.4 Final Considerations

In this chapter, the physical problem of foam-mat drying has been addressed. Specialattention is given to egg white and yolk, which are protein-rich foods. Here, thetheoretical (via groupedmodels) and experimental (observed in experimental design)approaches are made with the aim of obtaining powder product.


Table 3.9 Statistic parameters of the modified Page’s model after fitting the experimental data forthe drying of the duck egg yolk at temperature of 50, 60, and 70 °C

Experiment Parameters

X0 (db) K (min−1) a (–) n (–) R2 (–) S (–)

1 0.8338 0.0026 0.9877 1.1945 0.9992 0.0041

2 1.1588 0.0042 1.0002 1.0556 0.9985 0.0061

3 0.8095 0.0027 0.9634 1.2139 0.9975 0.0131

4 0.8370 0.0013 0.9686 1.3740 0.9985 0.0078

5 0.8616 0.0040 0.9678 1.3419 0.9979 0.0086

6 1.1551 0.0072 0.9951 1.1194 0.9992 0.0024

7 0.7836 0.0061 0.9832 1.2222 0.9992 0.0036

8 0.8348 0.0036 0.9848 1.3750 0.9994 0.0027

9 1.0756 0.0047 0.9844 1.1253 0.9994 0.0023

10 0.9976 0.0042 0.9765 1.1962 0.9989 0.0044

11 1.0133 0.0081 0.9987 1.0961 0.9983 0.0063

Fig. 3.20 Comparison between predicted (modified Page’s model) and experimental results of themoisture content ratio during the foam-mat drying process of duck egg yolk at 50 °C

From the obtained results, it can be concluded that:

(a) For the duck egg white, the drying-air temperature, the stirring rate, and thestirring time influenced the final moisture content of the obtained powder. Forthe duck egg yolk, the drying-air temperature, Emustab® concentration and


stirring time influenced the final moisture content. Verifying that the higher thetemperature the shorter the drying time.

(b) The drying curves for both duck egg white and yolk showed approximatelyconstant and falling drying rate. The modified Page’s model was the empiricalmodel with best fit to the experimental data.

(c) Duck egg white foams dried at 50 and 70 °C were considered to be egg whitepowder only for a stirring time greater than 5 min (moisture content, X < 8%).For the duck egg yolk, yolk powder was obtained in all experimental conditions.

(d) The production of the duck egg powder obtained with the foam-mat dryingprocess proved to be a viable alternative. A batch averaged time at 3 h for theegg white and 5 h for the egg yolk were obtained.

Acknowledgments The authors are grateful for the financial support provided by CNPq, CAPES,and FINEP (Brazilian ResearchAgencies).We also acknowledge scientific support from the authorsmentioned in this chapter.

References

Arzhavitina, A., Steckel, H.: Foams for pharmaceutical and cosmetic application. Int. J. Pharm.394(1–2), 1–17 (2010)

Baniel, A., Fains, A., Popineau, Y.: Foaming properties of egg albumen with a bubbling apparatuscompared with whipping. J. Food Sci. 62(2), 377–381 (1997)

Biazus, J.P.M.: Optimization of zea mays malt drying. Food Sci. Technol. 26(4), 787–792 (2006)Brennan, J. G.: FoodDehydration: ADictionary andGuide, 189 p. Buttenvorth-Heinemann, Oxford(1994)

Broch, A., Jena, U., Hoekman, S.K., Langford, J.: Analysis of solid and aqueous phase productsfrom hydrothermal carbonization of whole and lipid-extracted algae. Energies 7(1), 62–79 (2014)

Brygidyr, A., Rzepecka, M., Mcconnell, M.: Characterization and drying of tomato paste foam byhot air and microwave energy. Can. Inst. Food Sci. Technol. J. 10(4), 313–319 (1977)

Carlesso, V.O., Berbert, P.A., Silva, R.F., Detmann, E.: Evaluation of thin mat drying models ofyellow passion fruit seeds. Braz. J. Seeds 29(2), 28–37 (2007)

Cornejo, F.E.P., Nogueira, R.I., Wilberg, V.C.: Drying as a method of preserving fruit. Riode Janeiro: Embrapa (2003). http://www.ctaa.embrapa.br/upload/publicacao/doc54-2003.pdf.Accessed October (2019)

Davis, J.P., Foegeding, E.A.: Comparisons of the foaming and interfacial properties of whey proteinisolate and egg white proteins. Colloids Surf., B 54(2), 200–210 (2007)

Dehghannya, J., Pourahmad, M., Ghanbarzadeh, B., Ghaffari, H.: Heat and mass transfer modelingduring foam-mat drying of lime juice as affected by different ovalbumin concentrations. J. FoodEng. 238(June), 164–177 (2018)

Dickinson, E.: Proteins at interfaces and in emulsions Stability, rheology and interactions. J. Chem.Soc. Faraday Trans. 94(12), 1657–1669 (1998)

Doymaz, I.: Drying behaviour of green beans. J. Food Eng. 69(2), 161–165 (2005)Falade, K.O., Solademi, O.J.: Modelling of air drying of fresh and blanched sweet potato slices.Int. J. Food Sci. Technol. 45(2), 278–288 (2010)

Fellows, P.: Food Processing Technology. Principles and Practice, 2 edn, p. 562. CRC Press, NewYork (2000)

http://www.ctaa.embrapa.br/upload/publicacao/doc54-2003.pdf


Fioreze, R.: Principles of Drying Biological Products, vol. 229. University Publisher/UFPB, JoãoPessoa (2004)

Francis, F.J.: Encyclopedia of Food Science and Technology, vol. 12907, 2nd edn.Wiley, NewYork(2000)

Franco, T.S.: Dehydration of yacon juice by the foam mat method. Doctoral Thesis in FoodEngineering. Federal University of Paraná, Curitiba, Brazil (2015). (In Portuguese)

Gava, A.J.: Food Technology: Principles and Applications. Nobel, São Paulo (2008)Gouveia, J.P.G., Moura, R.S.F., Almeida, F.A.C., Oliveira, A.M.V., Silva, M.M.: Evaluation ofcashew drying kinetics through experimental design. Braz. J. Agri. Environ. Eng. 6(3), 471–474(2002)

Hart, M.R., Graham, R.P., Ginnette, L.F., Morgan Jr., A.I.: Foam-mat drying requires stiff, stablefoams. Food Technol. 17(10), 90–92 (1963)

Kadam, D.M., Wilson, R.A., Kaur, S.: Determination of biochemical properties of foam-mat driedmango powder. Int. J. Food Sci. Technol. 45(8), 1626–1632 (2010)

Karim, A.A., Chee-Wai, C.: Characteristic of foam prepared from starfruit (Averrhoa carambolaL.) puree by using methyl cellulose. Food Hydrocolloids 13(2), 203–210 (1999)

Kinsella, J.: Functional properties of proteins: possible relationships between structure and functionin foams. Food Chem. 7, 273–288 (1981)

Liu, K., Johnson, L. A., Knapp, H.: Soybeans as Functional Foods and Ingredients. In: Soyfoods, L.,KeShun (eds.) Chapter 1: Soybeans as a Powerhouse of Nutrients and Phytochemicals, pp. 1958–2053. Champaign: AOCS Press (2004)

Liu, Q., Martins, M.D., Bakker-Arkema, F.W.: Stochastic modelling of grain drying: Part 1:experimental investigation. J. Agri. Eng. Res. 66(4), 267–273 (1997)

Lomakina, K., Mikova, K.: A study of the factors affecting the foaming properties of egg white—areview. Czech J. Food Sci. 24(3), 110–118 (2006)

Mangueira, E.R.: Study of duck egg (foammat drying).Master´s dissertation, in Chemical Engineer.Federal University of Paraiba, João Pessoa (2017). (In Portuguese)

Mapa, M.D.: Regulation of industrial and sanitary inspection of animal origin product (2005)Marques, G.M.R.: Drying of sugarcane juice in foam mat and sensory evaluation of the product.Dissertation (Master in Food Engineering)—State University of the Southwest of Bahia,Itapetinga, Brazil (2009). (In Portuguese)

Mayor, L., Sereno, A.M.:Modelling shrinkage during convective drying of foodmaterials: a review.J. Food Eng. 61(3), 373–386 (2004)

Meloni, P.L.S.: Dehydration of Fruits and Vegetables. Frutal Institute (2003). http://www.eteavare.com.br/arquivos/20_1959.pdf. Accessed October (2019)

Meloni, P.L.S.: Dehydration of Fruits and Vegetables, p. 87. Frutal Institute, Fortaleza (2003)Midilli, A., Kucuk, H., Yapar, Z.A.: New model for single-layer drying. Dry. Technol. 20(7), 1503–1513 (2002)

Mounir, S.: Foam Mat Drying. In: Prabhat, K., Nema, B.P.K., Mujumdar, A.S. (eds.) DryingTechnologies for Foods-Fundamentals and Applications. CRC Press, New York (2017)

Muthukumaran, A., Ratti, C.; Raghavan, V.G.S.: Foam-mat freeze drying of egg white and mathe-matical modeling. Part I: optimization of egg white foam stability. Dry. Technol. 26(4), 508–512(2008)

Narchi, I., Vial, C., Djelveh, G.: Effect of protein–polysaccharide mixtures on the continuousmanufacturing of foamed food products. Food Hydrocolloids 23, 188–201 (2009)

Negreiros, J.K.S.: Study of the kinetics of drying of egg in a foam mat (foam-mat drying) and thecharacterization of the obtained product. 63 p. Final course report (Undergraduate in ChemicalEngineering), Federal University of Paraíba, João Pessoa, Brazil (2016). (In Portuguese)

Nishinari, K., Fang, Y., Guo, S., Phillips, G.O.: Soy proteins: a review on composition, aggregationand emulsification. Food Hydrocolloids 39, 301–318 (2014)

Ordonéz, J.A.: Food Technology, vol. I. Artmed, Porto Alegre (2005)Park, K.J., Yado, M.K.M., Brod, F.P.R.: Drying study of sliced Bartlett pear (Pyrus sp.). Food Sci.Technol. 21(3), 288–292 (2001)

http://www.eteavare.com.br/arquivos/20_1959.pdf


Park, S.K., Shanbhag, S.R., Dubin, A.E., DeBruyne,M.,Wang,Q., Yu, P., Shimoni, N., D’Mello, S.,Carlson, J.R., Harris, G.L., Steinbrecht, R.A., Pikielny, C.W.: Inactivation of olfactory sensillaof a single morphological type differentially affects the response of Drosophila to odors. J.Neurobiology. 51(3), 248–260 (2002)

Park, K.J., Antonio, G.C., Oliveira, R.A., Park, K.J.B.: Process concepts and drying equip-ment. Campinas, 121 p. (2007). http://www.feagri.unicamp.br/ctea/manuais/concproceqsec_07.pdf. Accessed October (2007). (In Portuguese)

Pereira, T.S.: Foam-mat drying study ofwhite egg.Master´s dissertation inAgri-industrials Systems,Federal University of Campina Grande, Pombal, Brazil (2015). (In Portuguese)

Prins, A.: Principles of foam stability. In: Dickinson, E., Stainsby, G. (eds.) Advances in FoodEmulsions and Foams, pp. 91–122. Elsevier, London (1988)

Rajkumar, P., Kailappan, R., Viswanathan, R., Raghavan, G.S.V., Ratti, C.: Foam mat drying ofalphonso mango pulp. Dry. Technol. 25(2), 357–365 (2007a)

Rajkumar, P., Kailappan, R., Viswanathan, R., Raghavan, G.S.V.: Drying characteristics of foamedalphonso mango pulp in a continuous type foam mat dryer. J. Food Eng. 79, 1452–1459 (2007b)

Sagar, V.R., Kumar, S.P.: Recent advances in drying and dehydration of fruits and vegetables: areview. J. Food Sci. Technol. 47(1), 15–26 (2010)

Sangamithra, A., Venkatachalam, S., John, S.G., Kuppuswamy, K.: Foam mat drying of food mate-rials: a review. J. Food Process. Preserv. 39(6), 3165–3174 (2015).https://doi.org/10.1111/jfpp.12421

Sousa, C.C.: Definition of parameters for foam-mat drying of anas platyrhynchos domesticus eggwhite and yolk. João Pessoa, 54 p. Final course report (Undergraduate in Chemical Engineering),Federal University of Paraíba, João Pessoa, Brazil (2017). (In Portuguese)

Strumillo, C., Kudra, T.: Drying: Principles. Applications and Design. Gordon and Breach SciencePublishers, New York (1986)

Tariq, M.R., Sameen, A., Khan, M.I., Huma, N., Yasmin, A.: Nutritional and therapeutic propertiesof whey. Ann. Food Sci. Technol. 14(1), 19–26 (2003)

Townsend, A.A., Nakai, S.: Relationships between hydrophobicity and foaming characteristics offood proteins. J. Food Sci. 48(2), 588–594 (1983)

Vega-Mercado, H., Gongora-Nieto, M.M., Barbosa-Canovas, G.V.: Advances in dehydration offoods. J. Food Eng. 49(4), 271–289 (2001)

Vernon-Carter, E.J., Espinosa-Paredes, G., Beristain, C.I., Romero-Tehuitzil, H.: Effect of foamingagents on the stability, rheological properties, drying kinetics and flavour retention of tamarindfoam-mats. Food Res. Int. 34(4), 587–598 (2001)

Zayas, J.F.: Functionality of Proteins in Food. Chapter 5: Foaming Properties of Proteins, pp. 122–134. Springer, Heidelberg (1997)

Zhang, Q., Litchfield, J.B.: An optimization of intermittent corn drying in a laboratory scale thinlayer dryer. Dry. Technol. 9, 383–395 (1991)

Zhang, M., Bhandari, B., Fang, Z.: Handbook of Drying of Vegetables and Vegetable Products.CRC Press, Boca Raton (2017)

http://www.feagri.unicamp.br/ctea/manuais/concproceqsec_07.pdf

https://doi.org/10.1111/jfpp.12421

Chapter 4Drying Process of Jackfruit Seeds

T. M. Q. de Oliveira, R. A. de Medeiros, V. S. O. Farias, W. P. da Silva,C. M. R. Franco, and A. F. da Silva Júnior

Abstract This chapter presents the application of an analytical solution for thediffusion equation in cylindrical coordinates, considering a boundary condition ofthe third kind. This diffusive model was used to verify the influence of the presenceof the seed coat in jackfruit seeds on the mass transfer at the product surface and onthe drying time. For this, jackfruit seeds were dried with and without the seed coat at60 and 70 °C. In order to obtain the optimal values of effective mass diffusivity andBiot number, the analytical solution was coupled to an optimizer developed froman inverse method. A program was developed in Fortran language to execute theoptimizer coupled to the analytical solution. The results showed that the seed coathad a strong influence on the drying time and on the Biot number, indicating that theboundary condition of the third kind is the most suitable for the drying simulationof this type of product.

T. M. Q. de Oliveira · R. A. de MedeirosPostgraduate Program in Natural Sciences and Biotechnology, Federal University of CampinaGrande, Olho D’Água da Bica, S/N, Cuité, PB 58175-000, Brazile-mail: [email protected]

R. A. de Medeirose-mail: [email protected]

V. S. O. Farias · C. M. R. Franco · A. F. da Silva Júnior (B)Physics and Mathematics Department, Federal University of Campina Grande, Olho D’Água daBica S/N, Cuité, PB 58175-000, Brazile-mail: [email protected]

V. S. O. Fariase-mail: [email protected]

C. M. R. Francoe-mail: [email protected]

W. P. da SilvaPhysics Department, Federal University of Campina Grande, Av. Aprígio Veloso 882 Bodocongó,Campina Grande, PB 58429-900, Brazile-mail: [email protected]; [email protected]


89









https://doi.org/10.1007/978-3-030-47856-8_4

90 T. M. Q. de Oliveira et al.

Keywords Diffusion equation · Analytical solution · Mass transfer · Seed coat ·Optimization

4.1 Introduction

Jackfruit (Artocarpus heterophyllus Lam.) is a species widely cultivated in the Asiancontinent and in tropical climate areas, including Brazil. Its fruits reach an averageof 3.5 kg to a maximum of 25 kg and are composed of arils with yellowish and sweetpulp and brown seeds wrapped in a hard shell (Swami et al. 2012).

Jackfruit pulp has high nutritional value and is rich in sugars, mainly sucrose,fructose, and glucose, as well as minerals, dietary fiber, carboxylic acids, andvitamins. Due to the great versatility of its use as food, it can be eaten fresh orprocessed by adding sugar or another component into products such as jams andcakes (Anaya-Esparza et al. 2018).

Another very important component is the seeds, which represent about 10–15%of the total weight of the fruit and stand out for having high amounts of protein,fiber, minerals, and fatty acids (Pacheco et al. 2015; Tulyathan et al. 2002). Its greattechnological value directly influences its economic potential, which is linked tothe wide possibility of use in biotechnology, especially as a food source. It can beeaten cooked, candied, in flour form, and used as preparation and/or meal enrichmentingredients or as a substitute for peoplewith dietary restrictions (Anaya-Esparza et al.2018).

The seed when kept fresh has favorable conditions for rapid deterioration, causingloss and damage. Therefore, the drying of these seeds to obtain the flour has beenwidely used as an alternative to increase the useful life and expansion of technologicalapplications, especially in the food industry. Due to its nutritional content consistingof 78% carbohydrates, 11.2% protein, and 0.99% lipids, it is being implemented asan enrichment strategy in the development of cappuccinos, breads, and meatballs(Tulyathan et al. 2002; Landim et al. 2015; Santos 2012; Spada et al. 2018).

Although drying is one of the most commonly used preservation techniques, it isknown that its use requires a large expenditure of energy, in addition to modifyingthe nutritional and sensory properties of the product, resulting in financial losses forindustries. With a view to reducing costs and obtaining a good quality product, thedescription of drying kinetics through mathematical simulation is a strategy that canbe used to predict variables such as time, temperature, and dryer types best suitedfor use in the processing of the studied product (Gan and Poh 2014).

In addition to the variables often studied in the drying process such as temperature,pressure, and air velocity, product constituents such as shells can influence importantprocess parameters. However, most studies available in the literature do not analyzethe influence of such elements on the thermo-physical parameters of drying.

Doymaz and Pala (Doymaz and Pala 2003) performed the drying of corn grainswith and without ethyl oleate pretreatment at 55, 65, and 75 °C. One of the modelsused to predict drying kinetics and to determine effective water diffusivity was a

4 Drying Process of Jackfruit Seeds 91

simplification of the solution of the diffusion equation in spherical coordinates (onlythe first term was considered). In addition, a boundary condition of the first kindwas imposed. Although these simplified models fit the experimental data well, theinfluence of product constituents (such as the seed coat) on the surface resistanceto mass transfer should be evaluated. However, this is only possible by assuming aboundary condition of the third kind.

A similar study was performed by Leite et al. (Leite et al. 2019) with germinatedseeds of jackfruit. In this research, germinated seeds of jackfruit were dried at 55,65, and 75 °C with air velocities of 1.0 and 1.3 m s−1. For the description of dryingkinetics, 12 empirical models were tested. To determine the effective diffusivity ofwater, the same simplification of the diffusive model used by Doymaz and Pala(Doymaz and Pala 2003) was adopted. Since the boundary condition was again ofthe first kind, it was not possible to evaluate the influence of the seed coat on masstransfer at the product surface.

In order to analyze the effect of seed coat presence on the drying process param-eters, four treatments were carried out (drying at 60 and 70 °C of seeds with andwithout seed coat). An analytical solution for the diffusion equation in cylindricalcoordinates for the two-dimensional case, assuming a boundary condition of the thirdkind, was considered to describe the processes.

4.2 Methodology

4.2.1 Experiments

The study was carried out using “soft” and “hard” jackfruit varieties obtained atthe local market of the city of Cuité, Paraiba, Brazil, pre-selected according tophysiological integrity and absence of mechanical damage to the fruit.

The technological processes of the experiment were carried out at the Food Tech-nology Laboratory of the Federal University of Campina Grande—UFCG, Campusof Cuité, Brazil. The seeds used in the drying process were obtained through fruitdisinfection, pulping, characterized by pulp and seed separation, and washing of theseed in drinking water. In addition, to remove the shell (seed coat), the jackfruit seedswere immersed in boiling water for about 1 min to facilitate the process. Then theseseeds were placed on a stainless steel sieve to remove surface water, and the shellswere removed with the help of a knife, as shown in Fig. 4.1. Immediately after, theseeds with and without seed coat were placed separately in a sealed plastic containerand subjected to the drying process.

An oven previously stabilized at 60 and 70 °C was used for drying. The sampleswere divided into four treatments reproduced in triplicate: T1—Jackfruit seeds withseed coat submitted to 60 °C, T2—Jackfruit seeds without seed coat submitted to60 °C, T3—Jackfruit seeds with seed coat submitted to 70 °C, and T4—Jackfruitseeds without seed coat submitted to 70 °C. In each treatment, the samples were


Fig. 4.1 Seed shell removalwith a stainless steel knife

Fig. 4.2 Jackfruit seedswithout the seed coatarranged in baskets for thedrying process

placed in basketswithmass previouslymeasured on a semi-analytical scale, as shownin Fig. 4.2. The masses of the samples were measured before drying began (time t= 0), and then at intervals of 2, 5, 10, 20, and 30 min and 1 hour (h), 2 h, and 3 huntil they reached equilibrium. Then, the samples were dried in an oven previouslystabilized at 105 °C for 24 h to obtain the dry mass. The moisture content of thesamples ranged from 1.069 to 1.321 (dry basis, d.b.) for the seeds with seed coat andfrom 0.977 to 1.35 (d.b.) for the seeds without seed coat.

4.2.2 Mathematical Modeling

In the present study, the liquid diffusion model for water migration in a product withfinite cylinder geometry was considered adequate to describe thin-layer drying ofjackfruit seed. This is a widely accepted model in the literature (Pacheco-Aguirreet al. 2014; Silva Júnior et al. 2018; Arunsandeep and Chandramohan 2018; Chayjanand Kaveh 2014). In addition, as the objective of this study was to analyze theinfluence of the presence of the seed coat on the mass transfer at the product surface,a boundary condition of the third kind was assumed.


4.2.2.1 The Model

The analytical solution of the diffusion equation will be presented for the finitecylinder, where the diffusive process is subject to the following hypotheses: (1)the cylinder must be considered homogeneous and isotropic; (2) the distributionof moisture content within the cylinder must have radial symmetry and must beinitially uniform; (3) the conditions of the dryingmedium remain the same throughoutthe process; (4) the only water transport mechanism inside the cylinder is liquiddiffusion; (5) dimensions of the cylinder do not vary during diffusion; (6) the effectivediffusivity does not vary during the process; and (7) the boundary condition is of thethird kind.

For the previously established hypotheses, the diffusion equation has analyticalsolution for several simple geometries, among which is the finite cylinder geometry.It is noteworthy that a finite cylinder can be obtained by intersecting two even simplersolids: the infinite cylinder and the infinite wall, as shown in Fig. 4.3a.

In order to present the analytical solution of the diffusion equation for the geometryof a finite cylinder of radius R and length L, such geometry is outlined as shown inFig. 4.3b.

The three-dimensional diffusion equation in cylindrical coordinates (r, y, ) is givenby:

∂X

∂t= 1

r

∂

∂r

(r D

∂X

∂r

)+ 1

r2∂

∂θ

(D

∂X

∂θ

)+ ∂

∂y

(D

∂X

∂y

)(4.1a)

For a symmetrical diffusion with respect to the r- and y-axes, only the radialand axial flows were considered and, therefore, the flow in the angular direction wasneglected. Thus, for the cylindrical geometry shown inFig. 4.3b, the two-dimensionaldiffusion equation can be written as follows:

(a) (b)

Fig. 4.3 a Intersection of an infinite cylinder and an infinite wall; b Finite cylinder of radius R andlength L


∂X

∂t= 1

r

∂

∂r

(r D

∂X

∂r

)+ ∂

∂y

(D

∂X

∂y

)(4.1b)

In Eq. (4.1b), r is defined relative to the central axis of the cylinder and, togetherwith the y-coordinate, defines the position of a point (r, y) within the solid to bestudied. Also, in this equation, D is the effective mass diffusivity, X is the moisturecontent on dry basis, and t is the time.

The boundary condition is of the third kind, which is expressed by imposingequality between the internal (diffusive) flow on the surface of the finite cylinder andthe external (convective) flow in the vicinity of this surface:

−D∂X (r, y, t)

∂r

∣∣r=R = h

[X (r, y, t)

∣∣r=R − Xeq

](4.2)

and

−D∂X (r, y, t)

∂y

∣∣y=±L/2 = h

[X (r, y, t)

∣∣y=±L/2 − Xeq

](4.3)

4.2.2.2 Exact Solution

For a homogeneous and isotropic cylinder of radius R and length L with uniformlydistributed initial moisture content Xi and equilibrium moisture content Xeq, thesolution X(r, y, t) of Eq. (4.1b) for the boundary conditions defined by Eqs. (4.2) and(4.3) can be obtained by separating the variables (Luikov 1968; Crank 1975) andresults in:

X (r, y, t) = Xeq + (Xi − Xeq)

∞∑n=1

∞∑m=1

An,1Am,2 J0(μn,1

r

R

)cos

(μm,2

y

L/2

)

× exp

[−

(μ2n,1

R2+ μ2

m,2

(L/2)2

)Dt

](4.4)

As mentioned earlier, this solution considers the idea that a finite cylinder can beobtained by intersecting two even simpler solids: an infinite cylinder of radius R andan infinite wall of thickness L.

Returning to Eq. (4.4), it should be noted that X(r, y, t) is the moisture content ondry basis at a cylinder position (r, y) at time t, and D is the effective mass diffusivity.Also, with respect to Eq. (4.4), the coefficients An,1 and Am,2 are defined as follows:

An,1 = 2Bi1J0(μn,1)(Bi21 + μ2

n,1)(4.5)


and

Am,2 = (−1)m+1 2Bi2(Bi22 + μ2m,2)

1/2

μm,2(Bi22 + Bi2 + μ2m,2)

(4.6)

In Eqs. (4.5) and (4.6), variables referring to the terms of the second member willbe defined later. On the other hand, the expression for the average moisture contentat time t is given as follows:

X(t) = 1

V

∫X (r, y, t)dV (4.7)

The solution of the diffusion equation for the mean value in a finite cylinder attime t is obtained by substituting Eq. (4.4) in Eq. (4.7), which results in:

X(t) = Xeq + (Xi − Xeq)

∞∑n=1

∞∑m=1

Bn,1Bm,2 exp

[−

(μ2n,1

R2+ μ2

m,2

(L/2)2

)Dt

](4.8)

where X(t) is the average moisture content on dry basis at time t.The coefficient Bn,1 is defined as follows:

Bn,1 = 4Bi21μ2n,1(Bi

21 + μ2

n,1)(4.9)

where Bi1 is the Biot number for the infinite cylinder and is given by

Bi1 = hR

D(4.10)

The coefficient Bm,2 is defined as follows:

Bm,2 = 2Bi22μ2m,2(Bi

22 + Bi2 + μ2

m,2)(4.11)

and in this expression Bi2 is the Biot number referring to the infinite wall, given bythe expression

Bi2 = h(L/2)

D(4.12)

In Eqs. (4.2), (4.3), (4.10), and (4.12), h is the convectivemass transfer coefficient,and, in the presented solution, the same value of hwas imposed to all external surfacesof the cylinder.


In Eqs. (4.5), (4.8), and (4.9), μn,1 are the roots of the characteristic equation forthe infinite cylinder and are calculated by the following transcendental equation:

J0(μn,1)

J1(μn,1)= μn,1

Bi1(4.13)

where J0 and J1 are Bessel functions of the first-order type 0 and 1, respectively.In Eqs. (4.6), (4.8), and (4.11), μm,2 are the roots of the characteristic equation

for the infinite wall and are calculated by the following transcendental equation:

cot μm,2 = μm,2

Bi2(4.14)

From the foregoing, Eqs. (4.4) and (4.8) can be used to determine X(r, y, t) andX(t) for any Biot numbers of interest. In the present study, aiming at the compu-tational implementation of Eq. (4.8), the first 20 roots of Eqs. (4.13) and (4.14)were calculated. The choice of this number of roots is based on the study by Silvaet al. (2012), which points out the relationship between the number of terms in theseries (Eq. 4.8) and the Biot number. Note that for each term in this series, a rootfor transcendental Eqs. (4.13) and (4.14) is required. A detailed description of theobtaining of these roots will be presented in the section related to computational codedevelopment.

It is worth noting that the Biot number is a widely used parameter in the literatureto determine if the internal resistance to mass flow is relevant (Incropera et al. 2012).Such resistance may be considered negligible if Bi < 0.1. In this case, the moisturedistribution inside the product becomes uniform during the process.

Equation (4.8) can be rearranged to express the moisture ratio, which is definedas follows:

X∗ = X(t) − Xeq

Xi − Xeq(4.15)

In this study, the experimental data obtained for drying kinetics were used in thedimensionless form using Eq. (4.15).

4.2.2.3 Optimization Procedure

A program in the Fortran language was developed on the Windows platform. Equa-tion (4.8), which presents the average moisture content for any time instant, wasimplemented in this program. However, to obtain the average moisture contentthrough Eq. (4.8), it is necessary to find the roots of the transcendental equations,which in turn depend on Bessel functions and Biot numbers.

The input data of the computational code are the experimental data, initialmoisturecontent, equilibriummoisture content, and the length and radius of the cylinder. Once


input data are provided, the developedoptimizer begins the process of determining theBiot numbers Bi1 and Bi2 for the infinite cylinder and the infinite wall, respectively,and the effective water diffusivity.

For each value of the Biot numbers supplied by the optimizer, it is necessary tocalculate the roots μn,1 and μm,2. For the calculation of μn,1, the code proceeds asfollows: the Bessel functions of order 0 and 1 are calculated for each n, considering80 terms of the factorial in the expression. Then their values are replaced in thetranscendental equation and, after that, the Secant method with an accuracy of 10−12

is used to calculate these roots. Thus, the value ofμn,1 is obtained and, consequently,by Eq. (4.13), the value of Bi1 is obtained for each n.

For the calculation of μm,2, the Newton Method with an accuracy of 10−16 isapplied to Eq. (4.14). Thus, for each m, the respective value of μm,2 is obtained.

The optimizer used in the present work was developed in order to obtain theoptimal values of parametersD, Bi1, and Bi2. This optimizer was developed throughan inverse method, which initially requires the user to provide initial values for thethree parameters. These values are then corrected to minimize an objective function,which in this case is chi-square, defined as:

χ2 =Np∑i=1

[X expi − X sim

i (D,Bi1,Bi2)]2 1

σ 2i

, (4.16)

where X expi is the i-th experimental point; X sim

i (D,Bi1,Bi2) is the average value ofX obtained by the analytical solution at the same time as X exp

i ; σi is the standarddeviation of the experimental average moisture content at point i ; D is the effectivemass diffusivity; and Np is the number of experimental points. In the present work,all σi were considered equal to 1.

Once all the necessary elements for the determination of the value of χ2 areobtained, the next step is to adjust the initial values of the parameters Bi1, Bi2, andD, by minimizing the chi-square. For this, the optimizer follows the following steps:

First, with the initial user-supplied parameter data, the optimizer calculates thefirst value for chi-square.

Second, the optimizer starts looking for ranges where the optimal values for theparameters Bi1, Bi2, and D are found. Initially, with the Bi2 and D parameter valuesfixed, the algorithm corrects the initial Bi1 parameter value by adding 0.1% to thecurrent value (if the optimal value is higher) or subtracting 0.1% from the currentvalue (if the optimal value is lower). At each correction of parameter Bi1, a new valuefor χ2 is calculated and compared with the previous one. This process is repeateduntil the χ2 value is higher than the previous one. Finally, it is considered that theoptimal value of Bi1 is within the interval

[Bik−1

1 ,Bik1], where the indices k and k −

1 represent the iterations where the chi-square increases and the previous iteration,respectively.

Third, once the range containing the optimal value for the parameter is found, themidpoint is calculated, which will divide the range into two new ranges. Then, thechi-square at the midpoints of the two new intervals obtained is calculated, and the


choice of the best midpoint is made by decreasing the chi-square. This process isrepeated until the chi-square can no longer be minimized.

In each iteration, the second and third steps should be applied to each parameter.At the end of each iteration, the optimizer checks the relative error of each parameter.The optimization process is terminated when the relative error of each parameter isless than 10−16. This error is calculated by the following formula:

Erel =∣∣Pcurrent − Pprevious

∣∣Pprevious

, (4.17)

where Erel denotes the relative error, Pcurrent is the parameter value in the currentiteration, and Pprevious is the parameter value in the previous iteration.

In the optimizations performed, no significant differences were observed betweenBi1 and Bi2. Thus, the values of these parameters were considered equal to a singlevalue Bi.

4.3 Results Analysis

The physical parameter optimization processes were performed using the analyt-ical solution presented in Sect. 4.2. The results of these processes are presented inTable 4.1.

It is possible to notice the influence of the presence of the seed coat also on thedrying time by observing the graphs shown in Fig. 4.4. From the observed dryingtimes, it can be concluded that the drying of the samples with the presence of seedcoat at temperatures of 60 and 70 °C lasted about 66% longer than the drying of thesamples without seed coat. Thus, the energetic cost for seed processing with seedcoat is high, being justified only if these seeds have relevant nutritional indicators.

Figure 4.5 shows the drying kinetics for the four treatments performed.By analyzing the kinetics for seed with seed coat, one can observe the influence

of temperature. On the other hand, this influence is not observed on the kinetics forseeds without seed coat. However, further studies are necessary considering other

Table 4.1 Values obtained for the parameters of the drying process of jackfruit seeds with andwithout the presence of the seed coat

Temperature/Presence ofseed coat

Dw (m2 m−1) h (m m−1) Bi R2 χ2

60 °C/present 6.46 × 10−7 6.21 × 10−6 8.84 × 10−2 0.991 3.64 × 10−2

60 °C/absent 6.21 × 10−8 1.32 × 10−4 19.01 0.998 4.15 × 10−3

70 °C/present 7.99 × 10−7 7.99 × 10−6 9.19 × 10−2 0.998 6.92 × 10−3

70 °C/absent 6.43 × 10−8 1.28 × 10−4 18.85 0.999 2.04 × 10−3


(a) (b)

(c) (d)

Fig. 4.4 Fits obtained for samples with seed coat at temperatures of a 60 °C and b 70 °C and forsamples without seed coat at temperatures of c 60 °C and d 70 °C

Fig. 4.5 Simulation ofdrying kinetics for the fourtreatments

temperatures in order to analyze whether this influence is dominated by the presenceof the seed coat.

Figure 4.6 presents simulations of the moisture distribution inside the seeds forthe four treatments.

As can be seen, the simulations presented in Fig. 4.6 correspond to the half of thecylinder that represents the seeds. It is also possible to notice a very small moisturegradient. This phenomenon may be related to the high resistance observed through


(a) (b) (c)

Fig. 4.6 Simulation of moisture distribution for treatment at 60 °C with seed coat at times: a t =30.72 min, b t = 120 min, and c 330.20 min

the Biot number presented in Table 4.1. This resistance causes a kind of “brake” tothe water flow, resulting in the uniformity of moisture inside the product.

By comparing Figs. 4.6 and 4.7, it can be observed that the seed coat is whatdetermines the existence of moisture gradients inside the product, since the gradients(which were small in Fig. 4.6) increase in Fig. 4.7. This phenomenon can also beobserved when comparing the simulations for 70 °C, presented in Figs. 4.8 and 4.9.

By comparing the simulations of 60 and 70 °C, one can note an influence oftemperature on the distribution of moisture inside the product. Moreover, in simu-lations for the time near 120 min, gradient is observed only in the drying at 60 °C.In the simulation for drying at 70 °C, a uniform distribution of moisture inside theproduct is noted.

The influence of the seed coat on the moisture distribution inside the productobserved in the simulations for drying at 60 °C is also seen in Figs. 4.8 and 4.9.Moreover, when comparing the simulations for drying at 60 and 70 °C of the samples

(a) (b) (c)

Fig. 4.7 Simulation of moisture distribution for treatment at 60 °C without seed coat at times: a t =30.36 min, b t = 120.1 min, and c 330 min


(a) (b) (c)

Fig. 4.8 Simulation of moisture distribution for treatment at 70 °C with seed coat at times: a t =30.40 min, b t = 120.70 min, and c 330.60 min

(a) (b) (c)

Fig. 4.9 Simulation of moisture distribution for treatment at 70 °C without seed coat at times: a t =30.24 min, b t = 120.20 min, and c 330.50 min

without seed coat, there are slight differences between themoisture distributions. Thiscan also be observed through the kinetics presented in Fig. 4.5.


In this chapter, the effect of the presence of the seed coat in jackfruit seeds on theprocess parameters was studied. It was concluded that the presence of this elementcontributed to the increase in drying time and influenced the resistance of the productsurface tomass transfer. Theproposedmodel adequately described the dryingkineticsof seeds with and without seed coat. Moreover, from the values obtained for the Biotnumber, the most appropriate boundary condition for describing the drying of this


type of seed is that of the third kind. Finally, the methodology used in this chaptercan be applied to describe the drying of other seeds in order to verify the influenceof their seed coat on the process parameters.

Acknowledgments Prof. Wilton would like to thank CNPq (Conselho Nacional de Desen-volvimento Científico e Tecnológico) for his research grant (Process Number 301708/2019-3;PQ-1A).

References

Anaya-Esparza, L.M., González-Aguilar, G.A., Domínguez-Ávila, J.A., Olmos-Cornejo, J.E.,Pérez-Larios, A.,Montalvo-González, E.: Effects ofminimal processing technologies on jackfruit(Artocarpus heterophyllus Lam.) Qual. Paramet. Food Biopro. Technol. 11, 1761–1774 (2018)

Arunsandeep, G., Chandramohan, V.P.: Numerical solution for determining the temperature andmoisture distributions of rectangular, cylindrical, and spherical objects during drying. J. Eng.Phys. Thermophys. 91(4), 895–906 (2018)

Chayjan, R.A., Kaveh, M.: Physical parameters and kinetic modeling of fix and fluid bed drying ofterebinth seeds. J. Food Process. Preserv. 38, 1307–1320 (2014)

Crank, J.: The Mathematics of Diffusion, 414 p. Clarendon Press, Oxford, UK (1975)Doymaz, I., Pala, M.: The thin-layer drying characteristics of corn. J. Food Eng. 60, 125–130 (2003)Gan, P.L., Poh, P.E.: Investigation on the effect of shapes on the drying kinetics and sensoryevaluation study of dried jackfruit. Int. J. Sci. Eng. 7, 193–198 (2014)

Incropera, F.P.,DeWitt,D.P., Bergman,T.L., Lavine,A.S.: Fundamentals ofHeat andMassTransfer.LTC, Rio de Janeiro (2012). (In Portuguese)

Landim, L.B., Bonomo, R.C.F., Reis, R.C., Silva, N.M.C., Veloso, C.M., Fontan, R.C.I.: Kibbehformulation with jackfruit flour. J. Health Sci. 14, 87–93 (2015). (In Portuguese)

Leite, D.D.F., Queiroz, A.J.M., Figueirêdo, R.M.F., Lima, L.S.L.: Mathematical drying kineticsmodeling of jackfruit seeds (Artocarpus heterophyllus Lam.), vol. 50, pp. 361–369. AgronomicScience Magazine (2019). In Portuguese

Luikov, A.V.: Analytical Heat Diffusion Theory, 685 p. Academic Press, Inc. Ltd, London (1968)Pacheco, C.S.V., Ferreira, A.N., Rocha, T.J.O., Tavares, I.M.C., Franco, M.: Use of the jackfruitseed for obtaining endoglucanase from aspergillus niger by solid state fermentation. J. HealthSci. 14, 25–29 (2015). (In Portuguese)

Pacheco-Aguirre, F.M., Ladrón-González, A., Ruiz-Espinosa, H., García-Alvarado, M.A., Ruiz-López, I.I.: A method to estimate anisotropic diffusion coefficients for cylindrical solids:application to the drying of carrot. J. Food Eng. 125, 24–33 (2014)

Santos, D. B. French bread development with the addition of jackfruit flour (Artocarpos integrifóliaL.). Biosph. Encycl. 8, 597–602 (2012). (In Portuguese)

Silva Júnior, A.F., Silva, W.P., Farias, V.S.O., Silva, C.M.D.P.S., Lima, A.G.B.: Description ofosmotic dehydration of banana slices dipped in solution of water and sucrose followed bycomplementary drying using hot air. In: Transport Phenomena inMultiphase Systems: AdvancedStructured Materials, 1 edn, pp. 273–304. Springer International Publishing (2018)

Silva, W.P., Farias, V.S.O., Neves, G.A., Lima, A.G.B.: Modeling of water transport in roof tiles byremoval of moisture at isothermal conditions. Heat Mass Transf. 48, 809–821 (2012)

Spada, F.P., Silva, P.P.M., Mandro, G.F., Margiotta, G.B., Spoto, M.H.F., Canniatti-Brazaca,S.G.: Physicochemical characteristics and high sensory acceptability in cappuccinos made withjackfruit seeds replacing cocoa powder. PLoS One 13, 1–12 (2018)


Swami, S.B., Thakor, N.J., Haldankar, P.M., Kalse, S.B.: Jackfruit and its many functional compo-nents as related to human health: a review. Compr. Rev. Food Sci. Food Saf. 11, 565–576(2012)

Tulyathan, V., Tananuwong, K., Songjinda, P., Jaiboon, N.: Some physicochemical properties ofjackfruit (Artocarpus heterophyllus Lam) seed flour and starch. Sci. Asia 28, 37–41 (2002)

Chapter 5Spouted Bed Drying of Fruit Pulps:A Case Study on Drying of Graviola(Annona muricata) Pulp

F. G. M. de Medeiros, I. P. Machado, T. N. P. Dantas, S. C. M. Dantas,O. L. S. de Alsina, and M. F. D. de Medeiros

Abstract The spouted bed dryer with inert particles has been researched as an alter-native for the drying fruit pulps in order to obtain powdered products. Depending onthe composition and physical properties of the pulps, the dryer is subject to agglom-eration and accumulation problems that can be minimized by the addition of dryingadjuvants, especially carbohydrates, such as maltodextrin; sources of proteins, suchas whey protein andmilk itself. In this work, the advantages of the spouted bed dryer,regarding its mixing capacity, temperature uniformity, high heat and mass transferrates, and reduced processing time are emphasized. A review of the fundamentals ofthe spouted bed is presented in this chapter, as well as the relevant and recent worksrelated to drying fruit pulps in the spouted bed, addressing the use of adjuvants and theimpact of the process on phytochemicals present in fruits and other vegetables. Thechapter is concluded with the presentation of a case study on the drying of graviolafruit pulp with the addition of milk in the spouted bed dryer, where the results related

F. G. M. de Medeiros (B) · I. P. Machado · S. C. M. Dantas · M. F. D. de Medeiros (B)Department of Chemical Engineering, Federal University of Rio Grande do Norte, Av. SenadorSalgado Filho, 3000, Natal, RN 59078-970, Brazile-mail: [email protected]

M. F. D. de Medeirose-mail: [email protected]; [email protected]

I. P. Machadoe-mail: [email protected]

S. C. M. Dantase-mail: [email protected]

T. N. P. DantasFederal Institute of Education, Science and Technology of Rio Grande do Norte, Campus CurraisNovos, R. Manoel Lopes Filho, 773, Currais Novos, RN 59380-000, Brazile-mail: [email protected]

O. L. S. de AlsinaDepartment of Chemical Engineering (retired), Federal University of Campina Grande, R.Aprigio Veloso, 743, Campina Grande, PB 58429-140, Brazile-mail: [email protected]


105









https://doi.org/10.1007/978-3-030-47856-8_5

106 F. G. M. de Medeiros et al.

to production, thermal efficiency, product characteristics, and process modeling arepresented with intermittent pulp feeding.

Keywords Spouted bed dryer · Graviola pulp · Phytochemicals · Process modeling

5.1 Introduction

Brazil is the third-largest fruit producer in the world and ranks among the leadingexporters of several tropical such as pineapple, papaya, mango, oranges, melons,and others (Altendorf 2017). However, due to the perishable condition of fruits, thedevelopment of efficient post-harvest processing strategies is a major concern of thefood industry, in order to avoid food waste. According to FAO (FAO 2019), 20–30%of world’s fruits and vegetables’ production goes to waste between the post-harvestand retail levels.

For many years, drying has been regarded as an efficient conservation method anda versatile post-harvest processing alternative for fruits and other highly perishablematerials (Zhang et al. 2020; Souza da Silva et al. 2019). The lowering of mois-ture content on dried fruit is a key parameter for extending products’ shelf life andmaintaining a stable fruit products’ supply chain, since low water activity on driedproducts is related to reducedmicroorganism growth and delayed enzymatic process,which leads to higher storage stability (Rocha et al. 2011; Karam et al. 2016).

The growingmarket demand for natural-based products has been pushing the foodindustry toward innovative product-oriented technologies in order to take full advan-tage of the dietary and phytochemical values of fruits (Belwal et al. 2018; Demirkoland Tarakci 2018). In this sense, the versatility of dehydration as a processing tech-nique is highlighted on a new product-development point of view. From ready-to-eatand ready-to-drink products (Dantas et al. 2019; Cappato et al. 2018) to food ingredi-ents (Correia et al. 2017;Moraes et al. 2017), dried fruit products have been attractingattention and space on the food industry.

The choice of drying method is, therefore, of utmost importance, since the impactof the heat and mass transfers during the dehydration process are directly relatedto the final composition and quality aspects of the dried product (Demirkol andTarakci 2018). In addition to the industrially popular spray dryer and freeze dryer,the spouted bed dryerwith inert particles is an alternative drying technique that allowsthe production of powdered matrices from liquid and paste-like foods (Dantas et al.2018). Combining operation flexibility with lower costs, when compared to the spraydryer, several studies have demonstrated the efficiency of the spouted bed drying forthe production of high-quality powdered products (Rocha et al. 2011; Medeiros et al.2002; Lucas et al. 2018).

5 Spouted Bed Drying of Fruit Pulps … 107

5.2 Fundamentals of Spouted Bed Drying

The spouted bed technique was reported for the first time by Mathur and Gishler(1955), when the authors investigated the performance of this unconventional tech-nique for the drying of wheat grains. In that original work, the authors reported thatthe vigorous air and particles circulation through the system facilitated the removalof water from the wheat grains, when compared to traditional fluidized bed dryers.

In the late 1960s, the Leningrad Institute of Technology successfully applied thespouted bed dryerwith inert particles for the drying of solutions. The authors reportedthat the spouted bed drying of organic dyes, salt and sugar solutions, and chemicalreagents resulted in quality fine powders (Mathur and Epstein 1974).

Several designs have been proposed for processing suspensions and pastes in aspouted bed dryer (Costa et al. 2006; Passos et al. 1997; Pallai et al. 2007), but theconventional dryer is composed of a cylindrical vessel (drying column or dryingchamber) with a conical base with an inlet orifice for air injection (Fig. 5.1). Inertparticles are used as drying support for the feed suspension. A thin layer of materialis accumulated around the particles, covering them, and, after drying, the powdersare separated from the particles due to the friction of the particles’ bed and carriedby the inlet air (Araújo et al. 2015).

The spouted bed drying system is initiated with inlet air injection at the conicalbase of the dryer’s chamber. When air flow is sufficient to pneumatically move theinert particles, an upward movement is noticed and the inert particles are carried to

Fig. 5.1 Schematic representation of a conventional spouted bed dryer. (1) Air blower; (2) Airvalve; (3) Heater; (4) Temperature sensor; (5) High-density polyethylene bed; (6) Control panel;(7) Cylindrical column; (8) Lapple cyclone; (9) Outlet air temperature and humidity sensors; (10)Digital thermo-hygrometer and anemometer; (11) Powder collector


levels above the bed, forming a high-porosity spouting region. A low-porosity regionis formed in the annular section of the drying chamber by the downwardmovement ofthe inert particles. The particles then return to the conical base and are carried againinto the spouting region, in a cyclic movement (Delgado and Lima 2014; Nascimentoet al. 2015).

The feed pastes and suspensions may be drip-fed or sprayed through a nozzle ontothe moving and spouting particles bed, which allows for an increased contact surfacearea. The inlet feed is usually performed on the top of the drying chamber, sincestudies have shown that this leads to higher processing stability and lower materialaccumulation inside the system (Costa et al. 2006; Freire et al. Freire et al. 2011).

The study of the fluid dynamic behavior of the spouted bed dryer with inert parti-cles, taking into account the presence of the feed suspension in the bed is extremelyrelevant, although neglected bymany authors. The fluid dynamic behavior influencesthe process operation conditions, which can be optimized for greater production effi-ciency, absence of instability, more economical process, and better product quality.Among the factors that influence the fluid dynamic behavior of inert particles in thespouted bed, the minimum spouting air velocity, the stable spouting air velocity, andthe maximum pressure drop are worth to highlight (Vieira et al. 2004). In additionto the parameters of the inlet drying air, the geometric configuration of the dryer, thephysical characteristics and composition of the suspensions, and properties of theinert material are also responsible for influencing the process stability (Nascimentoet al. 2015; Moreira da Silva et al. 2019).

The heat transfer in the spouted bed is carried out by conduction in the inertparticles and convection of the hot drying air. The heat and mass transfers promotethe drying of the material accumulated in the thin layer around the inert particleswhich progressively become fragile and friable. These characteristics of the driedmaterial allow it to be removed, in the powder form, by the successive collisions towhich the inert particles are subjected. The powder is then carried by the inlet airand collected in separation cyclone. In a spouted bed drying system, removal ratesshould be high enough to avoid agglomeration and mass accumulation inside thedrying chamber (Freire et al. 2011; Sousa et al. 2019).

The inert particles’ collision energy is also affected by a number of variables,including the solid circulation rates, the ratio between paste/suspension inlet feedand the inert particles load in the bed and the drying rate. The solids circulation ratedetermines the time required for a complete drying cycle: from particle coating todried film removal. The increasing drying rate favors increased dried film friabilityand positively affects the process. The paste/suspension inlet feed rate should becarefully controlled to prevent bed collapse caused by fluid dynamic instability,particle growth, or agglomeration. The material inlet feeding rate must be low ormoderate, resulting in low production of dry products, compared to the spray dryer,and is therefore an important limitation of this drying technique (Freire et al. 2012;Santos et al. 2015; Benelli et al. 2013b).

In addition, the high pressure drop through the inert particles bed, the high airflow necessary for maintaining spouting stability, the difficult process scaling up, the


strong adhesion of the dry powder to the equipment walls and the particle agglom-eration, which is related to the composition of the paste/suspension feed, are amongthe main limitations involved with the spouted bed drying process (Pallai et al. 2007;Bacelos et al. 2007).

Despite said limitations, the spouted bed drying technique has several advan-tages, which are responsible for attracting interest from research and developmentsectors, such as promoting good mixture between the particles and the fed suspen-sion, minimal friction, temperature uniformity throughout the bed and elevated heatand mass transfer coefficients. In addition, the spouted bed drying process presentshigh drying rates due to the large surface contact area between the inert particles andthe drying gas, that results in reduced processing times, which is indicated for heat-sensitive products, such as phytochemicals (Pallai et al. 2007; Pablos et al. 2018;Niksiar and Nasernejad 2017; Niksiar et al. 2013).

5.3 Spouted Bed Drying of Fruit Pulps

Drying is one of the most commonly used techniques for handling foods with highmoisture content, such as fruits and vegetables (Zhang et al. 2020; Kumar et al.2014). The drying of fruits and fruit pulps on a spouted bed dryer is a simpler andcost-reduced alternative technology, when compared to traditional freeze or spraydrying (Rocha et al. 2011; Medeiros et al. 2002).

Over the last three decades, several studies have described the drying of fruitpieces and fruit pulps using a spouted bed dryerwith inert particles. Such studies havemainly focused on the influence of feed composition (Rocha et al. 2011; Medeiroset al. 2002; Larrosa et al. 2015; Braga and Rocha 2013), drying parameters (Fujitaet al. 2013; Nascimento et al. 2019; Sales et al. 2019), powder production and qualityparameters (Lucas et al. 2018; Benelli et al. 2013a, b; Braga and Rocha 2013; Bragaand Rocha 2015), and use of drying carriers (Dantas et al. 2019; Fujita et al. 2013;Butzge et al. 2015, 2016; Rocha et al. 2018).

Medeiros et al. (2002) investigated the influence of the composition of fruit pulps,using mango pulp as a model formulation, on the fluid dynamics and powder produc-tion efficiency for spouted bed drying. In this study, the composition of the fruit pulpswas adjusted in relation to the contents of reducing sugars, starch, pectin, lipids, fibers,water, and total acidity. The authors reported that the fiber content of modified fruitpulps did not influence the fluid dynamic behavior of the drying system. Other carbo-hydrates, on the other hand, were related to instabilities on the spouted bed dryer:reducing sugars promoted instability of the bed, while starch and pectin accountedfor higher spouting stability. In addition, the authors reported that lipids, starch, andpectin concentrations positively influence the powder production efficiency.

These results were further confirmed by Rocha et al. (2011) have also reportedthat while high reducing sugars concentrations were related to spouting stability,fruit pulps with higher concentrations of starch and lipids promoted a more stablefluid dynamic regime of the spouting bed. In addition, the authors also verified that,


despite a significant sharp decrease on pressure drop just after the pulp feedinginto the drying chamber, pressure drop increased as the drying process reached astable regime. Moreover, authors also highlighted that the powder retention insidethe drying chamber, due to inadequate powder removal rates, may also influence thefluid dynamics of the spouting bed.

In a recent study, Nascimento et al. (2019) reported the obtention of driedbacaba fruit powder by spouted bed drying. The authors reported the optimiza-tion on processing conditions in order to obtain a high yielding and quality driedproduct. Authors investigated the influence of temperature, maltodextrin concentra-tion (as a drying carrier) and drying air velocity on the drying yield, moisture content,anthocyanins, and phenolic compounds retention.

In this study, the authors reported findings that agree with Costa et al. (2015),who investigated the spouted bed drying of açaí fruit pulp: increased temperatureis related to lower moisture content on the dried product and maltodextrin concen-trations around 20% increased process production and phytochemicals retention. Inaddition, both studies have suggested that there must be a balance between dryingtemperature (>70 °C) and drying air velocity in order to avoid further degradationon nutritional and bioactive components of fruit pulps.

Braga and Rocha (2015) evaluated the spouted bed drying of pure blackberrypulp and milk-added blackberry pulp. In addition, they also evaluated the impact ofmaltodextrin, casein, and palm oil as composition-modulators on the performanceof the spouted bed drying of blackberry pulp. The authors reported that despite themodifications on protein and lipid content of the pulp composition, the drying of pureblackberry pulp was not possible on the spouted bed dryer, since the pulp feedingwas responsible for significant instability that resulted in bed collapse due.

The use of milk as a drying carrier, on the other hand, was reported successfulin this study. The authors described that the addition of 25% (v/v) of whole milkin the paste formulation yielded a high-quality (around 3% moisture, 77 mg/100 ganthocyanins, and 19% protein) product and increased fluid dynamic stability.

In a recent study by our research group, Dantas et al. (2019) reported the dryingof acerola pulp (Malpighia emarginata DC) using milk and milk whey protein asdrying carriers. The authors analyzed the influence of these diary adjuvants on boththe fluid dynamics and the final product quality of dried acerola-based powders. Itwasreported that the addition of 1% whey protein to the acerola pulp jeopardize spoutedbed drying due to high pressure drop on the spouting bed that led to instability andcollapse.

On the other hand, confirming the results previously reported by Braga and Rocha(2013, 2015), the use of milk as a drying carrier for fruit pulps was successful. Dantaset al. (2019) used a model formulation in which the drying carrier corresponded to50% of the total solids on the final composition, and reported that the addition of milkpowder increased the production yield, prevented spouting instability and allowedthe most efficient processing in terms of the equipment thermal requirements. Onproduct quality parameters, the authors also reported that the use of milk as a dryingadjuvant increased calcium content on the final product and permitted a high ascorbicacid retention (around 70%) after thermal processing.


5.4 Phytochemicals on Spouted Bed Dried Fruit Powders

Over the last decade, the growing awareness for the benefits of health-promotingdiets has led the food industry toward research and development strategies in orderto take full advantage of the functional potential of fruits and vegetables (Cappatoet al. 2018; Willett et al. 2019). Studies have shown that fruits play a major role inthe balanced diets due to their vast phytochemical and fiber contents, which haveprotective properties against several diseases (Siriamornpun et al. 2012; Habauzitand Morand 2012).

Phytochemicals are naturally occurring extra-nutritional plant metabolites, suchas vitamins, phenolic acids, flavonoids, that can be related to biological activities inthe human organism (Chang et al. 2016; Fang and Bhandari 2017). In fact, the bioac-tive performance of several groups of phytochemicals has already been documented.Anti-inflammatory activity of blueberries (Grace et al. 2019), wound-healing prop-erties of strawberries and blackberries (Van de Velde et al. 2019), neuroprotectiveeffects of camu–camu (Myrciaria dubia HBK McVaug) (Azevêdo et al. 2016) andantioxidant potential of acerola (Malpighia emarginata DC) (Cruz et al. 2019) havebeen consistently reported.

Despite the several health benefits related to these bioactive components, thepotential of such phytochemicals is still in the verge of exploitation. In addition totheir occurrence in small quantities in fruits (Kris-Etherton et al. 2002), their avail-ability for the final consumer is limited due to the seasonal aspect of fruit production,as well as the low storage stability, which is usually associated with these compounds(Karam et al. 2016).

Studies have shown that drying of fruits can, in addition to extending products’shelf life, help stabilizing the phytochemical contents of the dried powders (Correiaet al. 2017; Moraes et al. 2017). Naturally sensitive, these bioactive compounds maybe affected by a number of processing, storage, and delivery conditions, such as pHvariations, temperature, presence of light, and oxygen (Patras et al. 2010), whichmay alter their molecular structure and compromise the biological functionality.

In this sense, the use of the spouted bed drier has been regarded as an effectivealternative for dealing heat-sensitive materials (Lucas et al. 2018; Alves et al. 2016),due to the possibility of milder operation conditions and the use of drying adjuvantsthat may act as a protection for the labile components (Dantas et al. 2019; Costaet al. 2015). Some aspects of the impact of spouted bed drying on the phytochemicalsfound on fruit pulps will be discussed as follows, which focus on total phenolics,anthocyanins, and ascorbic acid.


5.4.1 Impact of Spouted Bed Drying on the PhytochemicalsContent

5.4.1.1 Total Phenolic Compounds

The known potential for promoting health benefits has drawn much attentionfor increasing the presence of phenolic compounds on the human diet. Phenoliccompounds are plant secondary metabolites structured around benzene rings withhydroxyl substituents (Lin et al. 2016). The anti-inflammatory, cardio- and neuro-protective properties, antioxidant and chemo-preventive activities of phenoliccompounds can be related to several biological mechanisms, some of them stillnot fully described on the literature, that involve radical scavenging and inactivation,metal-ion chelation and single oxygen quenching (Oliveira et al. 2016; Sauceda et al.2018).

Studies have shown that the biological activities of polyphenols are concentration-dependent (Heleno et al. 2015), which highlights the drying strategy as an effec-tive way of producing polyphenol-rich products that increase these phytochemi-cals’ concentration and stability while maintaining functionality (Correia et al. 2017;Hoskin et al. 2019). The total phenolic content was evaluated on spouted bed driedpepper and aromatic extracts (Benelli et al. 2013a, b), camu–camu (Fujita et al. 2013),bacaba fruit (Nascimento et al. 2019), cubiu fruit (Sales et al. 2019) and vegetablepastes (Larrosa et al. 2015).

Camu–camu (Myrciaria dubiaHBKMcVaugh) is a small, round Amazonian fruitknown for its high nutritional and nutraceutical value. It is known for its high contentsof phytochemicals (phenolic compounds, β-carotene, vitamin C) and micronutrients(potassium, iron, phosphorus, amino acids) (Akter et al. 2011). Fujita et al. (2013,2015) conducted studies on the impact of spouted bed drying on the physico- andphytochemical characteristics of camu–camu pulp. In addition, the research groupalso evaluated the impact of other drying techniques (spray drying and freeze drying)on the biological activities of camu–camu phytochemicals.

The drying of camu–camu pulp was carried in a classical conical base spoutedbed dryer, using high-density polyethylene (HDPE) for the inert particles bed. Inthis study, different temperatures (60, 80, 95, and 110 °C) were evaluated in order toassess the final impact on the products’ quality. Freeze drying of camu–camu pulpwas performed for comparison reasons (Fujita et al. 2013). Authors reported a highconcentration of phenolic compounds on the fresh camu–camu pulp (81.6 ± 6.5milligrams of equivalent gallic acid per gram of dried sample [mg GAE/g DW]) andthe average impact of the drying process on the phenolic content of camu–camu pulpwas around 33–42%, but the increasing temperature did not statistically affect thephenolic results. In fact, although temperature-sensitive, the increase in temperaturewas followed by a reduction in processing time, which may have compensated thelosses (Vega-Gálvez et al. 2012).

In a follow-up study, the authors investigated the biological activities of driedcamu–camu (Fujita et al. 2015). Although the drying technique reported in this


study was spray drying, the authors indicated that the presence of several phenoliccompounds such as gallic acid, syringic acid, ellagic acid, quercetin, andmyricetin onthe camu–camupulp anddried powderswere linked to anti-diabetic and antimicrobialactivities, and cellular regeneration properties on planaria models.

Cubiu (Solanum sessiliflorum Dunal) is an Amazonian fruit of the Solanaceaefamily, which is known by the indigenous communities in the Amazonia forest for itshealth-promoting benefits (Andrade Júnior et al. 2012). The biological activities asso-ciated with the phytochemicals from the cubiu fruit range from hypoglycemic andhypocholesterolemic control, anti-genotoxic, and antioxidant activities (Hernandeset al. 2014). Sales et al. described the drying of the cubiu pulp on a lab-scale spoutedbed dryer in order to evaluate the influence of the drying temperature on the degra-dation of the phenolic compounds (Sales et al. 2019). The authors investigated theinfluence of two drying temperatures (50 and 70 °C) in the total phenolic contentof cubiu pulp dried without the addition of drying carriers. The reduction in thetotal phenolic content from the dried cubiu pulp was temperature-dependent. In thiscase, the degradation of the phenolic compounds increased from 33.54 to 59.12%following the increase in temperature.

Studies have shown that the use of drying carriers may help to reduce the degra-dation of phenolic compounds, as well as other phytochemicals, during spouted beddrying of fruit pulps. The use of such drying adjuvants will be discussed in thefollowing section.

5.4.1.2 Anthocyanins

Anthocyanins are water-soluble flavonoid pigments found in tubers, flowers, andfruits. Chemically, the anthocyanins are known for their particular structure of anaromatic ring bonded to an oxygen-containing heterocyclic ring and linked to a thirdaromatic structure. As pigments, this group of bioactive compounds is responsiblefor the red, blue, and purple colors, while as nutraceuticals, the anthocyanins arelinked to several health benefits (Frank et al. 2003).

The low bioavailability of anthocyanins is related to their low stability in foodsystems (Khoo et al. 2017). Several factors such as temperature, pH variations,oxygen, and light exposure, type of solvent and co-pigment, contact with degradingenzymes, metal ions, and some antioxidant agents are responsible for affecting themolecular stability of these compounds and jeopardizing their functionality (Lalehet al. 2006; Castañeda-Ovando et al. 2009). On the other hand, recent studies haveshown that drying is an effective way of increasing anthocyanins stability (Correiaet al. 2017; Moraes et al. 2017; Roopchand et al. 2013).

In addition, the in vivo and in vitro biological activities related to the anthocyaninscontent on dried powders have also been documented, and studies report the pres-ence of hypoglycemic (Roopchand et al. 2012; Grace et al. 2009), anti-inflammatory(Esposito et al. 2014), cardio-protective (Bell and Gochenaur 2006), and anticar-cinogenic (Wang et al. 2009) activities, among others. The anthocyanins content wasevaluated on spouted bed dried grapes (Butzge et al. 2015), bacaba fruit (Nascimento


et al. 2019), açai fruit (Lucas et al. 2018; Costa et al. 2015), blueberries (Feng et al.1999), blackberries (Braga and Rocha 2015) and purple flesh sweet potato (Liu et al.2015).

Lucas et al. (2018) compared the impact of three drying processes (spouted beddrying, freeze drying, and spray drying) on the production of açai powder withoutthe addition of drying adjuvants. On a physicochemical point of view, the authorsreported that the moisture content of spouted bed dried açai powder (4.75 ± 0.21%)did not differ statistically from the moisture of the spray dried samples (4.75 ±0.22%). Medeiros et al. (2002) have previously indicated that, with the proper tuningon operation conditions, the spouted bed obtained products can meet the overallquality parameters of spray dried powders, with lower production costs.

When it comes to the phytochemical content, the anthocyanins contentwas consid-erably affected according to the chosen drying method. The authors reported that thetotal anthocyanins content on spouted bed dried açai powders (1.36 ± 0.02 mg/g)represented a 30% lower degradation of these phytochemicals, when compared tothe powders obtained by spray drying (0.53 ± 0.04 mg/g) (Lucas et al. 2018). Whilethe constant agitation of the spouted bed may provide a higher contact with oxygen(Oliveira et al. 2016), the temperature required for the spouted bed processwas lower,when compared to spray drying (90 °C and 210 °C, respectively), which may explainthe higher retention on the spouted bed dried samples (Braga and Rocha 2015).

Regarding the pigments’ color stability, the authors (Lucas et al. 2018) alsoreported that the spray dried samples presented the highest total color difference(�E; 16.28 ± 0.30), while the �E for the spouted bed dried samples did not differfrom the freeze dried samples (11.79 ± 0.47 and 12.22 ± 0.26, respectively).

5.4.1.3 Ascorbic Acid

Ascorbic acid, or vitamin C, is a water-soluble vitamin found in fruits and vegetables.Essentialmicronutrient, the bioactive capacity of vitaminC iswell-documented in theliterature, being related to strengthening of the immune system, antioxidant activities,skin health promotion, scurvy, cancer, and chronical diseases prevention (Manela-Azulay et al. 2003; Pullar et al. 2017). Vitamin C is a particularly heat-sensitivecompound, and evaluating the impact of the drying processes on the degradation ofthis phytochemical is a key parameter for assessing the overall quality and efficiencyof the process (Kamiloglu et al. 2016; Santos and Silva 2008).

Fujita et al. (2013) investigated the impact of the spouted bed drying process onthe vitamin C content on the camu–camu fruit pulp. In that occasion, the authorsdetermined that the ascorbic acid retention on the dried powders was temperature-dependent. Despite the lower drying period associated with the higher temperatures,the sensitivity of the vitamin C to the increasing temperature was more significantand the retention varied from 55 to 36%, when temperature increased from 60 to110 °C.

The spouted bed drying of Tommy-variety mango pulp was described by Cunhaet al. (2006) and the authors also evaluated the impact of the drying process on the


ascorbic acid content. The authors described that the degradation of vitamin C wasboth temperature- and time-dependent. In the continuous process described in thatstudy, authors reported that by the increasing of processing time, the accumulatedmass on the spouted bed dryer was submitted to longer periods of exposure to temper-ature and oxygen,which are degrading factors for the ascorbic acid. However, authorshighlighted that a freeze-drying process was performed for comparison purposes andthe degradation of vitamin C on freeze dried samples were around 50%, while thedegradation after spouted bed reached 65%. In this sense, the hypothesis was that inaddition to temperature, other deleterious factors also contributed to the degradationof ascorbic acid.

5.4.2 Use of Drying Carriers

Feed composition plays a major role on the efficiency of the spouted bed dryingprocess. Studies have shown that the chemical composition is directly related to theglass transition temperature of the inlet feed, which may be responsible for alteringthe heat and mass transfer phenomena on the drying process. The presence of highconcentrations of reducing sugars (glucose, fructose, lactose), for example, showsa negative effect on both powder production and the products’ quality parameters(Medeiros et al. 2002; Braga and Rocha 2015; Souza et al. 2009).

Drying carriers have been used in the spouted bed drying process in order toalter the feed composition and improve both the process efficiency and the finalproducts’ quality (Souza and Oliveira 2012). Maltodextrins, cyclodextrins, proteinsources (whey protein, collagen, plant proteins), modified starch, and milk are someexamples that have been mentioned in the literature as effective drying carriers forincreasing powder production, solubility, and storage stability (Dantas et al. 2019;Butzge et al. 2016, 2015; Rocha et al. 2018; Costa et al. 2015).

The combination of the adequate drying carriers and drying processing conditionsmay result in the encapsulation of the phytochemicals found on the fruit pulps. Forencapsulation, the drying carrier is used in order to build a protective coat around thetargeted compounds, in this case, the phytochemicals, which will be less exposed todeleterious agents (pH, moisture, temperature, light) and, hence, increasing storagestability (Correia et al. 2017; Fang and Bhandari 2017; Fang and Bhandari 2010).Studies have shown that the spouted bed dryer is an alternative for producing encap-sulated products, which are usually core-shell type large microcapsules formed bycoating mechanisms favored by the fluid dynamics of the spouted bed process (Jonoet al. 2000; Baracat et al. 2008).

Milk has been used as an alternative drying carrier in order to produce ready-to-consume dried powders. The use of milk powder and reconstituted milk in formu-lations for spouted bed drying has been reported for acerola fruit (Dantas et al.2019) and blackberries (Braga and Rocha 2013). In both cases, the use of the dryingcarriers helped in increasing the phytochemicals retention on the dried powders byprotecting these compounds from further degradation due to the thermal processing.


Dantas et al. (2019) reported that the use of milk powder yielded a 72.9% of ascorbicacid retention on acerola fruit formulations, while Braga and Rocha (2013) describeda 14% degradation on the anthocyanins content on the blackberry dried powders.

Maltodextrin is a versatile form of hydrolyzed starch and it is frequently used asa drying carrier in order to modulate both the feed composition, process efficiency,and final powder characteristics. Souza and Oliveira (2012). Several are the reportedbenefits of maltodextrin as a drying carrier, such as high solubility, mild residualflavor, high glass transition temperature, and low hygroscopicity. In addition, authorshave reported increased encapsulation efficiency and production under storage whenmaltodextrin is used (Zhang et al. 2018; Ballesteros et al. 2017; Vidovic et al. 2014).

Costa et al. (2015) reported that maximum anthocyanins retention on the spoutedbed drying of açai fruit pulp was achieved when 20% maltodextrin was used asdrying carrier, 65 °C of air temperature, and air velocity corresponding to 1.25-timesthe minimum spouting air velocity. The same operation conditions were used byNascimento et al. (2019) to produce bacaba fruit powder. The authors reported thatusing 20%maltodextrin resulted in anthocyanins and phenolic compounds retentionaround 90% and 80%, respectively.

5.5 Spouted Bed Drying of Graviola (Annona muricata)Pulp: A Case Study

The studies regarding the spouted bed drying of fruit pulps carried out by the researchgroups at the Federal University of Rio Grande do Norte (UFRN) and the FederalUniversity of Campina Grande (UFCG), in partnership with the State University ofCampinas (UNICAMP) and the University of Tiradentes (UNIT) have successfullyevolved in the last 20 years (Conrado et al. 2019).

Based on the studies at UNICAMP (Braga and Rocha 2013, 2015), the UFRNresearch group developed work on the spouted bed drying of graviola fruit (Annonamuricata) using milk and albumin as drying carriers, which presented promisingresults for processing efficiency and production yields (Machado et al. 2015;Machado 2015; Dantas and Machado 2015). In a follow-up study, Dantas et al.(2018; Dantas 2018) investigated the influence of the physical properties of graviolafruit mixtures and the operational conditions (drying carriers concentration andtemperature) on the modeling of mathematical equations that described the powderproduction and the drying behavior on the spouted bed dryer, taking into account theintermittent feeding strategy.

From themixtures’ physical properties and thematerial accumulation data, severalmathematical models were proposed in order to describe the powder production andthe outlet air temperature behaviors. Suchmodelswere validatedwith the previous setof experimental data fromMachado (2015), with satisfactory adjusts to the predictedvariables. This case study is comprised of the relevant data gathered during the


development of a master (Machado 2015) and a doctoral (Dantas 2018) thesis, whichdescribes the drying of graviola fruit pulp and mixtures with milk in a spouted beddryer.

5.5.1 Fundamentals

Graviola (Annona muricata L.) is a popular fruit grown in all tropical regions, nativefrom the Caribbean, Central and South America, and valued for its pleasant char-acteristics: moderate, aromatic acidity, juicy pulp, and distinct flavor (Quek et al.2013). The fruits of the graviola are oval, large, and wide, about 10–30 cm long, andcan weigh up to 4.5 kg (Nwokocha and Williams 2009). The edible pulp of the fruitcorresponds to about 67.5% of the total fruit mass (Badrie and Schauss 2010). Whenit reaches physiological maturity, the graviola completes ripening within six days,which makes the graviola fruit extremely perishable (Oliveira et al. 2019).

Among the enzymes found in the graviola fruit, pectinesterase stands out, a moreheat resistant enzyme, which can lead to geleification and precipitation of pectin inpulps and graviola juices and polyphenol oxidase. This enzyme is responsible fordarkening the fruit pulp (Badrie and Schauss 2010).

Studies on the presence of compounds with phytochemical and pharmacologicalproperties are being carried out and reveal the existence of new acetogenins in allparts of the graviola fruit. Among the pharmacological properties, the following standout: cytotoxicity and anti-leishmanicide activity of the fruit pericarp; antiviral abilityagainst the herpes-causingHSV-1virus; anticarcinogenic and genotoxic effects (exis-tence of acetogenins with antitumor property); activity for healing injuries andantimicrobial capacity (Coria-Téllez et al. 2018). Antibacterial activities againstStaphylococcus aureus, Stapylococcus epidermidis, Propionibacterium acne, andPseudomonas aeruginosa were also found positive (Pai 2016).

Due to the fruit’s fragility and ease of suffering injuries, graviola is usually indi-cated for processing, being used in themanufacture of juices, nectars, syrups, shakes,sweets, jams, ice cream, powders, and flakes (Quek et al. 2013; Gratão et al. 2007). Inparallel with the growth of fruit production, there has been an increase in consump-tion of fruit-based beverages in recent years. In these preparations fruits are usuallyassociated with dairy compounds such as milk and whey protein. The developmentof these flavored dairy foods becomes an alternative that adds functional and moreattractive value to the product (Moura et al. 2015).

Considering the characteristics of graviola fruit and the importance of the studyof drying this fruit minimizing the use of additives and incorporating nutritionalingredients that act as agents that enable the good performance of the process, thedrying of the graviola pulp with addition of milk in a spouted bed dryer with inertparticles was investigated (Machado 2015). The effects of milk concentration onthe mixture, drying air temperature, intermittent feeding time and air flow on yield,production rate, powder moisture, drying rate, and thermal efficiency, as well as theimpact of the process on the physicochemical characteristics and physical properties


ofmixtures reconstituted bypost rehydrationwere assessed. This studywas expanded(Dantas et al. 2018;Dantas 2018) investigating the influence of the physical propertiesof graviola pulp + milk mixtures and temperature in order to generate mathematicalequations and models for the prediction of recovered powder and the spouted beddryer behavior, based on mass and energy balances, using intermittent feeding.

5.5.2 Materials and Methods

5.5.2.1 Materials

Graviola pulp (GP) was obtained by manual depulping of ripe fresh graviola fruitsacquired in the local market (Natal, Brazil). The fruit pulp was processed with adomestic blender and sieved through a nylon cloth (0.5 mm) in order to furtherremove any parts of peels and seeds. The GP was then frozen to −20 °C until use.Pasteurized whole milk was obtained from the local market.

High-density polyethylene (HDPE) particleswere used for the inert bed. The parti-cles were characterized through the mean diameter (as a sphere of equal volume) anddensity by liquid-phase picnometry. The inert bed apparent density was calculatedas the ratio between the inert load mass (2.5 kg) and the apparent volume of the bed.The porosity of the static bed (ε) was estimated according to Eq. 5.1. All measureswere taken in triplicate.

ρap = (1 − ε)ρinert (5.1)

where ρap is the apparent density of the inert bed, ε is the porosity of the static bed,and ρinert is the density of the inert particles.

5.5.2.2 Drying Apparatus

The spouted bed dryer used in this work is similar to the apparatus shown in Fig. 5.1.The dryer was composed of a stainless steel cylindrical column (72 cm height, 18 cmdiameter) with a conical base (60° angle, 13 cm height, 3 cm inlet air diameter)and a Lapple-type cyclone (40 cm height, 10 cm diameter, 5 cm overflow, 2.5 cmunderflow).

The inlet air was supplied by a 7 hp centrifugal blower (model CR-6, IBRAM-Weq, Brazil) and heated by a set of 2 kW electrical resistances. The mixtures inletfeed was atomized using a twin-fluid nozzle coupled with a peristaltic pump. A lowpower compressor supplied the atomization air.

A digital thermo-hygrometer, digital anemometer, digital K-type thermocouplethermometers, and a U-type manometer were used to measure the air temperatureand relative humidity, air flow, air temperature in the cyclone outlet and in the dryingchamber walls, and the bed pressure drop, respectively.


Table 5.1 Study variables of the full 24 factorial experimental design

Value XL (%) Tge (°C) tinter (min) v∗/vjm−1 30 70 10 1.2

0 40 80 12 1.35

+1 50 90 14 1.5

Legend: XL—milk concentration; Tge—inlet air temperature; tinter—intermittent feeding time;

v∗/vjm—ratio between inlet air velocity and minimum spouting air velocity

5.5.2.3 Experimental Design and Drying Conditions

A full 24 factorial design with three repetitions on the central point (total 19 exper-iments) was used to investigate the influence of milk concentration (XL; %), inter-mittent feed time (tinter; min), drying temperature (Tge; °C), and ratio between inletair velocity and minimum spouting air velocity (v∗/vjm) on the drying yield (Y; %),powder moisture (Upo; %), powder production rate (Wpo; g/min), drying rate (K; g/s),and process thermal efficiency (EFF; %). The levels for each one of the four studyvariables are shown in Table 5.1.

After the operation conditions were set, the feeding was initiated at a rate of 7.0± 0.8 mL/min using a twin-fluid atomizer nozzle. Six feeding cycles of 6 min wereperformed, while the intermittent feeding time was defined as the interval betweenthe stop after 6 min feeding and the start of a new feeding cycle. Throughout thedrying experiments, outlet air temperature and humidity were measured every 2 min.After the six feeding cycles, the inert particles were weighted in order to assess theamount of fruit powder not entrained and accumulated within the bed.

5.5.2.4 Samples Characterization

GP samples and GP + milk mixtures were characterized for soluble solids, densityand viscosity. Soluble solids (SST; °Brix) measures were performed by direct readin a digital refractometer (model Smart-1, Atago, USA). The density was assessedby picnometry at 25 °C, according to AOAC method 952.22 (AOAC 2006). Forviscosity, the rheological data of all samples were taken by a digital viscosimeter(model DV-II + Pro, Brookfield Engineering, USA), for 300 mL samples. Readswere performed in 5 min. Total acidity (ATT) was determined by titration and resultswere expressed as citric acid equivalents (g/100 g) (AOAC 2006).

5.5.2.5 Drying Yields

Drying yield (Y; %) was calculated as total solids recovery. It was defined as theratio between the total solids content on the powdered samples (recovered at thecyclone outlet) and the total solids content on the initial sample formulations (GP +


milk), according to Daza et al. (2016). For the spouted bed drying experiments, thepowder production data was used to adjust a linear model and determine the powderproduction rate (Wpo; g/min).

5.5.2.6 Powder Characterization

For the dried powders, sampleswere assessed for pH,moisture content,water activity,total titratable acidity, solubility, and reconstitution time. Samples pH was deter-mined using a digital potentiometer (model Tec-5, Tecnal, Brazil), water activitywas determined using a digital dew point hygrometer Aqualab® (model series 3 TE,Decagon Devices, USA) at room temperature (23 °C). Moisture was assessed by thegravimetric method at 70 °C (Tontul et al. 2018).

Solubility was assessed according to Rocha et al. (2011). Samples (1 g) weremixed with 100 mL of distilled water, stirred for 5 min, and centrifuged (3000 rpm,5 min). Supernatant aliquots (20 mL) were transferred to Petri dishes and dried at70 °C to constant weight. Solubility was calculated as percentage of material solublein the supernatant (%).

Reconstitution time was evaluated by dissolving the powdered samples indistilled water under constant stirring until the initial soluble solids content of thenon-processed mixture was achieved and no agglomerated material was observed.

5.5.2.7 Thermal Efficiency

The thermal efficiency of the spouted bed drying process was evaluated based onenergy and mass balances and calculations according to Passos et al. (2004) andSaldarriaga et al. (2015). The overall thermal efficiency (EFF; %) was defined asthe ratio between the energy (heat) used in the drying process for water evaporation(Qevap) and the energy (heat) provided by the inlet drying air flow (Qinlet), calculatedaccording to Eqs. 5.2–5.4.

Qevap(kJ/s) = Wevap × Λ (5.2)

Qinlet(kJ/s) = Winlet × Cp × (Tge − Tea

)(5.3)

EFF (%) = Qevap/Qinlet × 100 (5.4)

whereWevap is the evaporated water molar flow (kmol/s), Λ is the enthalpy of vapor-ization of water (kJ/kmol), Winlet is the inlet air molar flow (kmol/s), Tge is the inletair temperature (°C), and Tea is the room temperature (°C).


5.5.2.8 Mathematical Modeling

For constructing a mathematical model of the spouted bed drying of graviolapulp + milk mixtures, further drying experiments were performed, as describedin Sect. 5.2.2. The sample mixtures of graviola pulp + 30% milk (GP-30M),graviola pulp + 40% milk (GP-40M), and graviola pulp + 50% milk (GP-50M)were dried at three different temperatures (60, 70 and 80 °C) using two differentinert particles for the dryer’s bed, polypropylene (PP) and high-density polyethylene(HDPE). The intermittent feeding period defined for the experiments was 4 min. Thephysicochemical composition of the sample mixtures can be found in Table 5.2.

The physical properties ofmixtures and inert particles, as a function of the compo-sition of materials and the temperature of the drying process, considered for thedefinition of the equation describing the production of graviola-based powders inthe spouted bed dryer were viscosity, surface tension, density, contact angle, adhe-sion work, fat concentration, and reducing sugars concentration. The Vaschy–Buck-ingham theorem was applied in order to mathematically represent the inlet flow ofthe mixtures.

The energy balance of the process was constructed based on the outlet air temper-ature, the mathematical model for powder production (powder removal from thedryer), the operational conditions of the drying process, the correlations for dryingrates, and the dryerwall temperature. Themathematicalmodel for the energy balance,based on the first law of Thermodynamics, considering the powder accumulationinside the dryer, can be written as Eq. 5.5.

dTgsdt

= WgecpgeTge + WpecppeTpe − WgscpgsTgs − cppoTgsWpo − k�Hv − Q

mgcpgs + mpicppi + m jcp j Tgs + Mcppo(5.5)

where Tgs is the temperature of the outlet air flow (°C), Wge is inlet air mass flow(g/s), cpge is the specific heat of the inlet air flow (J/g K), Tge is the temperature ofthe inlet air flow (°C), Wpe is the mixture inlet mass flow (g/s), cppe is the specificheat of the mixture inlet flow (J/g K), Tpe is the temperature of the mixture inletflow (°C), Wgs is the outlet air mass flow (g/s), cpgs is the specific heat of the outletair flow (J/g K), cppo is the specific heat of the product powder (J/g K), Wpo is the

Table 5.2 Physicochemicalcomposition of the graviolapulp + milk sample mixtures

Parameter GP-30M GP-40M GP-50M

Reducingsugars (%)

3.45 ± 0.21 2.75 ± 0.17 2.07 ± 0.13

Fat (%) 0.94 ± 0.08 1.25 ± 0.10 1.56 ± 0.11

Watercontent (%)

12.42 ± 0.98 11.94 ± 0.95 11.63 ± 0.87

Legend: GP-30M—graviola pulp + 30% milk; GP-4M—graviolapulp + 40% milk; GP-50M—graviola pulp + 50% milk


Table 5.3 Inert particlescharacterization results

Properties Results

Real density (g/cm3) 0.875 ± 0.468

Mean diameter (cm) 0.320 ± 0.050

Apparent density (g/cm3) 0.537

Static bed porosity 0.386

powder production rate (g/s), k is the drying rate (g/s), �Hv is the enthalpy of watervaporization (J/g), Q is the heat lost to the spouted bed dryer surroundings (J/s), mg

is the outlet air flow mass (g), mpi is the inert particles mass load (g), cppi is thespecific heat of the inert particles (J/g K), and t is time (s).

The procedure for estimating the unknown parameter of the model, the heat lostto the dryer surroundings (Q), was based on minimizing the objective function ofthe least square technique using the heuristic method of optimization PSO (ParticleSwarm Optimization), an algorithm developed by Kennedy and Eberhart (1995) andalso known as a particle swarm method (Prata et al. 2009).

5.5.3 Results and Discussion

5.5.3.1 Inert Material Characterization

The results for the inert HDPE particles are presented in Table 5.3. From the charac-teristic curve of the inert particle bed, which represents the pressure drop in the beddue to the air surface velocity inside the column, the minimum spouting air velocity0.8 m/s and stable spouting pressure drop of 319.37 Pa were determined. In orderto work under stable fluid dynamic conditions, we chose to work in an air velocityrange between 20 and 50% above the minimum spouting air velocity found for thebed without adding the mixtures of GP and milk.

5.5.3.2 Characterization of Graviola Pulp and Sample Formulations

Table 5.4 shows the physicochemical characterization of graviola pulp and the sampleformulation with the addition of 30% (GP-30M), 40% (GP-40M), and 50% (GP-50M) of pasteurized whole milk, prior to the spouted drying.

According to Brazilian legislation (BRASIL 2000), the graviola pulp shouldpresent minimum values for total soluble solids of 9 °Brix, pH 3.5, total acidityof 0.6 g/100 g, and total solids of 12%. The results found in this study, where thegraviola pulp was obtained without water addition, meet the legislation parameters.All found values are above the minimum required.

Canuto et al. (2010) analyzed the GP produced in the Brazilian state of Pará andfound values of 88.1%, 12 °Brix, and 3.7 for moisture, total soluble solids, and pH,


Table 5.4 Physicochemical characterization of graviola pulp and graviola pulp + milk sampleformulations

Parameter GP Milk GP-30M GP-40M GP-50M

Moisture (%) 82.4 ± 0.9 87.60 ± 0.35 85.33 ± 0.49 85.55 ± 0.14 85.73 ± 0.64

SST (°Brix) 15.7 ± 0.34 12.99 ± 0.06 12.89 ± 0.07 11.76 ± 0.30 9.69 ± 0.16

pH 4.13 ± 0.02 6.57 ± 0.02 4.17 ± 0.08 4.22 ± 0.08 4.47 ± 0.02

ATT 0.77 ± 0.04 ND 0.53 ± 0.04 0.48 ± 0.02 0.46 ± 0.04

Legend: GP—graviola pulp; GP-30M—graviola pulp + 30% milk; GP-40M—graviola pulp +40% milk; GP-50M—graviola pulp + 50% milk; SST—total soluble solids; ATT—total titratableacidity; ND—not detected

respectively. Marcellini and Cordeiro (2003) presented results of analysis of graviolafruits produced andmarketed in the Brazilian state of Sergipe: 88.3%moisture, 12.21°Brix for soluble solids, pH 4.36 and 0.578 g/100 g of total acidity. The GP charac-terized in the present study contains less water, higher concentration of soluble solidsand acidity, and pH among the values cited by the authors. It is important to mentionthat the in natura pulps present variations in their physicochemical characteristicsdue to variations in the physiological conditions of the fruit.

The addition of milk with lower concentration of soluble solids and higher mois-ture content results in wetter mixtures with lower soluble solids content than naturalGP. Since milk presents a basic character, its addition elevates the pH of the GP +milk mixtures compared to that of fruit pulp, and consequently lowers the acidity(Table 5.4).

5.5.3.3 Drying Process Performance

Thematrix for the full 24 factorial experimental design and the results observed in thespouted bed drying ofGP+milk formulations are presented inTable 5.5. In all dryingexperiments, the fluid dynamic conditions of the spouted bed dryer remained stable,without instabilities or bed collapse. However, in most experiments, low powderproduction was observed, which can be related to the accumulation of dried materialin the dryer walls and the retention of powder in the inert bed (20.7 ± 5.7 g, onaverage)

For all experiments, the powder production data as a function of time werelinearized and the correlation coefficients presented good adjusts (>0.90). Theangular coefficient for all the adjusted linearmodels represents the powder productionrates. Figure 5.2 illustrates the linear adjusted models representing the cumulativepowder production for experiments carried out with intermittent feeding time of10 min. The other experiments presented similar behavior. These results are compat-ible with those reported by previous authors (Dantas et al. 2019; Braga and Rocha2015; Souza Júnior 2012).


Table 5.5 Full 24 factorial design and responses for the spouted bed drying of graviola pulp +milk formulations

Run XL (%) Tge (°C) tinter (min) v∗/vjm Y (%) Upo (%) Wpo (g/min) K (g/s) EFF(%)

1 −1 (30) −1 (70) −1 (10) −1 (1.2) 14.28 6.39 0.078 0.083 38.49

2 1 (50) −1 (70) −1 (10) −1 (1.2) 24.54 5.48 0.181 0.142 60.38

3 −1 (30) 1 (90) −1 (10) −1 (1.2) 3.90 6.98 0.018 0.056 20.22

4 1 (50) 1 (90) −1 (10) −1 (1.2) 17.32 6.17 0.099 0.091 27.86

5 −1 (30) −1 (70) 1 (14) −1 (1.2) 4.70 9.99 0.024 0.092 44.65

6 1 (50) −1 (70) 1 (14) −1 (1.2) 34.17 6.72 0.142 0.100 45.43

7 −1 (30) 1 (90) 1 (14) −1 (1.2) 5.16 6.00 0.021 0.084 29.41

8 1 (50) 1 (90) 1 (14) −1 (1.2) 10.98 5.39 0.036 0.081 33.62

9 −1 (30) −1 (70) −1 (10) 1 (1.5) 16.97 7.49 0.105 0.094 41.80

10 1 (50) −1 (70) −1 (10) 1 (1.5) 42.65 6.24 0.303 0.102 55.07

11 −1 (30) 1 (90) −1 (10) 1 (1.5) 10.95 5.43 0.069 0.116 22.40

12 1 (50) 1 (90) −1 (10) 1 (1.5) 33.96 4.40 0.203 0.070 19.87

13 −1 (30) −1 (70) 1 (14) 1 (1.5) 32.47 7.11 0.143 0.045 16.86

14 1 (50) −1 (70) 1 (14) 1 (1.5) 30.44 5.74 0.155 0.098 49.83

15 −1 (30) 1 (90) 1 (14) 1 (1.5) 10.06 5.26 0.055 0.067 16.82

16 1 (50) 1 (90) 1 (14) 1 (1.5) 36.28 4.18 0.151 0.066 21.99

17 0 (40) 0 (80) 0 (12) 0 (1.35) 20.72 6.32 0.087 0.083 33.39

18 0 (40) 0 (80) 0 (12) 0 (1.35) 15.97 7.27 0.067 0.104 29.33

19 0 (40) 0 (80) 0 (12) 0 (1.35) 17.44 5.85 0.089 0.081 28.71

Legend: XL—milk concentration; Tge—inlet air temperature; tinter—intermittent feeding time;

v∗/vjm—ratio between inlet air velocity and minimum spouting air velocity; Y—powder production

yield; Upo—powder moisture; Wpo—powder production rate; K—drying rate; EFF—thermalefficiency

As presented in Table 5.5, the moisture content of the powdered samples variedfrom 4.18 to 9.99%. Lower moisture values are noted for tests performed at thehighest temperature. These results corroborate the values found by Souza (2009) forthe spouted bed drying mixtures of mango, umbu, and seriguela pulps (4.4–7.5%).The powder production rates ranged from a minimum of 0.018 g/min in Run 3 to amaximum of 0.303 g/min in Run 10 with yields of 3.9% and 42.5%, respectively. Byanalyzing the responses for the full 24 factorial experimental design, the influence ofthe independent variables (study factors) on the moisture content, powder productionrate and yields can be verified in the Pareto diagrams (Fig. 5.3), at a confidence levelof 95%.

As shown in Fig. 5.3a, none of the study variables, alone or combined with theother variables, presented significant effects on the moisture content, although it isnoticeable in the Pareto diagram the trend for higher temperatures to produce powders


Fig. 5.2 Representative behavior of powder production for the spouted bed drying of graviola pulp+ milk formulations, at intermittent feeding time of 10 min

with lower moisture contents. These results can be justified by the low feeding flowof the mixture, kept virtually constant.

In Fig. 5.3b, c are illustrated the Pareto diagrams for the powder productionrate and drying yield, respectively. For the powder production rate, all study factorsindependently have significant effects on the response. The effects of air flow andsolid concentration are positive and of greater intensity, while inlet air temperatureand intermittent feeding time negatively influence the powder production. Theseresults are compatible with phenomenological observations of the process and withthe literature. The positive effect of milk concentration is justified by its fat content(Medeiros et al. 2002) and high glass transition temperature.

The negative effect of the inlet air temperature on the powder production rateis cited by several authors. With the inert bed heated above the glass transitiontemperature of the dehydrated fruit pulp, the film adhered to the surface of the inertmaterial. It behaves like a rubber-like material with hygroscopic characteristics, andits compromised detachment only occurs due to the action of shock and friction ofinert material (Collares et al. 2004; Hofsetz et al. 2007). When the mixture feedingis suspended for a longer period and the air temperature is high, the bed becomesmore heated and the glass transition temperature of the dehydrated pulp is achievedresulting in powder adherence and compromising powder production (Souza 2009).

Higher air flow rates promote higher solid circulation rate and frequency of shocksbetween the inert particles, facilitating detachment of adhered film. Figure 5.3cshows that only the air flow showed a significant and positive effect on drying yield.The effects of milk concentration and inlet air temperature were almost significant,positive and negative, respectively, as expected since yield is a function of powderproduction. In the calculation of yield, the moistures of the fed mixture and thepowder produced are included. The moisture of the mixtures has undergone smallvariations that depended on the characteristics of the processed graviola pulp. On


Fig. 5.3 Pareto diagrams forthe influences of the studyvariables on the dryingresponses: a moisturecontent, b powder productionrate, c drying yields


the other hand, the moisture of the inlet air flow (not controlled in the experiments)and the temperature interfere in the moisture of the recovered powder. In a combinedway, these variables ended up interfering in the yield and nullifying the statisticalsignificance of the other variables. These interactions justify why the other operatingvariables presented statistically less significant and lower intensity effects on yield,although with the same trend observed in the powder production rate.

Since noneof the independent variables presented significant effects on the powdermoisture content, statistical models were adjusted to the experimental data of thepowder production rate and drying yield, and they are represented in Eqs. 5.6–5.7.For the powder production rate, effects that did not present statistical significancewere eliminated from the models. For yield, the “almost significant” effects of inletair temperature (Tge) and v∗/vjm ratio was considered in the models.

Wpo = 0.109 + 0.044 × XL − 0.033 × Tge − 0.025 × tinter + 0.040 v∗/vjm (5.6)

Y = 20.155 + 8.24 × XL − 4.476 × Tge + 6.171 v∗/v jm (5.7)

where XL—milk concentration; Tge—inlet air temperature; tinter—intermittentfeeding time; v∗/vjm—ratio between inlet air velocity and minimum spouting airvelocity; Y—powder production yield; Wpo—powder production rate.

The adjusted models for both the powder production rate and yield have a reason-able quality of agreement with the experimental data. The determination coeffi-cients indicate a satisfactory adjustment between the values observed and predictedby the correlations (R2 > 0.80). However, F tests for both regression models andlack of fit tests indicate that both models are statistically significant and that thereis a satisfactory adjustment of the first-order model to experimental observations.Figure 5.4 illustrates the satisfactory adjust between the experimental data and thevalues predicted by the adjusted regression models.

5.5.3.4 Drying Rates and Thermal Efficiency

Before analyzing the behavior of drying rates and thermal efficiency of the spoutedbed drying in the processing of GP + milk formulations, it is necessary to evaluatethe temperature and humidity conditions of the outlet air flow, as these variableswere used in the mass and energy balances and calculation of the drying and heatexchange rates and, consequently, in determining the thermal efficiency of the dryer.

Figure 5.5 illustrates the experimental data of air humidity (Fig. 5.5a) and temper-ature (Fig. 5.5b) for the dryer outlet air flow, for a representative set of experimentalconditions. This set of conditions includes the behavior observed in all experiments.In all curves, the same behavior reported by Dantas (2013) is observed, tempera-ture oscillations due to discontinuation of the feeding flow (intermittent feed). Theseoscillations become more evident in the tests with longer intermittent feeding timesand greater flow of air, represented by the v∗/vjm ratio.


Fig. 5.4 Experimental data versus adjustedmathematicalmodels for powder production rate (a) andyield (b)


Fig. 5.5 Representative experimental behavior of air humidity a and temperature b of the spoutedbed dryer’s outlet air flow

As shown in Fig. 5.5, the behavior of air humidity is the same observed fortemperature,with alternatingoscillations as a functionof the intermittent feeding timeof GP + milk formulations. It is also observed that oscillations are attenuated whenthe intermittent feeding time is shorter. There is also a small influence of the inlet airtemperature on the air humidity at the dryer’s outlet air flow. The air leaves the dryerwith lower humidity content when drying occurs at higher temperatures. However,an important effect of the initial air humidity is observed, which corresponds to thehumidity of the air fed to the dryer.Coincidentally, in experiments carried out at 90 °C,the fed air was much drier. This variable may have interfered more significantly inthe air humidity curve along the drying process.

The drying rates are subjected to variations of the initial air humidity (notcontrolled in thiswork), since theywere calculated from themass and energybalancesfor the inlet and outlet air flows. On the other hand, the GP+milk formulations feedflow also suffered mild variations (7.0 ± 0.8 mL/min) due to the physical properties


(density and viscosity) of the sample formulations. Figure 5.6 illustrates, at the samescale, the feeding and drying rates of a representative set of experiments.

The drying rate results presented in Table 5.5 represent an average of the dryingrates observed during the feeding periods, since the drying ratewas almost null duringthe periods when feeding was suspended. The results regarding the drying rates areconsistent with those found by other authors (Souza Júnior 2012; Dantas 2013)and can predict the condition of constant drying rate with continuous pulp/mixturefeeding, as cited by Moraes Filho (2013).

The drying rates are subject to variations in the initial air humidity (not controlled).The heat exchange rates used for water evaporation during the drying process and

the heat exchange rates lost to the dryer surroundings were calculated and are shownin Fig. 5.7.

Figure 5.7 shows the same oscillatory behavior verified for the other variablespreviously analyzed, resulting from the intermittent feeding of the GP + milkformulations. The heat exchange rates used for water evaporation follow the samebehavior as drying rates, and present lower values than the energy lost to the dryer’ssurroundings (Fig. 5.7a, b).

It is important to highlight the gap in the peaks of each curve and the mostpronounced heat losses in the period in which the feed is suspended, when the heatspent on evaporation is minimal. As a result, the heat exchange rates lost fluctuateless over the drying process. Considering that the mixture feeding flow was constantin all experiments, an analysis of the results demonstrates that the dryer operatesabove the thermal conditions necessary to enable the evaporation rates required inthe drying process. In addition to the temperature, the air flow required to maintainthe stability conditions of the spouting bed with high circulation rate of solids andsufficient friction for the breakup of the adhered dried film extrapolates the thermaldemands of the drying process.

In the conditions illustrated in Fig. 5.7c, the behavior is different from thatobserved in Fig. 5.7a, b. It is observed that the peaks in heat exchange rates spenton evaporation coincide with the heat losses. Oscillatory behavior is maintainedin these conditions, being less evident in the heat losses data, with a tendency tobecome constant. Heat losses to the dryer surroundings are in a range lower thanthose observed in Fig. 5.7a, b, which can be justified by the concomitant conditionsof lower temperature and inlet air flow to the dryer.

The drying rates ranged from a minimum of 0.046 g/s in Run 13 to a maximumof 0.142 g/s in Run 2 (Table 5.5). For Run 2 the high evaporation rate may be due tothe high mixture feeding flow. Regarding the dryer’s thermal efficiency, the valuesobserved in Table 5.5 are low and, for the most part, below 50% as expected. TheRuns 2, 13, and 15 presented the highest and lowest thermal efficiencies, 60.80%,16.86%, and 16.82%, respectively.

Figure 5.8 shows the Pareto diagrams for the responses drying rate (Fig. 5.8a) andthermal efficiency (Fig. 5.8b) in relation to the study factors.

From the analysis of Fig. 5.8, it is verified that none of the study factors, aloneor combined, had statistically significant effects on the drying rates. This resultwas expected and agrees with other results found in the literature (Dantas 2013;


Fig. 5.6 Representative experimental behavior of feeding and drying rates for a Run 3, b Run 6,and c Run 7


Fig. 5.7 Representative experimental behavior of the heat exchange rates used onwater evaporationduring the drying process (Qevap) and the heat exchange rates lost to the dryer’s surroundings (Qp)for a Run 3, b Run 6, and c Run 7


Fig. 5.8 Pareto diagrams for the influences of the study variables on the drying responses: a dryingrate, b thermal efficiency


Bacelos 2005) which shows the strong dependence on drying rates with the mixturefeeding flow. As in this study, except for the variations due to the control difficulties,the mixture feeding flow was virtually constant, and the effects of the other studyvariables were not statistically significant.

Regarding the dryer thermal efficiency, only the variable intermittent feedingtime showed no significant effect. The effects of temperature and inlet air flow arenegative, with the temperature presenting the highest intensity, which was expectedand agrees with the previous discussion on extrapolation of these operating variables.The concentration ofmilk also interfered significantly and positively on dryer thermalefficiency. The influence of this study factormay be attributed to the higher inletwaterflow to be evaporated since the higher concentration ofmilkmeans a lower percentageof solids in the feeding mixture. As previously mentioned, milk contains a lowersolids content when compared to graviola pulp. In addition, the higher fat contentin the inlet feeding mixture facilitates the particles’ flowability and bed stability,which can also imply better use of thermal potential for water evaporation. Someinteractions between the variables also had significant effects on thermal efficiency,as observed in the Pareto diagram (Fig. 5.8b).

Since none of the study factors presented significant effects on the drying rate, amathematical model was adjusted only to the experimental data of thermal efficiency(Eq. 5.8). Non-significant effects from study factors and variables interactions werenot considered in the model, which presented good adjust to the experimental data(R2 = 0.892).

EFF = 33.50 + 5.18 × XL − 10.05 × Tge − 3.50 × v∗/vjm − 3.37 × XL × Tge+ 3.19 × Tge × tinter + 3.22 × XL × tinter × v∗/vjm (5.8)

Figure 5.9 shows the relation between the experimental data for the dryer thermalefficiency and the predicted values by the adjusted mathematical model, representingthe satisfactory agreement between them.

5.5.3.5 Powder Characterization

For the physicochemical characterization of dried powder, the experimental condi-tions that presented the highest yields were chosen. Therefore, Run 10 (XL = 50%,Tge = 70 ◦C, tinter = 10min, v∗/vjm = 1.5, Y = 42.65%), Run 13 (XL = 30%,Tge = 70 ◦C, tinter = 14min, v∗/vjm = 1.5, Y = 32.47%), and Run 16 (XL = 50%,Tge = 90 ◦C, tinter = 14min, v∗/vjm = 1.5, Y = 36.28%) were selected. The resultsfor moisture content, water activity (aw), total titratable acidity, and solubility of thedried powders are presented on Table 5.6.

Moisture content and water activity are important parameters for food conser-vation. The moisture content represents the total water present in the food matrix,while water activity represents the free or available water content in the food matrixto be used on microbial, enzymatic, and biochemical reactions (Nóbrega et al. 2015;


Fig. 5.9 Experimental data versus adjusted mathematical model for the dryer thermal efficiency

Table 5.6 Physicochemicalcharacterization of the driedgraviola pulp + milk onselected high-yieldingconditions

Parameter Run 10 Run 13 Run 16

Moisturecontent (%)

5.68 ± 0.61 7.17 ± 0.09 4.41 ± 0.32

aw 0.331 ± 0.001 0.375 ± 0.003 0.274 ± 0.007

ATT(g/100 g)

3.22 ± 0.13 4.46 ± 0.02 3.81 ± 0.02

Solubility(%)

64.18 ± 0.19 70.20 ± 1.38 66.52 ± 0.21

Legend: aw—Water activity

Casciatori et al. 2015). The range established for dried and stable foods, from amicrobiological point of view, is aw < 0.6 and moisture content below 25% (Dantaset al. 2019; Moraes et al. 2017). The powders obtained here are within the desirableranges in relation to the two parameters. Dantas et al. (Dantas et al. 2019) reportedsimilar values for moisture content (5.28–7.04%) and water activity (0.362–0.374)for spouted bed dried acerola pulp using milk powder and concentrated whey proteinas drying carriers.

Regarding the total acidity (expressed in g citric acid/100 g), comparing the resultsof the powders (Table 5.6)with those of the naturalmixtures (Table 5.4), it is observedthat the powders aremore acidic, whichwas expected due towater evaporation. There


Fig. 5.10 Dried powdersand water reconstitutedmixtures for a Run 13 andb Run 16

is also the highest acidity of the powder produced from the drying of the mixtureswith 30% milk, due to the higher concentration of the fruit with acid characteristic.

Solubility is an important physical property that can be defined as the ability ofthe solute (dried powders) to remain in homogeneous mixture with water (Borgeset al. 2016). The powders presented high solubility, with values close to those foundby Souza (Souza 2009) for the mixtures of siriguela, umbu, and mango with theaddition of starch, pectin, and palm fat, 60.15 and 67.82%. The solubility results arecomparable to those reported by Dantas et al. (2019) for spouted bed dried acerolapulp (61.5–75.4%), and higher than those reported by Correia et al. (2017) for spraydried blueberry extract using vegetal proteins as drying carriers (28.1–52.4%)

Figure 5.10a, b display the images of the powders obtained in Runs 13 e 16,respectively, and the reconstituted mixtures obtained by rehydration with water. Asobserved, the reconstituted mixtures are homogeneous and very similar to naturalmixtures.

Table 5.7 shows the results for the physicochemical attributes of GP + milkmixtures prior to drying and the reconstituted mixtures from the rehydration of thepowders obtained in Runs 10, 13, and 16.

The pH of the reconstituted mixture remained close to that of the fresh mixtures,and in the acid foods classification range. No relevant changes were verified betweenthe physicochemical attributes of initial GP + milk mixtures and the water recon-stituted powders. The minor variations can be attributed to the eventual losses onvolatile and other heat-sensitive components due to the drying process (Souza 2009;Borges et al. 2016), which may not be noticeable, from a sensory point of view, inface of the physicochemical results presented here.


Table 5.7 Physicochemical attributes of graviola pulp + milk mixtures and reconstituted powders

Parameter In natura Reconstituted

GP-30M GP-50M Run 10 Run 13 Run 16

SST (°Brix) 12.89 ± 0.07 11.76 ± 0.30 12.59 ± 0.33 12.99 ± 0.07 10.91 ± 0.16

pH 4.17 ± 0.08 4.22 ± 0.08 4.48 ± 0.02 4.04 ± 0.06 4.43 ± 0.106

ATT 0.53 ± 0.04 0.48 ± 0.02 0.496 ± 0.000 0.775 ± 0.131 0.543 ± 0.022

Reconstitutiontime (s)

– – 80 120 90

Legend: GP-3M—graviola pulp + 30% milk; GP-50M—graviola pulp + 50% milk; SST—totalsoluble solids; ATT—total titratable acidity

Powders with 50% milk were reconstituted faster than powder with 30% milk.It can be noted from Fig. 5.10 that the powder with 50% milk presents a looseraspect, different from the powder with 30% milk, which apparently presents moreagglomerate.

5.5.3.6 Density and Rheological Attributes

For a more detailed evaluation of the effect of milk addition, the study of the rheo-logical behavior of the in natura GP and GP + milk mixtures at room temperaturewas performed. Also, the rheogram of the reconstituted mixture from Run 10 wasobtained. Figure 5.11 shows viscosity curves as a function of viscosimeter rotation.Both the GP and GP + milk mixtures in different concentrations, and the recon-stituted mixture (Run 10) presented the same rheological behavior. They behaveas non-Newtonian fluids (n < 1) with pseudoplastic characteristics, since viscositydecreases with increasing the rotation speed of the viscosimeter.

Fig. 5.11 Rheograms of samples of graviola pulp (GP), graviola pulp + 30% milk (GP-30M),graviola pulp+ 40%milk (GP-40M), graviola pulp+ 50%milk (GP-50M) and water reconstitutedRun 10 powder


Table 5.8 Rheological attributes of graviola pulp + milk mixtures

Sample n μ (cP) 30 rpm μ (cP) 60 rpm ρ (g/cm3)

GP 0.483 1080 963.9 1.015

GP-30M 0.359 535.9 395.9 1.019

GP-40M 0.395 539.9 427.9 1.023

GP-50M 0.374 567.9 264.4 1.029

Reconstituted Run 10 0.356 304.9 205 1.048

Milk 1.000 1.65 1.65 1.032

Legend: GP—graviola pulp; GP-30M—graviola pulp + 30% milk; GP-40M—graviola pulp +40% milk; GP-50M—graviola pulp + 50% milk; μ—apparent viscosity; ρ—density; n—fluidflow index; cP—centipoise

Table 5.8 shows the values of the apparent viscosity of the unprocessed (GP, GP-30M, GP-40M, and GP-50M) and water reconstituted mixtures (Run 10) for 30 and60 rpm, as well as fluid flow index and density of samples.

The values of the apparent viscosity for the rotations of 30 and 60 rpm are compat-ible with those reported by Medeiros et al. (Medeiros et al. 2002) for tropic fruitpulps. The apparent viscosities of GP-50M to 30 rpm is higher than that of the Run10 reconstituted mixture; however, as the viscosimeter rotation increases (60 rpm)the values become closer. The specific mass (density) of the Run 10 reconstitutedmixture is higher which can be attributed to possible changes in its composition, orchanges in the physicochemical characteristics caused by the heating process. Thedensity of mixtures increases with the concentration of milk which is justified by thehigher density of milk.

5.5.3.7 Mathematical Modeling of the Spouted Bed Drying of GraviolaPulp with Intermittent Feeding

Based on experimental results and using the correlations for predicting physicalproperties as a function of temperature and milk concentration, the relationshipbetween the powder production rate (Wpo) and the reducing sugar and fat contents isrepresented by Eq. 5.9 (Dantas 2018).

Wpo =3.04 × 10−6 ×(

η

ρ1/3 × σ 1/2 × m1/6fat

)−2.44

×(mrs

mfat

)2.29

×(Wad

σ

)−6.13

× (mfat × σ)0.5 (5.9)

where Wpo is the powder production rate (g/s), η is the apparent viscosity (Pa s), ρis density (g/cm3), mfat is the fat content (g), mrs is the reducing sugars content (g),σ is the superficial tension (mN/cm), Wad is the adhesion work (mN/cm).


Evaluating the relationship between powder production and apparent viscosity, itwas noticed that the influence on this response due to the change in the inert type ismuch more evident in conditions in which this property has lower values, resultingfrom the increase in temperature and the highest percentage of milk in the mixture.In the condition of lower concentration of milk and, consequently, higher viscosity,the type of polymeric material did not interfere so intensely.

The relationship between powder recovery and density is centered on the variationof milk concentration, in which mixtures with a higher percentage of this ingredientresulted in larger densities and consequently higher powder production. There waslittle influence of process temperature on the variation of this physical property.

The relationship between powder recovery and surface tension indicates thattensions with lower values implicated higher yields, which is related to increasedtemperature and percentage of milk in the mixture.

There was an important increase in powder production with the increase in thevariables of milk concentration and drying temperature, when drying was performedwith HDPE, in these cases there was a reduction in the values of the adhesion work,which indicates that this inert was best suited for drying these materials.

For graviola pulp mixtures with lower percentage of milk, the large amount ofreducing sugars resulted in lower powder production during the drying process inthe spouted bed dryer. However, in mixtures with a greater amount of milk, due tothe increase in the fat concentration, there was a reduction in adhesion forces andthe significant increase in product recovery (Araújo et al. 2015; Benelli et al. 2013b;Braga and Rocha 2013).

By evaluating the adjust quality of Eq. 5.9 to the experimental data, it was foundthat 95.23% of Wpo variation is explained by the regression model, which indi-cates that it satisfactorily represents the experimental data. The adhesion work andsurface tension have the greatest influence on the estimation of the powder produc-tion (Eq. 5.9), a fact observed by the higher values of exponents for these properties,when compared to the other terms. This reflects the importance of the interactionbetween fluid and the inert particle used in the spouted bed dryer.

For the validation of powder production adjusted model (Eq. 5.9), data fromMachado (2015) (Table 5.5) on the production of graviola pulp + milk powderswere used. The mixtures of graviola pulp + milk (30–50%) were dried at 70–90 °Cusing HDPE. The experimental data and curves adjusted by the model (Eq. 5.9) areillustrated in Fig. 5.12.

In order to evaluate the application of the adjusted model based on the mass andenergy balances given by Eq. 5.5, the value of heat lost to the dryer surroundings(Q) was considered constant, determining an average value for each experiment. Thedetermined results for heat lost to the dryer surroundings were equal to 203.71 ±4.69W, 232.88± 3.72W, and 281.63± 5.85W, for experiments carried out at 60 °C,70 °C, and 80 °C, respectively.

These values agree with those reported by Machado (2015). In this work, theauthors found that 267 and 222W corresponded to the heat losses for the processingof graviola+milkmixtures with 30%milk and 50%processed at 70 °C, respectively.Using these experiments for validation of Eq. 5.5 and Q = 232.88W, the adjusted


Fig. 5.12 Experimental data for graviola + milk powder production (Machado 2015) versusadjusted model (Eq. 5.9)

Fig. 5.13 Experimental data for graviola + milk (Machado 2015) versus adjusted model for heatloss (Eq. 5.5)

models can be found on Fig. 5.13. The deviations observed for these simulationswere 2.35% and 4.82% for Figs. 5.13a and 5.13b, respectively.

As observed in the curves adjusted to the experimental data, the model was able topredict the behavior of air temperature at the outlet of the dryer in these experiments.The most evident deviations observed in Fig. 5.13b are due to the difficulty facedin controlling the feeding flow of the mixture in this experiment, in which in someperiods of intermittent feeding, theflowof the paste distanced itself from thepredictedmean.

5.5.4 Final Comments

The spouted bed dryer presented stable fluid dynamic behavior with uniform produc-tion rates although some tests presented low yield and large amount of materialretained in bed and adhered to the walls of the equipment.


All process variables presented significant effects on the powder production rate,with positive of milk concentration and air flow, and negative effects of tempera-ture and intermittent feeding time. For yield, the important positive effect was airflow. None of the process variables had a significant effect on powder moisture;however, drier powderswere obtained at higher air temperature. The first-order statis-tical models adjusted to the data of the production rate and yield were shown to besignificant and useful for predictive purposes.

The analytical resolution of the equations obtained by Vaschy–Buckinghamtheorem generated an empirical equation capable of predicting the behavior of thegraviola pulp + milk powder production rate, considering process variables andphysical properties of the mixtures. This model was used in the energy balance,in determining the air temperature at the outlet of the dryer, considering the accu-mulation of material in the drying system. The model described by the differentialequations adapted to the intermittent feeding condition considering the accumula-tion of mass in the dryer bed was able to describe the phenomena of heat and masstransfer occurred during the spouted bed drying of graviola pulp+milk under stableoperation.

The heat exchange analysis demonstrated that the dryer operated under conditionsthat extrapolated the drying thermal requirements. The first-order statistical modeladjusted to thermal efficiency data was significant and useful for predictive purposes.

The obtained graviola + milk powders presented moisture and water activityin the indicated range for dry foods, short reconstitution time, and high solubilitycompatiblewith the literature. The reconstitutedmixtures presented physicochemicaland rheological characteristics close to those of the unprocessed mixture, whichdemonstrates the low impact of the process on the dehydrated product.

5.6 Conclusions

Considering the most recent data reported on the drying of fruit pulps, it is perceivedthe current importance of research that seeks to enable the production of fruit powdersthrough low impact technologies on the product. The current search for products richin bioactive compounds and the consumption of healthier foods is an incentive toinvestigate drying methods that promote the production of high added value foodcomponents. The spouted bed dryer used in the drying of fruit pulps has presentedpromising results mainly with regard to the use of adjuvants such as milk thatpromotes the enrichment of the product without compromising sensory characteris-tics, and the rehydration capacity in water. Low performance problems are relatedto powder production or thermal efficiency need to be reevaluated by reusing thethermal potential of exhaust gas and techniques that will favor powder recovery.Studies on process modeling with intermittent feeding correlated with the composi-tion and physical properties of fruit pulp are important and need to be expanded andvalidated with data from other fruits.


Acknowledgments Fábio Medeiros was supported by Coordenação de Aperfeiçoamento dePessoal de Nível Superior (CAPES, Brazil), grant number 88882.375732/2019-01. The authorswould like to thank the Federal University of Rio Grande do Norte (UFRN) for the technicalsupport. We also acknowledge scientific support from the authors mentioned along this chapter.

References

Akter, M.S., Oh, S., Eun, J.B., Ahmed, M.: Nutritional compositions and health promoting phyto-chemicals of camu-camu (Myrciaria dubia) fruit: a review. Food Res. Int. 44, 1728–1732 (2011).https://doi.org/10.1016/j.foodres.2011.03.045

Altendorf, S.: Major Tropical Fruits Market Review 2017. FAO, Rome (2019). http://www.fao.org/economic/est/est-commodities/tropical-fruits/en/

Alves, N.N., Messaoud, G.B., Desobry, S., Costa, J.M.C., Rodrigues, S.: Effect of drying techniqueand feed flow rate on bacterial survival and physicochemical properties of a non-dairy fermentedprobiotic juice powder. J. Food. Eng. 189, 45–54 (2016). https://doi.org/10.1016/j.jfoodeng.2016.05.023

Andrade Júnior, M.C., Andrade, J.S.: Physicochemical changes in cubiu fruits (Solanum sessil-iflorum Dunal) at different ripening stages. Food Sci. Technol. 32,250–254 (2012). https://doi.org/10.1590/s0101-20612012005000049

AOAC: Official Methods of Analysis of AOAC International, 20th edn. AOAC InternationalAr-lington, USA (2006)

Araújo, A.D.A., Coelho, R.M.D., Fontes, C.P.M.L., Silva, A.R.A., Costa, J.M.C., Rodrigues, S.:Production and spouted bed drying of acerola juice containing oligosaccharides. Food Bioprod.Process. 94, 565–571 (2015). https://doi.org/10.1016/j.fbp.2014.08.005

Azevêdo, J.C.S., Borges, K.C., Genovese, M.I., Correia, R.T.P., Vattem, D.A.: Neuroprotectiveeffects of dried camu-camu (Myrciaria dubia HBK McVaugh) residue in C. elegans. Food Res.Int. 73, 135–141 (2016). https://doi.org/10.1016/j.foodres.2015.02.015

Bacelos, M.S., Passos, M.L., Freire, J.T.: Effect of interparticle forces on the conical spouted bedbehavior of wet particles with size distribution. Powder Technol. 174, 114–126 (2007). https://doi.org/10.1016/j.powtec.2007.01.023

Bacelos, M.S., Spitzner Neto, P.I., Silveira, A.M., Freire, J.T.: Analysis of fluid dynamics behaviorof conical spouted bed in presence of pastes. Dry. Technol. 23, 427–453 (2005). https://doi.org/10.1081/DRT-200054116

Badrie, N., Schauss,A.G.: Soursop (AnnonamuricataL.). In:Watson, R., Preedy,V. (eds.) BioactiveFoods in Promoting Health, 1st edn, pp. 621–643. Academic Press, Cambridge, USA (2010)

Ballesteros, L.F., Ramirez, M.J., Orrego, C.E., Teixeira, J.A., Mussatto, S.I.: Encapsulation ofantioxidant phenolic compounds extracted from spent coffee grounds by freeze-drying and spray-drying using different coating materials. Food Chem. 237, 623–631 (2017). https://doi.org/10.1016/j.foodchem.2017.05.142

Baracat, M.M., Nakagawa, A.M., Freitas, L.A.P., Freitas, O.: Microcapsule processing in a spoutedbed. Can. J. Chem. Eng. 82, 134–141 (2008). https://doi.org/10.1002/cjce.5450820117

Bell, D.R., Gochenaur, K.: Direct vasoactive and vasoprotective properties of anthocyanin-richextracts. J. Appl. Physiol. 100, 1164–1170 (2006). https://doi.org/10.1152/japplphysiol.00626.2005

Belwal, T., Devkota, H.P., Hassan, H.A., Ahluwalia, S., Ramadan,M.F.,Mocan, A., Atanasov, A.G.:Phytopharmacology of Acerola (Malpighia spp.) and its potential as functional food. Trends.Food. Sci. Technol. 74, 99–106 (2018). https://doi.org/10.1016/j.tifs.2018.01.014

Benelli, L., Souza, C.R.F., Oliveira, W.P.: Quality changes during spouted bed drying of Pepper-Rosmarin extract. Can. J. Chem. Eng. 91, 1837–1846 (2013a). https://doi.org/10.1002/cjce.21907

https://doi.org/10.1016/j.foodres.2011.03.045

http://www.fao.org/economic/est/est-commodities/tropical-fruits/en/

https://doi.org/10.1016/j.jfoodeng.2016.05.023

https://doi.org/10.1590/s0101-20612012005000049

https://doi.org/10.1016/j.fbp.2014.08.005


https://doi.org/10.1016/j.powtec.2007.01.023

https://doi.org/10.1081/DRT-200054116

https://doi.org/10.1016/j.foodchem.2017.05.142

https://doi.org/10.1002/cjce.5450820117

https://doi.org/10.1152/japplphysiol.00626.2005

https://doi.org/10.1016/j.tifs.2018.01.014



Benelli, L., Souza, C.R.F., Oliveira, W.P.: Spouted bed performance on drying of an aromatic plantextract. Powder Technol. 239, 59–71 (2013b). https://doi.org/10.1016/j.powtec.2013.01.058

Borges, K.C., Azevedo, J.C., Medeiros, M.F.D., Correia, R.T.P.: Physicochemical characterizationand bioactive value of tropical berry pomaces after spouted bed drying. J. Food.Qual. 39, 192–200(2016). https://doi.org/10.1111/jfq.12178

Borges, K.C., Bezerra, M.D.F., Rocha, M.P., Silva, E.S.D., Fujita, A., Genovese, M.I., Correia,R.T.P.: Fresh and Spray Dried Pitanga (Eugenia uniflora) and Jambolan (Syzygium cumini) Pulpsare Natural Sources of Bioactive Compounds with Functional Attributes. J. Probiotics Heal. 4,e1000145 (2016). https://doi.org/10.4172/2329-8901.1000145

Braga, M.B., Rocha, S.C.S.: Drying of milk-blackberry pulp mixture in spouted bed. Can. J. Chem.Eng. 91, 1786–1792 (2013). https://doi.org/10.1002/cjce.21918

Braga, M.B., Rocha, S.C.S.: Spouted bed drying of milk–blackberry pulp: analysis of powderproduction efficiency and powder characterization. Dry. Technol. 33, 933–940 (2015). https://doi.org/10.1080/07373937.2014.999372

BRASIL: IN n° 1-7/01/2000. Brasília, MAPA, Brazil (2000). http://www.agricultura.gov.br/assuntos/vigilancia-agropecuaria/ivegetal/bebidas-arquivos/in-no-1-de-7-de-janeiro-de-2000.doc/view. (In Portuguese)

Butzge, J.J., Godoi, F.C., Rocha, S.C.S.: Spouted bed drying efficiency of bovine hydrolyzedcollagen. Brazilian. J. Food. Technol. 19, e2015010 (2016). https://doi.org/10.1590/1981-6723.1015

Butzge, J.J., Hanao, F.H., Godoy, F.C., Rocha, S.C.S.: Drying of the hydrolyzed collagen-grapepulp mixture in a spouted bed: analysis of the efficiency of obtaining powder and the incorpora-tion of anthocyanins in the final product. In: XX Brazilian Congress of Chemical Engineering,pp. 6281–6288, São Paulo, EditoraBlücher (2015). https://doi.org/10.5151/chemeng-cobeq2014-1801-17486-147533. (In Portuguese)

Canuto, G.A.B., Xavier, A.A.O., Leandro, C.N., Benassi, M.T.: Physical and chemical charac-terization of fruit pulps from Amazonia and their correlation to free radical scavenger activity.Rev. Bras. Frutic. 32, 1196–1205 (2010). https://doi.org/10.1590/S0100-29452010005000122.(In Portuguese)

Cappato, L.P., Ferreira, M.V.S., Moraes, J., Pires, R.P.S., Rocha, R.S., Silva, R., Neto, R.P.C.,Tavares, M.I.B., Freitas, M.Q., Rodrigues, F.N., Calado, V.M.A., Raices, R.S.L., Silva, M.C.,Cruz, A.G.: Whey acerola-flavoured drink submitted Ohmic Heating: Bioactive compounds,antioxidant capacity, thermal behavior, water mobility, fatty acid profile and volatile compounds.Food Chem. 263, 81–88 (2018). https://doi.org/10.1016/j.foodchem.2018.04.115

Casciatori, F.P., Laurentino, C.L., Zanelato, A.I., Thoméo, J.C.: Hygroscopic properties of solidagro-industrial by-products used in solid-state fermentation. Ind. Crops. Prod. 64, 114–123(2015). https://doi.org/10.1016/j.indcrop.2014.11.034

Castañeda-Ovando, A., Pacheco-Hernández, M.L., Páez-Hernández, M.E., Rodríguez, J.A., Galán-Vidal, C.A.: Chemical studies of anthocyanins: a review. Food Chem. 113, 859–871 (2009).https://doi.org/10.1016/j.foodchem.2008.09.001

Chang, S.K., Alasalvar, C., Shahidi, F.: Review of dried fruits: phytochemicals, antioxidant effica-cies, and health benefits. J. Funct. Foods 21, 113–132 (2016). https://doi.org/10.1016/j.jff.2015.11.034

Collares, F., Finzer, J.R., Kieckbusch, T.: Glass transition control of the detachment of food pastesdried over glass plates. J. Food Eng. 61, 261–267 (2004). https://doi.org/10.1016/S0260-8774(03)00098-0

Conrado, L.S., Silva, O.S., Dantas, T.N.P., Silva, F.H.S., Cavalcante, J.A., Silva, G.F., Moraes,C.M., Lima, A.S., Medeiros, M.F.D., Alsina, O.L.S.: Particulate systems research in the BrazilianNortheast: Campina Grande, Natal, João Pessoa and Aracaju. In: Freire, J.T., Ferreira, M.C.,Freire, F.B.,Maia,G.D. (eds.)AnOverviewonParticulate Systems inBrazil, 1st edn, pp. 223–253.Federal University of São Carlos, São Carlos (2019)


https://doi.org/10.1111/jfq.12178

https://doi.org/10.4172/2329-8901.1000145


https://doi.org/10.1080/07373937.2014.999372

http://www.agricultura.gov.br/assuntos/vigilancia-agropecuaria/ivegetal/bebidas-arquivos/in-no-1-de-7-de-janeiro-de-2000.doc/view

https://doi.org/10.1590/1981-6723.1015

https://doi.org/10.5151/chemeng-cobeq2014-1801-17486-147533

https://doi.org/10.1590/S0100-29452010005000122


https://doi.org/10.1016/j.indcrop.2014.11.034


https://doi.org/10.1016/j.jff.2015.11.034

https://doi.org/10.1016/S0260-8774(03)00098-0


Coria-Téllez, A.V., Montalvo-Gónzalez, E., Yahia, E.M., Obledo-Vázquez, E.N.: Annona muricata:a comprehensive review on its traditionalmedicinal uses, phytochemicals, pharmacological activ-ities, mechanisms of action and toxicity. Arab. J. Chem. 11, 662–691 (2018). https://doi.org/10.1016/j.arabjc.2016.01.004

Correia, R., Grace,M.H., Esposito, D., Lila,M.A.:Wild blueberry polyphenol-protein food ingredi-ents produced by three dryingmethods: comparative physico-chemical properties, phytochemicalcontent, and stability during storage. Food Chem. 235, 76–85 (2017). https://doi.org/10.1016/j.foodchem.2017.05.042

Costa, E.F., Freire, F.B., Freire, J.T., Passos, M.L.: Spouted beds of inert particles for dryingsuspension. Dry. Technol. 24, 315–325 (2006). https://doi.org/10.1080/07373930600564563

Costa, R.G., Andreola, K., Mattietto, R.A., Faria, L.J.G., Taranto, O.P.: Effect of operating condi-tions on the yield and quality of açai (Euterpe oleraceaMart.) powder produced in spouted bed.LWT—Food Sci. Technol. 64, 1196–1203 (2015). https://doi.org/10.1016/j.lwt.2015.07.027

Cruz, R.G., Beney, L., Gervais, P., Lira, S.P., Vieira, T.M.F.S., Dupont, S.: Comparison of theantioxidant property of acerola extracts with synthetic antioxidants using an in vivo method withyeasts. Food Chem. 277, 698–705 (2019). https://doi.org/10.1016/j.foodchem.2018.10.099

Cunha, R.L., de la Cruz, A.G., Menegalli, F.C.: Effects of operating conditions on the quality ofmango pulp dried in a spout fluidized bed. Dry. Technol. 24, 423–432 (2006). https://doi.org/10.1080/07373930600611869

Dantas, S.C.M., Pontes Júnior, S.M., Medeiros, F.G.M., Santos Júnior, L.C., Alsina O.L.S.,Medeiros, M.F.D.: Spouted-bed drying of acerola pulp (Malpighia emarginata DC): effects ofadding milk and milk protein on process performance and characterization of dried fruit powders.J. Food. Process. Eng. 42, 1–13 (2019). https://doi.org/10.1111/jfpe.13205

Dantas, T.N.P., Machado, I.P., Medeiros, M.F.D.: Study of powder production and accumulationduring the spouted bed drying of graviola pulp and milk with intermittent feeding. In: XXXVIIBrazilianCongress of Particulate Systems, pp 1883–1892, SãoPaulo, EdgarBlücher Press (2015).https://doi.org/10.5151/ENEMP2015-SE-737. (In Portuguese)

Dantas, T.N.P., Moraes Filho, F.C., Souza, J.S., Oliveira, J.A., Rocha, S.C.S., Medeiros, M.F.D.:Study of model application for drying of pulp fruit in spouted bed with intermittent feeding andaccumulation. Dry. Technol. 36, 1349–1366 (2018). https://doi.org/10.1080/07373937.2017.1402785

Dantas, T.N.P.: Evaluation of the data drying fruit pulp suspensions in spouted bed with intermittentfeeding. Master’s dissertation in Research and Development in Regional Technologies, FederalUniversity of the Rio Grande do Norte (2013). https://repositorio.ufrn.br/jspui/handle/123456789/15840. (In Portuguese)

Dantas, T.N.P.: The influence of physical properties of soursop and additive on spouted bed dryingin intermittent feed. Doctoral Thesis in Chemical Engineering, Federal University of Rio Grandedo Norte (2018). https://repositorio.ufrn.br/jspui/handle/123456789/25449. (In Portuguese)

Daza, L.D., Fujita, A., Fávaro-trindade, C.S., Rodrigues, J.N., Granato, D., Genovese, M.I.: Effectof spray drying conditions on the physical properties of Cagaita (Eugenia dysenterica DC) fruitextracts. Food Bioprod. Process. 97, 20–29 (2016). https://doi.org/10.1016/j.fbp.2015.10.001

Delgado, J.M.P.Q., Lima, A.G.B.: Transport Phenomena and Drying of Solids and ParticulateMaterials, vol. 48. Springer, Heidelberg, Germany (2014)

Demirkol, M., Tarakci, Z.: Effect of grape (Vitis labrusca L.) pomace dried by different methods onphysicochemical, microbiological and bioactive properties of yoghurt. LWT—Food Sci. Technol.97, 770–777 (2018). https://doi.org/10.1016/j.lwt.2018.07.058

Esposito, D., Chen, A., Grace, M.H., Komarnytsky, S., Lila, M.A.: Inhibitory effects of wild blue-berry anthocyanins and other flavonoids on biomarkers of acute and chronic inflammation in vitro.J Agric. Food Chem. 62, 7022–7028 (2014). https://doi.org/10.1021/jf4051599

Fang, Z., Bhandari, B.: Spray Drying of Bioactives. In: Roos, Y.H., Livney, Y.D. (eds.) EngineeringFoods for Bioactives Stability and Delivery, 1st edn, pp. 261–284. Springer Nature, New York(2017)

https://doi.org/10.1016/j.arabjc.2016.01.004


https://doi.org/10.1080/07373930600564563

https://doi.org/10.1016/j.lwt.2015.07.027


https://doi.org/10.1080/07373930600611869

https://doi.org/10.1111/jfpe.13205

https://doi.org/10.5151/ENEMP2015-SE-737

https://doi.org/10.1080/07373937.2017.1402785

https://repositorio.ufrn.br/jspui/handle/123456789/15840


https://doi.org/10.1016/j.fbp.2015.10.001


https://doi.org/10.1021/jf4051599


Fang, Z., Bhandari, B.: Encapsulation of polyphenols—a review. Trends Food Sci. Technol. 21,510–523 (2010). https://doi.org/10.1016/j.tifs.2010.08.003

FAO.: The State of Food and Agriculture—Moving forward on food loss and waste reduction.Rome, FAO (2019). Available from: http://www.fao.org/policy-support/tools-and-publications/resources-details/en/c/1242090/

Feng, H., Tang, J., Mattinson, D.S., Fellman, J.K.: Microwave and spouted bed drying of frozenblueberries: the effect of drying and pretreatment methods on physical properties and retentionof flavor volatiles. J. Food Process. Preserv. 23, 463–479 (1999). https://doi.org/10.1111/j.1745-4549.1999.tb00398.x

Frank, T., Netzel,M., Strass, G., Bitsch, R., Bitsch, I.: Bioavailability of anthocyanidin-3-glucosidesfollowing consumption of red wine and red grape juice. Can. J. Physiol. Pharmacol. 81, 423–435(2003). https://doi.org/10.1139/y03-038

Freire, J.T., Ferreira, M.C., Freire, F.B.: Drying of solutions, slurries and pastes. In: Epstein, N.,Grace, J. (eds.) SPouted Spout-Fluid Bed, 1st edn, pp. 206–221. Cambridge University Press,Cambridge (2011)

Freire, J.T., Ferreira, M.C., Freire, F.B., Nascimento, B.S.: A review on paste drying with inert parti-cles as support medium. Dry. Technol. 30, 330–341 (2012). https://doi.org/10.1080/07373937.2011.638149

Fujita, A., Borges, K., Correia, R., Franco, B.D.G.M., Genovese,M.I.: Impact of spouted bed dryingon bioactive compounds, antimicrobial and antioxidant activities of commercial frozen pulp ofcamu-camu (Myrciaria dubiaMc. Vaugh). Food Res. Int. 54, 495–500 (2013). https://doi.org/10.1016/j.foodres.2013.07.025

Fujita,A., Sarkar,D.,Wu, S.,Kennelly, E., Shetty,K.,Genovese,M.I.: Evaluation of phenolic-linkedbioactives of camu–camu (Myrciaria dubiaMc. Vaugh) for antihyperglycemia, antihypertension,antimicrobial properties and cellular rejuvenation. Food Res. Int. 77, 194–203 (2015). https://doi.org/10.1016/j.foodres.2015.07.009

Grace, M.H., Ribnicky, D.M., Kuhn, P., Poulev, A., Logendra, S., Yousef, G.G., Raskin, I., Lila,M.A.: Hypoglycemic activity of a novel anthocyanin-rich formulation from lowbush blueberry,Vaccinium angustifolium Aiton. Phytomedicine 16, 406–415 (2009). https://doi.org/10.1016/j.phymed.2009.02.018

Grace, M.H., Xiong, J., Esposito, D., Ehlenfeldt, M., Lila, M.A.: Simultaneous LC-MS quantifi-cation of anthocyanins and non-anthocyanin phenolics from blueberries with widely divergentprofiles and biological activities. Food Chem. 27, 336–346 (2019). https://doi.org/10.1016/j.foodchem.2018.10.101

Gratão, A.C.A., Silveira, V., Telis-Romero, J.: Laminar flow of soursop juice through concentricannuli: friction factors and rheology. J. Food. Eng. 78, 1343–1354 (2007). https://doi.org/10.1016/j.jfoodeng.2006.01.006

Habauzit, V., Morand, C.: Evidence for a protective effect of polyphenols-containing foods oncardiovascular health: An update for clinicians. Ther. Adv. Chronic Dis. 3, 87–106 (2012). https://doi.org/10.1177/2040622311430006

Heleno, S.A., Martins, A., Queiroz, M.J.R.P., Ferreira, I.C.F.R.: Bioactivity of phenolic acids—metabolites versus parent compounds: a review. Food Chem. 173, 501–513 (2015). https://doi.org/10.1016/j.foodchem.2014.10.057

Hernandes, L.C.,Aissa,A.F., Almeida,M.R.,Darin, J.D.A.C., Rodrigues, E., Batista, B.L., Barbosa,F., Mercadante, A.Z., Bianchi, M.L.P., Antunes, L.M.G.: In vivo assessment of the cytotoxic,genotoxic and antigenotoxic potential of maná-cubiu (Solanum sessiliflorum Dunal) fruit. FoodRes. Int. 62, 121–127 (2014). https://doi.org/10.1016/j.foodres.2014.02.036

Hofsetz, K., Lopes, C.C., Hubinger, M.D., Mayor, L., Sereno, A.M.: Changes in the physicalproperties of bananas on applying HTST pulse during air-drying. J. Food. Eng. 83, 531–540(2007). https://doi.org/10.1016/j.jfoodeng.2007.04.003

Hoskin, R.T., Xiong, J., Esposito, D.A., Lila, M.A.: Blueberry polyphenol-protein food ingredients:the impact of spray drying on the in vitro antioxidant activity, anti-inflammatory markers, glucose


http://www.fao.org/policy-support/tools-and-publications/resources-details/en/c/1242090/

https://doi.org/10.1111/j.1745-4549.1999.tb00398.x

https://doi.org/10.1139/y03-038

https://doi.org/10.1080/07373937.2011.638149



https://doi.org/10.1016/j.phymed.2009.02.018



https://doi.org/10.1177/2040622311430006





metabolism and fibroblast migration. Food Chem. 280, 187–194 (2019). https://doi.org/10.1016/j.foodchem.2018.12.046

Jono, K., Ichikawa, H., Miyamoto, M., Fukumori, Y.: A review of particulate design for pharma-ceutical powders and their production by spouted bed coating. Powder Technol. 113, 269–277(2000). https://doi.org/10.1016/S0032-5910(00)00310-7

Kamiloglu, S., Toydemir, G., Boyacioglu, D., Beekwilder, J., Hall, R.D., Capanoglu, E.: A reviewon the effect of drying on antioxidant potential of fruits and vegetables. Crit. Rev. Food Sci. Nutr.56, S110–S129 (2016). https://doi.org/10.1080/10408398.2015.1045969

Karam, M.C., Petit, J., Zimmer, D., Baudelaire, D.E., Scher, J.: Effects of drying and grinding inproduction of fruit and vegetable powders: A review. J. Food. Eng. 188, 32–49 (2016). https://doi.org/10.1016/j.jfoodeng.2016.05.001

Karam, M.C., Petit, J., Zimmer, D., Djantou, E.B., Scher, J.: Effects of drying and grinding inproduction of fruit and vegetable powders: A review. J. Food. Eng. 188, 32–49 (2016). https://doi.org/10.1016/j.jfoodeng.2016.05.001

Kennedy, J., Eberhart, R.: Particle swarm optimization. Proc. IEEE Int. Conf. Neural Networks 4,1942–1948 (1995). http://dx.doi.org/10.1109/ICNN.1995.488968

Khoo, H.E., Azlan, A., Tang, S.T., Lim, S.M.: Anthocyanidins and anthocyanins: colored pigmentsas food, pharmaceutical ingredients, and the potential health benefits. Food Nutr. Res. 61,e1361779 (2017). https://doi.org/10.1080/16546628.2017.1361779

Kris-Etherton, P.M., Hecker, K.D., Bonanome, A., Coval, S.M., Binkoski, A.E., Hilpert, K.F., Griel,A.E., Etherton, T.D.: Bioactive compounds in foods: Their role in the prevention of cardiovasculardisease and cancer. Am. J. Med. 113, 71–88 (2002). https://doi.org/10.1016/S0002-9343(01)00995-0

Kumar, C., Karim, M.A., Joardder, M.U.H.: Intermittent drying of food products: A critical review.J. Food. Eng. 121, 48–57 (2014). https://doi.org/10.1016/j.jfoodeng.2013.08.014

Laleh, G.H., Frydoonfar, H., Heidary, R., Jameei, R., Zare, S.: The Effect of light, temperature,pH and species on stability of anthocyanin pigments in four berberis species. Pakistan J. Nutr. 5,90–92 (2006https://doi.org/10.3923/pjn.2006.90.92

Larrosa, A.P.Q., Cadaval, T.R.S., Pinto, L.A.A.: Influence of drying methods on the characteristicsof a vegetable paste formulated by linear programming maximizing antioxidant activity. LWT—Food Sci. Technol. 60, 178–185 (2015). https://doi.org/10.1016/j.lwt.2014.08.003

Lin, D., Xiao, M., Zhao, J., Li, Z., Xing, B., Li, X., Kong, M., Li, L., Zhang, Q., Liu, Y., Chen,H., Qin, W., Wu, H., Chen, S.: An overview of plant phenolic compounds and their importancein human nutrition and management of type 2 diabetes. Molecules 21, e1374 (2016). https://doi.org/10.3390/molecules21101374

Liu, P., Mujumdar, A.S., Zhang, M., Jiang, H.: Comparison of three blanching treatments on thecolor and anthocyanin level of the microwave-assisted spouted bed drying of purple flesh sweetpotato. Dry. Technol. 33, 66–71 (2015). https://doi.org/10.1080/07373937.2014.936558

Lucas, B.F., Zambiazi, R.C., Costa, J.A.V.: Biocompounds and physical properties of açaí pulpdried by different methods. LWT—Food Sci. Technol. 98, 335–340 (2018). https://doi.org/10.1016/j.lwt.2018.08.058

Machado, I.P., Delmiro, T.M., Machado, A.K.T., Medeiros, M.F.D.: Spouted bed drying of graviolaandmilkmixture: evaluation of the effects of operating variables on production parameters, dryingrate and thermal efficiency. In: XXXVII Brazilian Congress of Particulate Systems, pp. 1756–1765, São Paulo, Edgar Blücher Press (2015). https://doi.org/10.5151/ENEMP2015-SE-642. (InPortuguese)

Machado, I.P.: Thermal evaluation and performance of the drying process of graviola and milkmixtures in a spoutedbeddryer.Master’s dissertation inChemicalEngineering, FederalUniversityof Rio Grande do Norte (2015). https://repositorio.ufrn.br/jspui/handle/123456789/19691. (InPortuguese)

Manela-Azulay, M., Mandarim-de-Lacerda, C.A., Perez, M.A., Filgueira, A.L., Cuzzi, T.: VitaminC. An Bras Dermatol 78, 265–272 (2003). https://doi.org/10.1590/S0365-05962003000300002.(In Portuguese)


https://doi.org/10.1016/S0032-5910(00)00310-7

https://doi.org/10.1080/10408398.2015.1045969



http://dx.doi.org/10.1109/ICNN.1995.488968

https://doi.org/10.1080/16546628.2017.1361779

https://doi.org/10.1016/S0002-9343(01)00995-0


https://doi.org/10.3923/pjn.2006.90.92


https://doi.org/10.3390/molecules21101374

https://doi.org/10.1080/07373937.2014.936558


https://doi.org/10.5151/ENEMP2015-SE-642


https://doi.org/10.1590/S0365-05962003000300002


Marcellini, P.S., Cordeiro, C.E.: Physicochemical and sensory comparison of atemóia with pinecone and graviola produced and marketed in the state of Sergipe. Alim. Nutr. 14, 187–189 (2003).http://serv-bib.fcfar.unesp.br/seer/index.php/alimentos/article/view/857. (In Portuguese)

Mathur, K.B., Epstein, N.: Spouted Beds. Academic Press Inc., New York, USA (1974)Mathur, K.B., Gishler, P.E.: A study of the application of the spouted bed technique to wheat drying.J. Appl. Chem. 5, 624–636 (1955). https://doi.org/10.1002/jctb.5010051106

Medeiros, M.F.D., Rocha, S.C.S., Alsina, O.L.S., Jerônimo, C.E.M., Medeiros, U.K.L., Mata,A.L.M.L.: Drying of pulps of tropical fruits in spouted bed: Effect of composition on dryerperformance. Dry. Technol. 20, 855–881 (2002). https://doi.org/10.1081/DRT-120003767

Moraes Filho, F.C.: Evaluation of the use of models for pastes and suspensions drying in spoutedbed with continuous feeding. Master’s dissertation in Research and Development in RegionalTechnologies, Federal University of the Rio Grande do Norte (2013). https://repositorio.ufrn.br/jspui/handle/123456789/15843. (In Portuguese)

Moraes, F.P., Gonçalves, A.C., VeríssimoMiguel, T.B., Borges, K.C., Correia, R.T.P.: Freeze DriedAcerola (Malpighia emarginata) Pulp and Pomace: Physicochemical Attributes, PhytochemicalContent and Stability during Storage. J. Food. Ind. 1, 17 (2017). https://doi.org/10.5296/jfi.v1i1.11795

Moreira da Silva, C.A., Ferreira, M.C., Freire, F.B., Freire, J.T.: Analysis of the dynamics of pastedrying in a spouted bed. Dry. Technol. 37, 876–884 (2019). https://doi.org/10.1080/07373937.2018.1471699

Moura, S.C.S.R., Vissotto, F.Z., Ruffi, C.R.G., Alves Júnior, P.: Physical and rheological propertiesof fruit products. Brazilian J. Food. Technol. 19, e2015086 (2016). https://doi.org/10.1590/1981-6723.8615. (In Portuguese)

Nascimento, L.D., Corumbá, L.G., Rocha, S.C.S., Taranto, O.P., Costa, C.M.L., Faria, L.J.G.:Fluid-dynamics evaluation in a conical spouted bed and characterization of foxtail millet seeds.Particuology 23, 75–81 (2015). https://doi.org/10.1016/j.partic.2015.01.009

Nascimento, R.A., Andrade, E.L., Santana, E.B., Paixão Ribeiro, N.F., Costa, C.M.L., Faria, L.J.G.:Bacaba powder produced in spouted bed: An alternative source of bioactive compounds andenergy food product. Brazilian J. Food. Technol. 22, 1–15 (2019). https://doi.org/10.1590/1981-6723.22918

Niksiar, A., Nasernejad, B.: Activated carbon preparation from pistachio shell pyrolysis and gasifi-cation in a spouted bed reactor. Biomass Bioenergy 106, 43–50 (2017). https://doi.org/10.1016/j.biombioe.2017.08.017

Niksiar, A., Sohrabi,M., Rahimi, A.: Amodel for the dynamics of spouted bed dryers. Dry. Technol.31, 295–307 (2013). https://doi.org/10.1080/07373937.2012.729768

Nóbrega, E.M., Oliveira, E.L., Genovese, M.I., Correia, R.T.P.: The impact of hot air drying onthe physical-chemical characteristics, bioactive compounds and antioxidant activity of acerola(Malphigia emarginata) residue. J. Food Process. Preserv. 39, 131–141 (2015). https://doi.org/10.1111/jfpp.12213

Nwokocha, L.M., Williams, P.A.: New starches: Physicochemical properties of sweetsop (Annonasquamosa) and soursop (Anonna muricata) starches. Carbohydr. Polym. 78, 462–468 (2009).https://doi.org/10.1016/j.carbpol.2009.05.003

Oliveira, E.N.A., Santos, D.C., Santos, Y.M.G., Oliveira, F.A.A.: Agroindustrial use of graviola(Annonamuricata L.) for the production of liqueurs: sensory evaluation. J. Biotechnol. Biodivers.7, 281–290 (2019). https://doi.org/10.20873/jbb.uft.cemaf.v7n2.alvesoliveira. (In Portuguese)

Oliveira, S.M., Brandão, T.R.S., Silva, C.L.M.: Influence of drying processes and pretreatments onnutritional and bioactive characteristics of dried vegetables: a review. Food. Eng. Rev. 8, 134–163(2016). https://doi.org/10.1007/s12393-015-9124-0

Pablos, A., Aguado, R., Tellabide, M., Altzibar, H., Freire, F.B., Bilbao, J., Olazar, M.: A newfountain confinement device for fluidizing fine and ultrafine sands in conical spouted beds. PowderTechnol. 328, 38–46 (2018). https://doi.org/10.1016/j.powtec.2017.12.090

http://serv-bib.fcfar.unesp.br/seer/index.php/alimentos/article/view/857

https://doi.org/10.1002/jctb.5010051106

https://doi.org/10.1081/DRT-120003767


https://doi.org/10.5296/jfi.v1i1.11795

https://doi.org/10.1080/07373937.2018.1471699

https://doi.org/10.1590/1981-6723.8615

https://doi.org/10.1016/j.partic.2015.01.009

https://doi.org/10.1590/1981-6723.22918

https://doi.org/10.1016/j.biombioe.2017.08.017

https://doi.org/10.1080/07373937.2012.729768

https://doi.org/10.1111/jfpp.12213

https://doi.org/10.1016/j.carbpol.2009.05.003

https://doi.org/10.20873/jbb.uft.cemaf.v7n2.alvesoliveira

https://doi.org/10.1007/s12393-015-9124-0



Pai, B.M.: Anti-microbial efficacy of soursop leaf extract (Annona muricata) on oral pathogens: anin-vitro study. J. Clin. Diag. Res. 10, ZC01–ZC04 (2016). https://doi.org/10.7860/JCDR/2016/18329.8762

Pallai, E., Szentmarjay, T., Mujumdar, A.S.: Spouted bed dryer. In: Mujumdar, A.S. (ed.) Handbookof Industrial Drying, 3rd edn, pp. 389–410. CRC Press, Boca Raton (2007)

Passos, M.L., Massarani, G., Freire, J.T., Mujumdar, A.S.: Drying of pastes in spouted beds ofinert particles: design criteria and modeling. Dry. Technol. 15, 605–624 (1997). https://doi.org/10.1080/07373939708917249

Passos, M.L., Trindade, A.L.G., d’Angelo, J.V.H., Cardoso, M.: Drying of black liquor in spoutedbed of inert particles. Dry. Technol. 22, 1041–1067 (2004). https://doi.org/10.1081/DRT-120038579

Patras, A., Brunton, N.P., O’Donnell, C., Tiwari, B.K.: Effect of thermal processing on anthocyaninstability in foods; mechanisms and kinetics of degradation. Trends Food Sci. Technol. 21, 3–11(2010). https://doi.org/10.1016/j.tifs.2009.07.004

Prata,D.M., Schwaab,M.,Lima,E.L., Pinto, J.C.:Nonlinear dynamic data reconciliation andparam-eter estimation through particle swarm optimization: application for an industrial polypropylenereactor. Chem. Eng. Sci. 64, 3953–3967 (2009). https://doi.org/10.1016/j.ces.2009.05.028

Pullar, J.M., Carr, A.C., Vissers, M.C.M.: The roles of vitamin C in skin health. Nutrients 9: e866(2017). https://doi.org/10.3390/nu9080866

Quek, M.C., Chin, N.L., Yusof, Y.A.: Modelling of rheological behaviour of soursop juice concen-trates using shear rate–temperature–concentration superposition. J. Food. Eng. 118, 380–386(2013). https://doi.org/10.1016/j.jfoodeng.2013.04.025

Rocha, S.C.S., Souza, J.S., Alsina, O.L.S.,Medeiros,M.F.D.: Drying of tropical fruit pulps: Spoutedbed process optimization as a function of pulp composition. Dry. Technol. 29, 1587–1599 (2011).https://doi.org/10.1080/07373937.2011.585442

Rocha, S.F., Müller, T., Castro, J.V.O., Lima, H.Z., Pinto, L.A.A. Protein content maximization ofvegetable paste by incorporation of whey through the linear programming: drying and rehydrationevaluation. J. Food. Sci. Technol. 55, 2541–2551 (2018). https://doi.org/10.1007/s13197-018-3174-2

Roopchand,D.E.,Krueger,C.G.,Moskal,K., Fridlender,B., Lila,M.A.,Raskin, I.: Food-compatiblemethod for the efficient extraction and stabilizationof cranberry pomacepolyphenols. FoodChem.141, 3664–3669 (2013). https://doi.org/10.1016/j.foodchem.2013.06.050

Roopchand, D.E., Kuhn, P., Poulev, A., Oren, A., Lila,M.A., Fridlender, B., Raskin, I.: Biochemicalanalysis and in vivo hypoglycemic activity of a grape polyphenol-soybean flour complex. J. Agric.Food Chem. 60, 8860–8865 (2012). https://doi.org/10.1021/jf300232h

Saldarriaga, J.F., Grace, J., Lim, C.J., Wang, Z., Xu, N., Atxutegi, A., Aguado, R., Olazar, M.:Bed-to-surface heat transfer in conical spouted beds of biomass-sand mixtures. Powder Technol.283, 447–454 (2015). https://doi.org/10.1016/j.powtec.2015.05.046

Sales, M.L.F., Cavalcante, L.A., Silva, O.C., Aum, Y.K.P.G.: Evaluation of the influence of theoperational conditions of spouting bed drying on the maintenance of the phenolic components ofcubiu. In: Andrade, D.F. (ed.) Processos Químicos e Biotecnológicos, vol. 1, 1st edn, pp. 13–19.Belo Horizonte, Editora Poisson (2019). (In Portuguese)

Santos, K.G., Francisquetti, M.C.C., Malagoni, R.A., Barrozo, M.A.S.: Fluid dynamic behavior ina spouted bed with binary mixtures differing in size. Dry. Technol. 33, 1746–1757 (2015). https://doi.org/10.1080/07373937.2015.1036284

Santos, P.H.S., Silva, M.A.: Retention of Vitamin C in drying processes of fruits and vegetables—areview. Dry. Technol. 26, 1421–1437 (2008). https://doi.org/10.1080/07373930802458911

Sauceda, A.E.Q., Sayago-Ayerdi, S.G., Ayala-Zavala, J.F., Wall-Medrano, A., de la Rosa, L.A.,González-Aguilar, G.A., Álvarez-Parrilla, E.: Biological Actions of Phenolic Compounds. In:Yahia, E.M. (ed.) Fruit and Vegetable Phytochemicals: Chemistry and Human Health, 2nd edn,pp. 125–138. Wiley, Hoboken, USA (2018)

https://doi.org/10.7860/JCDR/2016/18329.8762

https://doi.org/10.1080/07373939708917249

https://doi.org/10.1081/DRT-120038579


https://doi.org/10.1016/j.ces.2009.05.028

https://doi.org/10.3390/nu9080866


https://doi.org/10.1080/07373937.2011.585442

https://doi.org/10.1007/s13197-018-3174-2


https://doi.org/10.1021/jf300232h


https://doi.org/10.1080/07373937.2015.1036284

https://doi.org/10.1080/07373930802458911


Siriamornpun, S., Kaisoon, O., Meeso, N.: Changes in colour, antioxidant activities and carotenoids(lycopene, β-carotene, lutein) of marigold flower (Tagetes erecta L.) resulting from differentdrying processes. J. Funct. Foods. 4, 757–766 (2012). https://doi.org/10.1016/j.jff.2012.05.002

Sousa, R.C., Ferreira, M.C., Altzibar, H., Freire, F.B., Freire, J.T. Drying of pasty and granularmaterials in mechanically and conventional spouted beds. Particuology 42, 176–183 (2019).https://doi.org/10.1016/j.partic.2018.01.006

Souza, C.R.F., Donida, M.W., Rocha, S.C.S., Oliveira, W.P.: The role of colloidal silicon dioxide inthe enhancement of the drying of herbal preparations in suspended state. Chem. Eng. Commun.196, 391–405 (2009). https://doi.org/10.1080/00986440802359543

Souza, C.R.F., Oliveira, W.P.: Drying of phytochemical preparations in a spouted bed: perspectivesand challenges. Dry. Technol. 30, 1209–1226 (2012). https://doi.org/10.1080/07373937.2012.692746

Souza da Silva, E., Rupert Brandão, S. C., Lopes da Silva, A., Fernandes da Silva, J.H., DuarteCoêlho, A.C., Azoubel, P.M.: Ultrasound-assisted vacuum drying of nectarine. J. Food. Eng. 246,119–124 (2019. https://doi.org/10.1016/j.jfoodeng.2018.11.013

Souza, J.S.: Drying of tropical fruit pulp mixture in spouted bed. Doctoral Thesis in Research andDevelopment in Regional Technologies, Federal University of the Rio Grande do Norte (2009).https://repositorio.ufrn.br/jspui/handle/123456789/15892. (In Portuguese)

Souza Júnior, F.E.: Drying of process acerola waste in spouted bed: Study of fluid dynamics andanalyze of performance of the dryer. Master’s dissertation in Research and Development inRegional Technologies, Federal University of the Rio Grande do Norte (2012). https://repositorio.ufrn.br/jspui/handle/123456789/15831. (In Portuguese)

Tontul, I., Eroglu, E., Topuz, A.: Convective and refractance window drying of cornelian cherrypulp: effect on physicochemical properties. J. Food Process. Eng. 41, 1–8 (2018). https://doi.org/10.1111/jfpe.12917

Van de Velde, F., Esposito, D., Grace, M.H., Pirovani, M.E., Lila, M.A.: Anti-inflammatory andwound healing properties of polyphenolic extracts from strawberry and blackberry fruits. FoodRes. Int. 121, 453–462 (2019). https://doi.org/10.1016/j.foodres.2018.11.059

Vega-Gálvez, A., Ah-Hen, K., Chacana, M., Vergara, J., Martínez-Monzó, J., García-Segovia, P.,Lemus-Mondaca, R., Di Scala, K.: Effect of temperature and air velocity on drying kinetics,antioxidant capacity, total phenolic content, colour, texture and microstructure of apple (var.Granny Smith) slices. Food Chem. 132, 51–59 (2012). https://doi.org/10.1016/j.foodchem.2011.10.029

Vidovic, S.S., Vladic, J.Z., Vaštag, Ž.G., Zekovic, Z.P., Popovic, L.M.: Maltodextrin as a carrierof health benefit compounds in Satureja montana dry powder extract obtained by spray dryingtechnique. Powder Technol. 258, 209–215 (2014). https://doi.org/10.1016/j.powtec.2014.03.038

Vieira, M.G.A., Donida, M.W., Rocha, S.C.S.: Adhesion of an aqueous polymeric suspension toinert particles in a spouted bed. Dry. Technol. 22, 1069–1085 (2004). https://doi.org/10.1081/DRT-120038580

Wang, L.S., Hecht, S.S., Carmella, S.G., Yu, N., Larue, B., Henry, C., McIntyre, C., Rocha, C.,Lechner, J.F., Stoner, G.D.: Anthocyanins in black raspberries prevent esophageal tumors in rats.Cancer Prev. Res. 2, 84–93 (2009). https://doi.org/10.1158/1940-6207.CAPR-08-0155

Willett,W., Rockström, J., Loken, B., Springmann,M., Lang, T., Vermeulen, S., Garnett, T., Tilman,D., DeClerck, F., Wood, A., Jonell, M., Clark, M., Gordon, L.J., Fanzo, J., Hawkes, C., Zurayk,R., Rivera, J.A., De Vries, W., Sibanda, L.M., Afshin, A., Chaudhary, A., Herrero, M., Agustina,R., Branca, F., Lartey, A., Fan, S., Crona, B., Fox, E., Bignet, V., Troell, M., Lindahl, T., Singh, S.,Cornell, S.E., Srinath Reddy, K., Narain, S., Nishtar, S.,Murray, C.J.L.: Food in the anthropocene:the EAT–lancet commission on healthy diets from sustainable food systems. Lancet 393, 447–492(2019). https://doi.org/10.1016/S0140-6736(18)31788-4

https://doi.org/10.1016/j.jff.2012.05.002

https://doi.org/10.1016/j.partic.2018.01.006

https://doi.org/10.1080/00986440802359543

https://doi.org/10.1080/07373937.2012.692746




https://doi.org/10.1111/jfpe.12917




https://doi.org/10.1081/DRT-120038580

https://doi.org/10.1158/1940-6207.CAPR-08-0155

https://doi.org/10.1016/S0140-6736(18)31788-4


Zhang, L., Liao, L., Qiao, Y., Wang, C., Shi, D., An, K., Hu, J.: Effects of ultrahigh pressure andultrasound pretreatments on properties of strawberry chips prepared by vacuum-freeze drying.Food Chem. 303, 125386 (2020). https://doi.org/10.1016/j.foodchem.2019.125386

Zhang, L., Zeng, X., Fu, N., Tang, X., Sun, Y., Lin, L.: Maltodextrin: a consummate carrier forspray-drying of xylooligosaccharides. Food Res. Int. 106, 383–393 (2018). https://doi.org/10.1016/j.foodres.2018.01.004

https://doi.org/10.1016/j.foodchem.2019.125386


Chapter 6Osmo-convective Dehydration of FreshFoods: Theory and Applicationsto Cassava Cubes

T. R. Bezerra Pessoa, A. G. Barbosa de Lima, P. C. Martins, V. C. Pereira,T. C. O. Alves, E. S. da Silva, and E. S. de Lima

Abstract This chapter focuses on the hybrid process of osmotic dehydration andconvective air drying of foods. Emphasis has been done to cassava cubes (Manihotesculenta Crantz.). The fresh cassava cubes had a water activity content of about0.954, 60.45%moisture on awet basis, 2.27%sucrose, and 0.13%sodiumchloride onawet basis. Herein, the kinetics of osmotic dehydration of cassava cubeswere studiedunder an optimized operating condition of the convective drying kinetics of freshand osmotically dehydrated cassava cubes which were evaluated at different dryingconditions. Under mathematical point of view, different lumped approaches are usedto estimation of average effective mass diffusivities (moisture and solids). Transientresults of moisture loss, solids gain, sodium chloride, and sucrose incorporation, andmoisture content are presented, compared with experimental data, and discussed.

T. R. Bezerra Pessoa (B) · P. C. Martins · V. C. Pereira · T. C. O. AlvesDepartment of Food Engineering, Federal University of Paraiba, João Pessoa, PB 58051-900,Brazile-mail: [email protected]

P. C. Martinse-mail: [email protected]

V. C. Pereirae-mail: [email protected]

T. C. O. Alvese-mail: [email protected]

A. G. B. de Lima · E. S. de LimaDepartment of Mechanical Engineering, Federal University of Campina Grande, Av. AprígioVeloso, 882, Bodocongó, Campina Grande, PB 58429-900, Brazile-mail: [email protected]

E. S. de Limae-mail: [email protected]

E. S. da SilvaDepartment of Civil and Environmental Engineering, Federal University of Paraíba, João Pessoa,PB 58051-900, Brazile-mail: [email protected]


151









https://doi.org/10.1007/978-3-030-47856-8_6

152 T.R. Bezerra Pessoa et al.

The hybrid process has generated a dry product with 11%moisture, 16.89% sucrose,and 5.94% sodium chloride on a dry basis at better operation conditions. The productobtained from the cassava cubes hybrid process can be used in the food productionat cassava base.

Keywords Osmotic dehydration · Cassava · Drying · Hybrid drying process

6.1 Introduction

6.1.1 Drying Fundamentals

Water is a major constituent of fresh food. It is intimately related to most of thephysicochemical changes taking place in food. This constituent is vital inmaintainingthe quality and extending the shelf life of the food materials (Li et al. 1998). Sincewater activity is the thermodynamic measure of chemical potential, it can be usedto determine the state of water in a solution or in a solid (Lewicki 2004). The watercontent is considered one of the most critical quality parameters, which influencesthe microbial growth and sensory attributes (texture, appearance, and flavor) of freshfoods (Hills et al. 1990). In this context, reduction in water content improves foodmaterials stability and extends their shelf life. Drying is one of the most frequentlyused preservation methods of fresh foods, particularly vegetables, fruits, and meatsthat contain highwater concentration.Drying provokes increases in the concentrationof solids in foodby removingwater either by evaporation or sublimation (Kudra 2004;Koyuncu et al. 2007). Different drying methods have been applied in the industryto remove water from foods, such as spray drying, fluidized bed drying, foam-matdrying, microwave drying, osmotic dehydration convective drying, etc. The dryingkinetics measurement and modeling can provide better insights into physical andchemical processes that take placewhen foodmaterials undergo drying. Such insightsprovide reliable determination of drying time, help meet quality specifications, andlead to better energy conservation (Feng et al. 2014).

Osmotic dehydration produces foods with an intermediate moisture content,whose shelf life is relatively short, and it can improve sensory characteristics (color,taste, texture, and others) of them; this drying technique has been used for manyresearches (Assis et al. 2018; Pessoa et al. 2017;Mierzwa andKowalski 2016; Corrêaet al. 2017;Kumar et al. 2017).Convective drying is a very simplewater removal oper-ation applied to wet porous solids that has better moisture removal results and prod-ucts with longer storage and consumption times under ambient conditions (Mercaliet al. 2010; Isquierdo et al. 2013; Yadav and Singh 2014).

Hybrid drying technologies are being developed to better preserve the naturalfood quality, better control of the residual moisture content, and to enhance dryingefficiency (Feng et al. 2014). Despite the importance of the single drying process, thehybrid process plays an important role in this area. The use of combined processesaims to use the advantages of each technique of a particular preservation method

6 Osmo-convective Dehydration of Fresh … 153

transformation of raw materials into differentiated products that can improve theiruse in formulations and consumption. Thus, osmotic dehydration associated withconvective drying of fresh foods represents a combined process of moisture reduc-tion techniques that can provide products with better color and texture stability andlonger shelf life. This new product should exhibit differentiated sensory character-istics from only convection dried material due to incorporation or solute loss duringosmotic dehydration and increased storage time (24–48 months) at ambient condi-tions promoted by convective drying, which may increase its acceptance and expandits commerce and consumer market (Castro et al. 2018; Pessoa et al. 2011).

6.1.2 The Focus of This Work

Brazil is one of the world’s largest cassava producers (Manihot esculenta Crantz),occupying the third position in the world ranking (Chicherchio 2014). This vegetableis a shrub, perennial plant, from Euforbiaceas family and dicots class. It has tuberousroots, which has high starch content in its composition. It is the only species of itsgenus commercially cultivated, aiming at the production of tuberous roots rich instarch (Fialho and Vieira 2011). There are several products that can be obtained fromthe cassava root. In the human food, it is consumed cooked, fried, and in other forms(Chicherchio 2014).

6.2 Application: Hybrid Drying of Cassava Cubes

6.2.1 The Raw Material

6.2.1.1 Samples Preparation

Experimental tests were performed with cassava (Manihot esculenta Crantz)purchased from local commerce in João Pessoa, Paraíba state, Brazil. The cassavawas peeled by hand until the peel was completely removed and the root was cut witha 2.5 × 2.5 × 2.5 cm3 cube slicer. For osmotic dehydration, solutions were preparedwith 56% w/w solute, 46% w/w sucrose, and 10% w/w sodium chloride. Concentra-tions of the solutions were verified through a benchtop refractometer. The previouslyweighed cassava cubes were placed in screw-capped 250 mL glass jars along withthe osmotic solution. The material: solution ratio of 1:15 was used to ensure that thesolution concentration remained constant throughout the process. Vials containingthe samples were brought to a refrigerated digital shaker bench incubator (modelLS4900-TZH, Alpax, Brazil) for 190 min at 52 °C and 180 rpm. Figure 6.1 showsthe raw material and devices used in the experiments.


Fig. 6.1 Fresh material, aluminum cutter, and incubator

6.2.1.2 Samples Physical and Chemical Characterization

The characterization experiments (moisture content, water activity, sodium chloridecontent, and non-reducing sucrose sugars) of the cassava cubes in natura and dehy-drated osmotically were performed in triplicate. Moisture content was determined bythe gravimetric method using heat, which is based on the weight loss of the materialwhen heated to 70 °C in a vacuum oven until it reaches constant weight, accordingto the AOAC methodology (AOAC 1995). For water activity, the LabMaster equip-ment (NOVASINA, Switzerland) was used at 25 °C. Sodium chloride content wasobtained by the Mohr method, based on titration with silver nitrate, using potassiumchromate as an indicator (Jeffery et al. 1989). Non-reducing sucrose sugars weredetermined by the Lane-Eynon method, consisting of the complete reduction of thecupric ions of Fehling’s reagent reducing to cuprous ions under the action of heat inalkaline medium (Lane and Eynon 1923).

6.2.2 Osmotic Dehydration Tests

6.2.2.1 Experimental Procedure

The samples were taken from the incubator at 15, 30, 45, 60, 75, 90, 110, 130, 150,180, 240, 300, 360, 420, and 480 min that correspond to 8 h of operation. In the testwas observed the behavior of the mass transfer process between the solid and thesolution. After removal, they were drained on stainless steel mesh to remove excessdehydrating solution and weighed. Thereafter, triplicate determinations of moisturecontent, sucrose, and sodium chloride were performed. The osmotic dehydrationkinetics were studied by monitoring moisture loss (PU), solids gain (GS), and incor-porations of sodium chloride (INaCl) and sucrose (ISac). Figure 6.2 illustrates thesamples before osmotic dehydration process.


Fig. 6.2 Fresh material and fresh cassava cubes inside osmotic solutions

6.2.2.2 Theoretical Procedure

The osmotic dehydration kinetics was theoretically studied using the Azuara’s model(1992). The authors developed an empirical model based on a mass balance that canbe used for different geometries (without geometric constraint) including cube. Theprocesses can be performed at short time intervals, as the model does not requirethat the equilibrium point has actually reached for the mass transport parameterprediction. Starting from a mass balance in the material that undergoes dehydration,the following equations are obtained for moisture loss, total solids gain, and sodiumchloride and sucrose incorporations:

MLt = S1t(ML∞)

1 + S1t= t(ML∞)

1S1

+ t(6.1)

SGt = S2t(SG∞)

1 + S2t= t(SG∞)

1S2

+ t(6.2)

NaClt = S3t(NaCl∞)

1 + S3t= t(NaCl∞)

1S3

+ t(6.3)

Suct = S4t(Suc∞)

1 + S4t= t(Suc∞)

1S4

+ t(6.4)

where MLt is the moisture loss fraction at any time; SGt is the solid gain fractionat any time; NaClt is the sodium chloride incorporation at any time; Suct is thesucrose incorporation any time; ML∞ is the moisture loss fraction at equilibriumcondition; SG∞ is the solid gain fraction at equilibrium condition; NaCl∞ is thesodium chloride incorporation fraction at equilibrium condition; Suc∞ is the sucroseincorporation fraction at equilibrium condition; S1 is a constant related to the waterdiffusion rate out from product; S2 is a constant related to the rate of solids diffusionin the product; S3 is a constant related to the rate of sodium chloride incorporationin the product; and S4 is a constant related to the rate of sucrose incorporation in the


product. Rewriting Eqs. 6.1, 6.2, 6.3, and 6.4, in the linear form we obtain

t

MLt= 1

S1ML∞+ t

ML∞(6.5)

t

SGt= 1

S2SG∞+ t

SG∞(6.6)

t

NaClt= 1

S3NaCl∞+ t

NaCl∞(6.7)

t

Suct= 1

S4Suc∞+ t

Suc∞(6.8)

Crank (1975) obtained a simplified equation for the Fick’s physics–mathematicalmodel, considering a small process time, transient regime, diffusion in a semi-infinitemedium, constant osmotic solution concentration, and external resistance to masstransfer negligible. This model is represented by the following equations:

MLt

ML∞= 2

(DeffML t

πL2

)1/2

(6.9)

SGt

SG∞= 2

(DeffSG t

πL2

)1/2

(6.10)

NaCltNaCl∞

= 2

(DeffNaCl t

πL2

)1/2

(6.11)

SuctSuc∞

= 2

(DeffSuc t

πL2

)1/2

(6.12)

where DeffML is the effective moisture loss diffusivity; DeffSG is the effective solidsgain diffusivity; DeffNaCl is the effective sodium chloride incorporation diffusivity;DeffSuc is the effective sucrose incorporation diffusivity, and L is the characteristicdimension.

Replacing Eqs. 6.9, 6.10, 6.11, and 6.12 in the Eqs. 6.5, 6.6, 6.7, and 6.8, respec-tively, four simple expressions are obtained to calculate the effective diffusivity ofmoisture loss, solids gain, sodium chloride incorporation, and sucrose incorporationat different times, as follows:

(DeffML

)t = π t

4

[(S1L

1 + SMLt

)·(ML mod

∞MLexp

∞

)]2

(6.13)

(DeffSG

)t = π t

4

[(S2L

1 + SSGt

)·(SG mod

∞SGexp

∞

)]2

(6.14)


(DeffNaCl

)t = π t

4

[(S3L

1 + SNaClt

)·(NaCl mod

∞NaClexp∞

)]2

(6.15)

(DeffSuc

)t = π t

4

[(S4L

1 + SSuct

)·(Suc mod

∞Sucexp∞

)]2

(6.16)

whereML mod∞ is themoisture loss value at equilibriumconditionobtainedbyEq. 6.1;

SGmod∞ is the solids gain value at equilibrium condition obtained by Eq. 6.2; NaClmod

∞is the sodium chloride incorporation value at equilibrium condition obtained byEq. 6.3; Sucmod

∞ is the sucrose incorporation value at equilibrium condition obtainedby Eq. 6.4;MLexp

∞ is themoisture loss value at equilibrium condition obtained experi-mentally; SGexp

∞ is the solids gain value at equilibrium condition obtained experimen-tally; NaClexp∞ is the sodium chloride incorporation value at equilibrium conditionobtained experimentally, and Sucexp∞ is the sucrose incorporation value at equilibriumcondition obtained experimentally.

Applying Eqs. 6.9, 6.10, 6.11, and 6.12 for a cubic geometry, considering thecharacteristic dimension L as the edge of the cube, and replacing them in Eqs. 6.1,6.2, 6.3, and 6.4, respectively, we obtain the following equations:

DeffML = π

4t13

[(S1L3

1 + S1t

)·(MLmod

∞MLexp

∞

)] 23

(6.17)

DeffSG = π

4t13

[(S2L3

1 + S2t

)·(SG mod

∞SGexp

∞

)] 23

(6.18)

DeffNaCl=π

4t13

[(S3L3

1 + S3t

)·(NaCl mod

∞NaClexp∞

)] 23

(6.19)

DeffSuc = π

4t13

[(S4L3

1 + S4t

)·(Suc mod

∞Sucexp∞

)] 23

(6.20)

Thus, the general average effective diffusivity obtained from the transport ofmaterials (water outflow, total solids input, sodium chloride, and sucrose) during ofcassava cube can be calculated by using Eq. 6.21, as follows:

Deff =

N∑i=1

(Deff)i

N(6.21)

where Deff is the average effective diffusivity in time; Deff is the effective diffusivitiesfor each time and N is the number of data used.

The mean relative error (E) was calculated using Eq. 6.22 to evaluate whether themodel was or not predictive (E < 10%).


E = 100

N

N∑i=1

∣∣∣∣Vexp − Vpre

Vexp

∣∣∣∣ (6.22)

where Vexp is the experimental value, Vpre is the predicted value, and N is the numberof experimental points.

6.2.3 Convective Drying Tests

6.2.3.1 Experimental Procedure

Drying tests were performed at different temperatures with fresh cassava cubesosmotically dehydrated. The process was carried out in a convective fixed bed dryerwith perpendicular air flow. Figure 6.3 shows the convective drying equipment.

The drying air temperatures chosenwere 50, 60, and 70 °C using constant velocity(1.35 m/s) and absolute humidity (0.060 kg water/kg solid) conditions of the dryingair. Prior screening of the air velocity profile was performed using a hot wireanemometer (model AK833, China) and the temperature and relative humidity inthe drying chamber using a portable thermo-hygrometer with probe (model AK625,brand AKSO). Figure 6.4 illustrates these devices.

Convective drying kinetics was obtained by experimental measurements of themass of the cassava cubes as a function of the drying time, with 60 min intervals until

Fig. 6.3 Convective dryerused in the experiments


Fig. 6.4 Anemometer andthermo-hygrometer

the final drying period. Drying air conditions were monitored during the experimentsand the tests were performed in triplicate.

The drying analysis was performed through the experimental curves of the mois-ture content as a function of the time and the drying rate as a function of the mois-ture content. Drying curves were expressed with moisture content on a dry basis,according to literature (Moyers et al. 1999).

The average final moisture content data of the cassava cubes (fresh dried andosmotically dehydrated) at three drying air temperatures were subjected to varianceanalysis at a significance level of 5% and Tukey test mean comparison by usingSTATISTICA®software (STATSOFT 1997).

According toMontgomery (Montgomery 2008), variance analysis, also known asANOVA, is an approach used to compare various interest groups. It seeks to assessif there are considerable differences between the investigated groups.

The Tukey test is based on an amplitude distribution of the T function. It is used tocalculate the minimum significant difference and comparing it with the means differ-ence obtained for each treatment, assuming a statistical significance level (Nogueira2007).

6.2.3.2 Transport Parameter Estimation

The average effective moisture diffusivity of cassava cubes exposed to convectivedrying was obtained through the Fick’s model simplified by Crank (1975), consid-ering uniform initial moisture distribution, absence of thermal effect in mass transfer,and applied to an infinite flat plate and long drying times. For a cube, all sides were


considered of equal dimension; thus, the solution of the Fick’s model applied to acube will be given as follows:

(M − Me

M0 − Me

)=

[(8

π2

)exp

(−π2Defft

(2L)2

)]3

∴ L = Lsample

2(6.23)

where Defft represent the effective diffusivity, M is the average moisture content, Me

is the equilibriummoisture content, M0 is the initial moisture content, t is the time, Lcorresponds to the characteristic length (half the thickness on each side of the cube).

6.2.4 Results and Analysis

6.2.4.1 Physicochemical Characterization of Cassava

The physicochemical characterization of Manihot esculenta crants in natura wascarried out according to the referenced methods in Sect. 2.1.2. Table 6.1 presents theresults obtained.

The cassava roots consist basically of water and sucrose, according to results inTable 6.1. The chemical composition of this material consisted of 60.45% moisture,2.27% sucrose, and 0.13% sodium chloride. The water activity value found in thecassava root is above the minimum water activity values for the development ofpathogenic microorganisms; thus, this raw material is not microbiologically stable(Chirife and Favetto 1992).

Luna et al. (2013) presented results for themoisture (35.31%) of raw cassava rootswell different from those obtained in this work. These differences may be related tovariations in soil moisture. Maieves (2010) evaluated the moisture content of cassavatubers at various harvest times and concluded that the roots collected in Februaryshowed higher moisture than those collected in the month of May. He says that rootsgrown in sandy soils have an average moisture of 60% (wet basis).

The values of non-reducing sugars in sucrose obtained in this research differ fromthose found by Aguiar et al. (2014), which obtained higher values, about 3.94% inthe root of the frozen Mandiocaba variety. Differences in sugar content vary with the

Table 6.1 Physicochemicalcharacterization of the freshcassava cubes

Analysis Fresh cassava cubes average valuesa

Water activity 0.954 ± 0.00

Moisture (w.b. %)b 60.45 ± 0.03

Sucrose (%) 2.27 ± 0.19

Sodium chloride (%) 0.13 ± 0.02

aMean value ± standard deviationbWet basis


Fig. 6.5 Moisture loss andtotal solids gain kinetics inthe osmotic dehydration ofcassava cubes in ternarysolution

harvest period. Couto (2013) observed that there was a decrease in the total sugarcontent in cassava roots harvested later. The plant’s development cycle consists of fivephysiological phases and in the first phase it needs more energy, producing a highersugar concentration. Rinaldi et al. (2015) studied the effect of different freezing formson cassava roots and concluded that the use of this conservation process causes lesschanges in the structure of the raw material, prolonging the conservation of its initialnutritional characteristics.

Valduga et al. (2011) found significant differences in the sodium levels of fivecassava cultivars (BRS Rosada, Casca Roxa, BRS Dourada, BRS Egg Yolk, andSaracura) harvested at 8 months after planting. The cultivar Casca Roxa showed asignificant content of sodium chloride 0.19% (dry basis); this value was close towhat was obtained in this work (0.13%). The authors concluded that the chemicalcomposition of cassava is specific not only for each cultivar, but also depends,mainly,on associated genetic factors.

6.2.4.2 Osmotic Dehydration Process

Drying Kinetics in the Optimal Condition

After different experimental tests of osmotic dehydration of cassava cubes werechosen the best drying condition for the study. Optimum conditions obtained internary solution of sucrose, sodium chloride, and water were 52 °C, 56%w/w solute,10%w/w sodium chloride, 190 min and 180 rpm. The kinetic parameters result fromthe osmotic dehydration of cassava cubes are presented through the moisture losscurves and solids gains shown in Fig. 6.5.

From the analysis of Fig. 6.5, in the early stages of operation (first 15 min) thehighest gradients of moisture loss and solids gain occurred. After this period, thesolids gain almost reached equilibrium after 30 min of operation. Moisture losscontinued to increase until reaching a maximum value of 24.89% and stabilizedafter 180 min of operation. An unexpected event occurred after 360 min of osmoticdehydration of the cassava cubes. There was a small decline in moisture loss and a


sudden increase in the solids gain of samples, whose parameters were re-establishedin values equal to 22.7 and 16.45% for moisture loss and solids gain, respectively.The solids gain stabilized before the moisture loss probably due to lower internalmass transfer resistance of the solutes (sucrose and salt) as compared to moisture.

The behavior of themass transfer rates ofmoisture and solutes between the cassavacubes and the hypertonic osmotic solution may be associated with the chemical andphysical characteristics of these solutes. Junqueira et al. (2017) have reported thathighmolecularweight solutes such as sucrose are responsible for increasingmoistureloss in the dehydrated product and promote low solids gain. The sucrose promotesan increase in the viscosity of the osmotic solution, which may lead to the formationof a barrier on the vegetable surface, limiting its impregnation in the product (Pereiraet al. 2006). However, lowmolecular weight solutes provide a higher solid gain whencompared to high molecular weight solutes because they are able to penetrate intothe food cell, increasing their concentration in the product (Junqueira et al. 2017;Pereira et al. 2006; Ruiz-López et al. 2011; Sritongtae et al. 2011). Considering theabove reports, sucrose was probably responsible for the greater moisture loss, andsodium chloride by the solids gain in the dehydration process of cassava cubes internary solutions.

High moisture loss and solids gain rates in the early hours of the osmotic dehy-dration process of guava were reported by Castro et al. (2018). Similar results werefound by Silva et al. (2012), when studying the osmotic dehydration of acerola.According to Ramya et al. (2014), the early stages of osmotic dehydration play animportant role because the transport phenomena are faster, causing greater impacton the process progress.

Results of moisture loss and solids gain similar to those found in this researchwere found by Alam et al. (2013) when using binary solution of sodium chloride andwater. They found a final value of 28.42% of moisture loss and 11.24% for the solidsgain in osmotic dehydration of onion under the conditions 25 °C, 6 h of processand concentration salt of 25 °Brix in the solution. However, when using a ternarysolution with 55 °Brix sucrose and 15 °Brix of salt, under these same conditionsof temperature and time, the moisture loss increased to 48.08% and the solids gainincreased slightly to 13.53%. According to these authors, an increase in moistureloss and solids gain occurs as the concentration of the solution increases.

Figure 6.6 shows the diffusion profile over time of sucrose and sodium chlo-ride incorporations for osmotic dehydration of cassava cubes in ternary solution ofsucrose, sodium chloride, and water.

The analysis of the results shown in Fig. 6.6 indicated that the kinetics of sucroseand sodium chloride incorporation presented the same behavior. Sucrose and saltgain occurred more intensely in the first 15 min of the process when it had alreadyincorporated approximately 3% and 1%, respectively. Then, we noticed a slowergain of these two response variables in a time interval of up to 180 min. From 180to 300 min of process, there was again an increase in sucrose and sodium chlorideincorporations, rising to 6% and 3%, respectively. At 300 min, stability in masstransfer rates was observed for all incorporations. At the end of the experiment, theincorporations were approximately 9% for sucrose and 4% for sodium chloride.


Fig. 6.6 a Sucrose and b Sodium chloride incorporations kinetics in the osmotic dehydration ofcassava cubes in ternary solution

In the study of osmotic dehydration kinetics of cassava slices in ternary solution,Carmo et al. (2017) found that in the early hours of the process, the presence of ahigh concentration of sugars provided a rapid mass transfer, leading to greater gainof soluble solids. The sugars balance condition was reached from 200 min with afinal value of 10%.

Similar results were found by Aires et al. (2016) and Castro et al. (2014) forguava osmotic dehydration, and by Borsato et al. (2010) for apple osmotic dehydra-tion. Araújo et al. (2014) studying the process of osmotic dehydration of carrots intemperature of 50 °C, 240 min and solution concentration of 50 °Brix, found solidsincorporation values using sucrose solution, similar to this research, of 22.13%.However, Hadipernata and Ogawa (2016) studying potato osmotic dehydration at20 °C in 8 h with 20% solution concentration, obtained in their research a smallersucrose gain of 1.75%, only.

Mercali (2009), when studying mass transfer kinetics in banana fruit, reported ahigh rate of sodiumchloride incorporation at the beginning of the dehydration processfollowed by lower rates in the final stages of the process. Vázquez-Vila et al. (2009)also observed that solids gain using sodium chloride solution at 17.22 and 26%w/w at25.35 and 45 °C increased at the beginning of the carrot osmotic dehydration process.Silva Júnior et al. (2015) observing that the incorporation of solids in dehydratedgreen beans with sodium chloride solution increased at the beginning of the process.Further, the authors found that the effective diffusivity of the solid increased withthe increase of sodium chloride concentration in the solution from 20 to 26.5%.Regarding the stabilization time of the transfer rate of soluble solids, sucrose, andsodium chloride, Mayor et al. (2006), similarly to the information obtained in thisresearch, found that the balance occurred around 5 h in pumpkin osmotic dehydrationin sodium chloride solutions between 5 and 25% w/w, at 12.25 and 38 °C with timesfrom 0 to 9 h. Kumar et al. (2017) found a solid incorporation content of 4.20%by employing sodium chloride solution in osmotically dehydrated chayote cubes.The conditions used were temperature 35 °C, process time 180 min, 10% sodium


Fig. 6.7 Osmoticallydehydrated cassava cube

chloride concentration, and 1:6 ratio between fruit and solution. Figure 6.7 illustratesthe cassava cube osmotically dehydrated on the specific condition.

Moisture and Total Solids Effective Diffusivities Estimation

Thedeterminationof themoisture and solutesmass transport parameter in theosmoticdehydration of cassava cubes was carried out using the empirical model proposed byAzuara et al. (1992). Initially, a linear regression related to moisture loss, solids gain,and sucrose and sodium chloride incorporations as a function of time, representedby t/ML, t/SG, t/NaCl, and t/Suc was performed. Figure 6.8 presents the linearizedexperimental results of these parameters for the determination of parameters of the(Eqs. 6.5–6.8).

From the analysis of the analyses of Fig. 6.8, we can see that the model usedsatisfactorily represented the experimental data for the four studied variables (in theselinear regressions the correlation coefficients (R2) were varied from 0.943 to 0.999).From the results of the fitted parameters, it was possible to determine diffusivitiesof moisture, solids gain, sucrose, and sodium chloride for osmotic dehydration ofcassava cubes in the desired optimum condition. The values of these parameters arepresented in Table 6.2.

By analyzing Table 6.2, the Azuara et al. (1992) model presented relative meanerror (E) ranging from 3.4 to 22.2%, and determination coefficients (R2) close to1.00 for all parameters indicating a good fit to the experimental data.

According to Table 6.1, the constants of sodium chloride (S3) and sucrose (S4)incorporations and the effective diffusion coefficient showed similar values, indi-cating that these two solutes were incorporated with the same velocity into the dehy-drated cassava cubes. This fact probably occurred due to thematerial structure aswellas the competition between the fluxes of the two solutes during the process. Sincethe molecular weight of the salt is lower than the sucrose, it spontaneously enters theplant cell, resulting in a reduction in the sucrose mass transfer coefficient. Further,the total solid gain velocity constant (S2) was higher than the moisture loss constant


Fig. 6.8 Comparison between the experimental and theoretical (Azuara et al. 1992) results of themoisture loss, solids gain, and sodium chloride and sucrose incorporations as a function of time

(S1). The absorption rate of total solids in the osmotically dehydrated cassava cubeswas about 63% higher than the water outlet velocity, resulting in the higher averageeffective diffusivity of the total solids in relation to moisture effective diffusivity.This behavior is probably related to the amount, type, and concentration of solutesused in the osmotic solution and the operating temperature.

Comparison between the effective diffusivity data cited in the literature is acomplicated task due to the different estimation methods and various modelsemployed, associated with changes in the chemical composition of the food andits physical structure. In addition, effective diffusivity varies throughout the processand the osmotic moisture gradient is not constant (Azoubel and Da Silva 2008;Mercali et al. 2011).

The effective diffusivities values for moisture and solids transport obtained in thisresearch were of the order of 10−8 m2/s, in which the average value of these transportparameters for osmotic dehydration of cassava cubes was 1.88 × 10−8 m2/s. Valuesfrom the same order of magnitude were obtained for several osmotically dehydratedvegetables such as carrot (Sutar and Prasad 2011),mango (Arias et al. 2017) nectarine(Rodríguez et al. 2013), and banana (Góis et al. 2010).


Table 6.2 Fitted parametersof the Eqs. 6.5–6.8 in thebest-operating conditions

Variables Parameters Value

Moisture loss T (min) 360

MLmod∞ (%) 27.967

S1 8.265 × 10−4

R2 0.995

E (%) 8.407

Deff (m2/s) 1.99 × 10−8

Solids gain t (min) 360

SGmod∞ (%) 12.923

S2 22.521 × 10−4

R2 0.999

E (%) 3.389

Deff (m2/s) 2.77 × 10−8

Sodium chloride incorporation t (min) 480

NaClmod∞ (%) 4.489

S3 1.883 × 10−4

R2 0.966

E (%) 15.678

Deff (m2/s) 1.36 × 10−8

Sucrose incorporation t (min) 480

Sucmod∞ (%) 9.573

S4 1.802 × 10−4

R2 0.943

E (%) 22.224

Deff (m2/s) 1.40 × 10−8

MLmod∞ = value of the moisture loss at equilibrium obtained by the

model; SGmod∞ = value of the solids gain at equilibriumobtained by

themodel; INaClmod∞ = value of the sodium chloride incorporation

at equilibrium obtained by the model; ISucmod∞ = value of thesucrose incorporation at equilibrium obtained by the model

Arias et al. (2017) and Rodríguez et al. (2013) associated the high diffusion coef-ficients with the temperature used in the osmotic dehydration process. Escobar et al.(2007) explained that high values of diffusivities are due to the effect of measure-ments that cause cell death of plant tissue before osmotic pretreatment, facilitatingmass transfer. The authors cite as an example bleaching. Maldonado et al. (2008)justified that high diffusion coefficients are linked to high moisture loss values.

Góis et al. (2010) reported that the differences in the order of magnitude of diffu-sivities probably derive from the type of geometry used in the material. Allali et al.


(2008) and Corzo et al. (2008) stated that the magnitude of effective moisture diffu-sivity for food materials varies in the range of 10−8 to 10−12 m2/s. This variation isexplained by the type of experimental analysis, composition and physiology of thefood and the method of data treatment.

Azarpazhooh and Ramaswamy (2012) observed that the effective moisture andsolid diffusivities in osmotic dehydration of apple cylinders reachedmaximumvaluesat temperatures of 50 °C and 50 °Brix solution concentration, close to the resultspresented in this work for osmotic dehydration of cassava cubes. Assis et al. (2017)found that the higher temperature (60 °C) promoted higher diffusion of water andsolute in the osmotic dehydration process of apple cubes. This behavior was alsoobserved by Abbasi Souraki et al. (2012) in osmotically dehydrated green beansranging from 30 to 50 °C.

Lower diffusivity results (order 10−9 m2/s) were obtained by Rodríguez et al.(2017) in plum osmotic dehydration. Assis et al. (2017) in osmotically dehydratedapple cubes, Singh et al. (2008) for pretreated carrot cubes in sodium chloridesolution, Hamedi et al. (2018) on osmotic dehydration of ultrasound-assisted agargel cylinders, and Azarpazhooh and Ramaswamy (2012) analyzing osmoticallydehydrated apple cylinders.

Cassava cubes were dehydrated in ternary solution of sucrose, salt, and waterat high concentration (56% w/w) combined with high temperature (52 °C). Hightemperatures increase the solubility of solutes and cause changes in plant cell struc-ture, increasing the diffusion rate of sodium chloride and sucrose into the cassavacube compared to water diffusion. Several authors have observed solid diffusivityvalues greater than water diffusivity in osmotic dehydration of vegetables (Ariaset al. 2017; Azarpazhooh and Ramaswamy 2012; Assis et al. 2017; Hamedi et al.2018; Zúñiga and Pedreschi 2012). Assis et al. (2017) found lower values of waterdiffusivity in relation to total solids in osmotic dehydration of apple cubes in sucroseand sorbitol solution, at temperatures ranging from 25 to 60 °C. They report that thesucrose solution has high viscosity due to the high molecular weight of the solute,making it difficult to transport water between the product and the solution.

Arias et al. (2017) found lower effective moisture diffusivity values in sleeves at50 °C by increasing the sucrose solution concentration from 45 to 60 °Brix. Theyexplained that this behavior is due to the fact that the more dilute the solution canpenetrate better into tissues, as opposed to concentrated solutions that are moreviscous and can form a sucrose surface layer, making it difficult for water to escapefrom thematerial. Similarly,Assis et al. (2017) found lower values ofwater diffusivitycompared to solids in the osmotic dehydration of apple cubes in sucrose and sorbitolsolution, at temperatures ranging from 25 to 60 °C. They proved that the type ofosmotic agent used, as well as its molecular weight, influenced the diffusion ofwater, obtaining smaller diffusivities when the osmotic dehydration was performedwith sucrose solution. The authors explained that sucrose solution is more viscousthan sorbitol and that sucrose has higher molecular weight, making it difficult totransport water between the product and the solution.

Hamedi et al. (2018) observed higher values of solid diffusivity in relation towater,in the osmotic dehydration of an agar gel cylinder, in sucrose solution in an ultrasonic


Fig. 6.9 Dimensions ofmoisture as a function oftime for drying process of innatura and osmoticallydehydrated cassava cubes atvarious process temperatures

bath (100% power). The authors explained that increasing the concentration of theosmotic solution resulted in greater absorption of solids in the sample due to theincreased osmotic pressure gradient between the solution and the dehydrated product.

Finally, we state that migration rates of total solids and moisture content, asshown in Fig. 6.6, and demonstrate that total solid gain reaches equilibrium morerapidly in relation to moisture loss in cassava cubes. This indicates a greater diffi-culty in migrating water from the solid matrix to the surrounding osmotic solutionas compared to its transfer of solutes (sucrose and salt) into the solid. Other consid-erations, such as the higher amount of moisture in migration, the synergistic effectof salt for the penetration of sucrose in the vegetal membrane, and others, can clarifythis difference of values between the average effective diffusivities of total solids andhumidity.

6.2.4.3 Convective Drying Process

Drying Kinetics for Cassava Cubes Dried in Natura and OsmoticallyDehydrated

Figure 6.9 shows the dimensionless moisture content as a function of time for twodifferent drying physical situations: dried in natura and osmotically dehydratedcassava cubes at the various drying air temperatures.

By comparing the curves for the two sample types it is evident that the shortestdrying time was detected for the dried samples without pretreatment. The in naturacassava cube dried at 70 °C presented the shortest drying time (≈12 h), and theosmotically dehydrated cassava cubes at the three temperatures had equal dryingtimes, totaling 24 h of process, twice from the in natura sample time dried at 70 °C.Castiglioni et al. (2013) reported that the shortest convective drying time of cassavafibrous mass was reached at the highest temperature studied at 67 °C.


Analyzing Fig. 6.9 for drying kinetics of fresh material dried at 50 and 60 °C,a similar trend is observed. However, by checking the drying curves separately forthe fresh sample at 50 and 70 °C and 60 and 70 °C, another type of behavior wasobserved, as the temperature increased, the curve became sharper.

This, the time required to reduce the moisture content to an almost equilibriumcondition is reduced too, as stated above. On the other hand, more than 50% of themoisture of fresh cassava cubes was removed during the first 5 h of drying at 70 °C,and during the first 8 h for drying at 50 and 60 °C. The remaining water contentwas eliminated over a comparatively longer period. This probably occurred due tothe shrinkage of the cube with the corresponding pore reduction that increased theresistance of water transport during the drying process (Pereira et al. 2009).

Osmotically dehydrated samples took longer drying times when compared tofresh samples at three temperatures. It was observed that the moisture of the osmoti-cally dehydrated material decreased rapidly at higher temperatures, generating morepronounced curves by increasing this parameter. More than 50% of moisture of theosmotically pretreated materials at the three temperatures analyzed were removedwithin the initial 10 h of the drying process.

Pavkov et al. (2011) observed a similar result when studying the drying kineticsof osmotically dehydrated nectarine seeds at 60 °C. Kowalski and Łechtanska (2015)also reported similar behavior when comparing the drying time for fresh beet andosmotically dehydrated in 25% NaCl solution at 65 °C.

The authors reported that the longer drying time in the dehydrated material wasdue to the crystallization of sucrose contained in the beet, and the impregnation of thesolutes on the food surface. The substances acted as a barrier to moisture output fromthe product. However,Kowalski andMierzwa (2011) stated that vegetables submittedto the osmotic dehydration process should dry out faster than fresh vegetables dueto their lower moisture content. Osidacz and Ambrosio-Ugri (2013) found that theosmotically dehydrated eggplant in 10% NaCl solution achieved a shorter dryingtime at 70 °C compared to in nature eggplant dried at the same temperature.

The drying rates of in natura and osmotically dehydrated cassava cubes as a func-tion of time for all drying condition are presented in Fig. 6.10. This figure reveals thatthere is no constant drying rate period for both types of materials studied, and thatthe entire drying process occurs in the decreasing rate period, being represented bythe first and second phase of the falling drying rate with internal migration control ofmoisture. Several authors have also observed this behavior for various types of vegeta-bles, such as Akoy (2014), Cabrera et al. (2016), Kek et al. (2013), and Rayaguruand Routray (2012).

In the period of decreasing rate, it gradually decreases due to decreased evapora-tion of water inside the material; the process is controlled by the moisture migrationmechanism inside the material, so that a dry layer begins to form on the productsurface. After the removal of bound moisture from the food, the phase change ofthe various types of intrinsic moisture in the food occurs, which are bound to thecomponents by physical and chemical forces (Pavkov et al. 2011).

The influence of selected drying air temperature levels and sample type on dryingkinetics is clearly visible in the images shown in Fig. 6.6. By comparing the drying


Fig. 6.10 Drying rate as a function of moisture content of in natura and osmotically dehydratedcassava cubes at various process temperatures

rate for both sample types at all temperatures analyzed. It should be noted thatthe highest drying rates were achieved in fresh materials due to their higher initialmoisture content compared to osmotically dehydrated samples. Kaya et al. (2016)researching the drying of fresh and osmotically pretreated Kiwui found a higherdrying rate in fresh samples at higher temperatures. They justified this behavior, asdue to the high moisture value of the fresh samples and explained that the increasein the temperature difference between the drying air and the product acceleratesthe water migration. The larger temperature difference between drying air and freshcubes increased the convective heat transfer coefficient, influencing the heat andmasstransfer rates. Several authors have reported similar results for the drying of freshand osmotically dehydrated fruits such as figs (Babalis and Belessiotis 2004; Guptaand Patil 2014; Sacilik and Elicin 2006; Togrul 2005).

The impregnation of sucrose and sodium chloride in dehydrated material duringosmotic pretreatment of cassava cubes was probably responsible for the decreasein the drying rate. Similar results were verified by several authors in their studieswith the drying of osmotically pretreated vegetables, such as Pavkov et al. (2011)for nectarine seeds, Osidacz and Ambrosio-Ugri (2013) for eggplant, Dionello et al.(2009) for pineapple, Kaya et al. (2016) for carrots, Andrés et al. (2007) for mango


and Sanjinez Argandoña et al. (2005) for guava, Azoubel et al. (2009) for cashewnuts, Guiné (2006) and Park et al. (2002) for pear, Korsilabut et al. (2010) for melon,Riva et al. (2005) for apricot, Sankat et al. (1996) for bananas, and Singh and Gupta(2007) for carrots.

Dionello et al. (2009) working with drying fresh pineapple and dehydrated insolutions of sucrose and invert sugar explained that the low humidity rates found inthe osmotically dehydrated samples occurred due to the concentration of the osmoticsolution and the type of solute used in it. Lower molecular weight solutes such asglucose and fructose found in invert sugar penetrate more easily than sucrose into thetissues of the top layer of the vegetable, entering more intensely to make it difficultto draw water inside the food, thus reducing the drying rate.

Andrés et al. (2007) and Sanjinez Argandoña et al. (2005) found that the presenceof sucrose molecules in pretreated mango and guava tissue, respectively, increasedthe internal resistance to water diffusion.

Pavkov et al. (2011), studying drying of nectarine seeds in natura and osmoticallydehydrated, explained that the difference between the partial pressures of watermolecules on the surface of the fresh material and in moist air is greater. Suchbehavior promotes a high convective mass transfer coefficient at the surface of thematerial, generating faster evaporation and increased drying rate. The reduction inmoisture of the osmotically pretreated sample generates a decrease between thepartial pressures of water molecules on the material surface and in the moist airduring the drying process. As the solute concentration in the plant tissue increases,the effective moisture diffusivity decreases, this increasing the drying time of theosmotically dehydrated sample.

The parameters that characterize the convective drying of the cassava cubes innatura and osmotically dehydrated are presented in Table 6.3. The humidity of bothtypes of samples was obtained dynamically, weighing the cubes until reaching aconstant weight in the convective drying process. The parameter studied was thedrying air temperature, which ranged from 50 to 70 °C.

As stated earlier, there was no constant drying rate period for both types ofmaterials. It can be seen from Table 6.3, through the transition moisture content(M tr) values, that there were two periods of decreasing drying rate with internalmoisture migration control, before that osmotically dehydrated and fresh cassavacubes reach the final moisture content (Mf). The times for the 1st stage and the 2ndstage correspond to the periods of the first and second phase of the decreasing rate,respectively.

Table 6.3 shows that the in natura samples reached equilibrium moisture contentin a shorter time than the osmotically dehydrated samples, as shown in Fig. 6.10.According to this table, the moisture contents found for the fresh and osmoticallydehydrated cassava cubes at all temperatures analyzed were below 13% on a wetbasis. These values are within the values established by Standard Resolution RDCNo. 23 of December 14, 2005 (Brazil 2005). This regulation establishes tolerancelimits for starch products derived from cassava root, which require moisture valuesof less than 14% and 15% on a wet basis for starch and tapioca, respectively.


Table6.3

Characterizationof

convectiv

edrying

ofcassavacubesin

natura

andosmotically

dehydrated

Sample

T(°C)

Ma 0

Mtr

Ma f

t tr1ststage

(h)

t2ndstage(h)

Totaltim

e(h)

(d.b.)

(w.t.)

(d.b).

(w.t.)

(d.b.)

(w.t.)

Innatura

501.38

0.58

1.11

0.53

0.07

0.065

120

21

601.67

0.63

1.09

0.52

0.06

0.060

218

20

701.88

0.65

1.00

0.50

0.05

0.051

210

12

Osm

otically

dehydrated

500.74

0.43

0.57

0.36

0.15

0.128

123

24

600.76

0.43

0.57

0.36

0.11

0.102

123

24

700.98

0.49

0.60

0.37

0.09

0.081

222

24

T=

Temperature;M

0=

Initialmoisturecontent;M

tr=

Transition

moisturecontent;M

f=

Finalm

oisturecontent;t=

Tim

ea Totalaveragevaluein

triplicatein

thedryandwetbasis,tr

=transitio

ntim

e


Table 6.4 Fitted parameters of the Fick’s model at different convective drying condition

Temperature (°C) Parameter (Deff × 1010 m2/s) in natura cube Osmotically dehydrated cube

50 5.45 2.75

60 5.83 3.61

70 9.85 4.82

FromTable 6.3, we can see that the equilibriummoisture content of the fresh driedcubes was almost 50% lower than cubes dried by hybrid process. This fact occurreddue to the high concentration of solids incorporated in thematerial during the osmoticdehydration step, forming an obstacle for water outlets in the convective drying step.The in natura cube dried at 70 °C reached the lowest equilibrium moisture content(5.11% on wet basis). A similar result was obtained by Pornpraipech et al. (2017)during drying process of cassava rectangular slices at 80 °C. However, Lugo et al.(2018) found 12% final moisture content for dry cassava at 70 °C in a hybrid dryingsystem.

Correa et al. (2017) observed lower equilibrium moisture content values in freshdried samples and higher samples in osmotically dehydrated samples in sucrose solu-tion when drying pineapple at 70 °C assisted by ultrasound. They justified that dryingat high temperatures probably caused the caramelization of the incorporated sugars,establishing additional barriers to the outflow of water from the solid pineapplematrix. As in this paper, other authors studying the drying of fresh and osmoticallypretreated products also found lower final moisture content values in fresh products(Osidacz and Ambrosio-Ugri 2013; Kaya et al. 2016; Singh and Singh Hathan 2016).In general, it is observed in Table 6.3 that the drying times of the in natura driedcubes were also shorter than the drying times of the osmotically pretreated cubes atthe same temperatures, decreasing with increasing temperature. However, for osmot-ically dehydrated cassava cubes, the total time was equal at the three temperatures.These results agree with those obtained by Kaya et al. (2016), who observed longerdrying times in osmotically dehydrated carrot slices in sucrose and sodium chlo-ride solution at 35 °C, while studying the drying of fresh and osmotically pretreatedcarrots. Garcia-Noguera et al. (2010) found drying times of 612 and 891 min forstrawberries dried in natura and osmotically dehydrated previously (50% sucrosesolution), respectively.

Moisture Effective Diffusivity Estimation

In this research, the simplified diffusional model (Fick’s 2nd Law) was fitted toexperimental data of convective drying of fresh and osmotically dehydrated cassavacubes for long drying times, without considering shrinkage. The aim was to estimatethe moisture diffusion coefficient.


Table 6.5 Variance analysis for final moisture content of in natura cassava cubes

Final moisture content

Source SS DF MS p-Value* Fc F tab

Samples 1.0860 2 0.5430 1.1460 1.1460 6.94

Temperatures 2.8152 2 1.4076 2.9708 2.9708 6.94

Error 1.8952 4 0.4738

Total 5.7964 8

SS = sum of squares; DF = degrees of freedom; MS = mean square; Fc = Calculated F; F tab =Tabulated F; *Statistically significant at p < 0.05 level

Table 6.4 presents the values of the effective moisture diffusivity obtained in thisnon-linear regression as applied to convective drying at temperatures 50, 60, and70 °C.

According to Table 6.4, an increase of the effective moisture diffusivity withincreased drying temperature for the two samples analyzed was observed. Freshsamples showed higher effective diffusivity values than osmotically dehydratedsamples due to the higher initial moisture content. The results obtained are in agree-ment with those reported in the literature (Singh and Gupta 2007; Aires et al. 2018;Ruiz-López et al. 2010).

The osmotically dehydrated cassava cubes presented lower diffusivity values dueto their lower initial moisture content and high concentration of incorporated solidsduring the drying process. Osmotic pretreatment resulted in a reduction of free waterin these samples, contributing to the reduction of the mass transfer rate in convectivedrying.

Aires et al. (2018) and Zuñiga and Pedreschi (2012) reported that solids gain cancause the formation of a barrier, making it difficult tomass transfer within the productduring convective drying.

Dehghannya et al. (2018) observed that potato cubes pretreated in solutions withhigher sucrose concentrations (50 and 70%) showed lower effective moisture diffu-sivity values than samples pretreated in solutions with lower sucrose concentrations(10 and 30%), after convective drying; they explained that the use of this high soluteconcentration in osmotic solutions caused changes in potato texture, which in turnmade it difficult to remove moisture from the product. According to Dehghannyaet al. (2015), osmotic solutions in high concentration can degrade the texture of thevegetable and stop the moisture diffusion during drying.

Determination of the Best Drying Condition

The determination of the best drying condition was based on the moisture content ofthe product and the operating time for both types of samples, according to the datapresented in Table 6.5.


Table 6.6 Tukey test forcomparison of averages finalmoisture content of cassavacubes and dried by hybridprocess

Temperatures (°C) Average final moisture content1

50 12.79(a)

60 10.22(ab)

70 8.05(b)

1Means followed by the same lowercase letter in the same columndo not differ from each other by the Tukey test at 5% probability

According to Table 6.4, it is observed that for the fresh material, the drying timeat 70 °C was shorter compared to the other drying times of fresh samples dried at50 and 60 °C. However, in terms of final moisture content, there is a proximity ofthe results obtained for fresh samples at the three temperatures analyzed. Thus, ananalysis of variance (ANOVA) was performed at a significance level of 5%, to verifyif there was a significant difference between the values of these parameters at thethree temperatures.

According to the analysis of variance for final moisture content of the freshsamples shown in Table 6.5, it can be seen that there was no significant differencebetween samples and temperatures (p > 0.05), with calculated F values lower thanthe tabulated F. Thus, the best drying condition for fresh cassava cubes was at 70 °C,as it presented a shorter drying time (12 h).

The Tukey test was used to verify the differences between the average final mois-ture content of the subjected to hybrid process (osmo-convective drying) cassavacubes at the three temperatures analyzed, as shown in Table 6.6.

By Tukey test, the average final moisture content of the products at temperaturesbetween 50 and 60 °C and 60 and 70 °C showed no significant difference. However,between 50 and 70 °C, there was a significant difference, so the temperature of 60 °Cwas chosen for convective drying of the osmotically dehydrated cassava cubes.

As a final comment, despite the importance of the statistical methodology appliedhere in aiming to obtain the best convective drying condition of in natura and osmot-ically dehydrated cassava cubes, this is a food product. In this case, new statisticaltests taking account nutritional aspects of the dried cassava cubes are strongly recom-mended, in order to obtain the best drying conditions based on the final moisturecontent, energy consumed nutritional and sensory parameters.

6.2.4.4 Evaluation of the Product Obtained by the Hybrid Process

To verify some changes that the hybrid process (osmotic dehydration and convectivedrying) can provoke on the final product, the physical–chemical characterizationof this material was carried out, comparing the results with the physical–chemicalinformation obtained for the cubes only dried at 60 °C and in natura cubes.

Table 6.7 presents the chemical composition results of the cassava cubes in naturaand osmotically dehydrated and dried at 60 °C.


Table 6.7 Composition ofcassava cubes in natura andosmotically dehydrated anddried at 60 °C

Parameter In natura Cassavacubes

Cassava cubesdried at 60 °C

Water activity 0.954 ± 0.00 0.232 ± 0.00

Sucrose (g/100 g ms)

5.745 ± 0.60 16.894 ± 0.42

Sodium chloride(g/100 g m s)

0.340 ± 0.05 5.946 ± 0.06

Mean value ± standard deviation

The hybrid moisture reduction process (combination of osmotic dehydration andconvective drying) produced a material with desirable shelf life, as it reduced thewater activity value for values below 0.6, which prevents the pathogenic microor-ganisms’ growth that is responsible to deteriorate the food (Chirife and Favetto 1992).The values of water activity close to those presented by the osmotically dehydratedand dried cubes were found by Silva et al. (2013). These authors found water activityvalue of 0.180 in tapioca flour. Vieira et al. (2010) found a water activity value of0.310 for sweet biscuits prepared with 15% cassava starch. The water activity reduc-tion is more pronounced during convective drying, because the free water in foodis evaporated, reducing the water vapor pressure, which acts on the food (Morenoet al. 2010). During the osmotic dehydration process, the reduction in water activityoccurs slowly, because diffusion phenomena occur in an aqueous medium.

Sodium is an alkali metal that constitutes approximately 40% of salt, i.e., inmean, 1 g salt contains 0.4 g of sodium (He andMacgregor 2010). The sodium value(2,136 mg) found in 100 g of the osmotically dehydrated and dried cassava cube at60 °C is close to the daily nutrient reference values established in Standard RDC nº360, on December 23, 2003. This standard reports the nutritional values of packagedfoods and establishes 2,400 mg sodium as the daily nutrient reference value (Brazil2003). The 2,136 mg value represents 89% sodium in a food portion. The maximumsodium limit recommended by the World Health Organization (WHO) is 2 g per day(Sarno et al. 2013). Then, the sodium content found in 100 g of the osmotically driedcassava cube at 60 °C exceeded the maximum sodium limit recommended byWHO.

According to the data in Table 6.7, sucrose in the osmotically dehydrated cube,and dried at 60 °C showed a value three times greater than its initial value. However,sodium chloride showed a higher incorporation power than sucrose, showing a 17-fold increase in its initial value.

Solutes with a higher molecular weight such as sucrose have lower mass diffusiv-ities due to its high molecule size, allowing less mobility in food materials throughexisting pores and free spaces of plant tissues.

Sugars are generally hydrophilic, unchargedmolecules that exhibit slow diffusionrates (Ruiz-López et al. 2011; Agnieszka and Andrzej 2010; Udomkun et al. 2015).Udomkun et al. (2015) observed high concentrations of glucose, fructose, and lowersucrose contraction value in osmotically pretreated and dried papaya cubes. Theyexplained that this factmay be related to the solute lowermolecular weight of glucose


and fructose that penetrate more easily in the vegetable’s superficial layer. Brandãoet al. (2003) found higher sucrose concentrations in osmotically dehydrated andsun-dried mangabas when compared to the mangaba in natura.


In this chapter, the drying process of food has been studied. Emphasis is given to thehybrid drying process (combination of osmotic dehydration and convective drying)as applied to cassava cubes. The study encompasses two analyses: experimental andtheoretical (used to process parameters estimation). Herein transient results of themoisture loss solid gain and sodium chloride and sucrose incorporation along theprocess are presented.

From the obtained results it can be concluded that

(a) The fresh cassava cubes showed 60.45% moisture (wet basis), 2.27% sucrose,and 0.13% sodium chloride.

(b) The study of osmotic dehydration kinetics in the optimized condition showedthat the moisture loss reached equilibrium in 180 min of process, the total solidsgain in 30min, and the incorporation of sodium chloride and sucrose in 300min.

(c) The highest values of the osmotic dehydration kinetics study parameters were24.90% moisture loss, 16.46% solids gain, 8.87% sucrose incorporation, and4.07% sodium chloride.

(d) The average effective moisture diffusivities, solid gain, incorporation of sodiumchloride and sucrose presented results equal to 1.99 × 10−8 m2/s, 2.77 × 10−8

m2/s, 1.36 × 10−8 m2/s, and 1.40 × 10−8 m2/s, respectively.(e) Convective drying of fresh cassava cubes presented shorter drying times than

previously osmotically dehydrated cassava cubes due to the presence of sucroseon the outer surface of the cubes making it difficult to remove moisture fromthe inside of the material.

(f) The entire convective drying process of the fresh and osmotically dehydratedcubes at 50, 60, and 70 °C occurred during the falling moisture migration rate.

(g) The fresh samples in convective drying showed higher drying rates than theosmotically pretreated material in sucrose solution and sodium chloride.

(h) The convective drying temperatures that produced a material with lower finalmoisture content was 70 °C for fresh cassava cubes and 60 °C for osmoticallydehydrated cassava cubes.

(i) The average effectivemoisture diffusivities obtained through the simplified Fickmodel for the convective drying of cassava cubes varied from2.75× 10−10 m2/s(Osmotically dehydrated cube at 50 °C) to 9.85 × 10−10 m2/s (in natura cubeat 70 °C).

(j) Cassava cubes dehydrated osmotically and dried at 60 °C showed 11%humidity,16.89% sucrose, and 5.94% sodium chloride on a dry basis


(k) The good results obtained with the cassava cubes after submitted to the hybridprocess of osmotic dehydration and convective drying proved that it can be usedin food production as raw material for the development of new cassava-basedproducts.

Acknowledgments The authors thanks to CNPQ, CAPES and FINEP (Brazilian ResearchAgencies) for their financial support.

References

Abbasi Souraki, B., Ghaffari, A., Bayat, Y.:Mathematical modeling ofmoisture and solute diffusionin the cylindrical green bean during osmotic dehydration in salt solution. J. Food Process. Preserv.90(1), 64–71 (2012)

Agnieszka, C., Andrzej, L.: Rehydration and sorption properties of osmotically pretreated freeze-dried strawberries. J. Food Eng. 97(2), 267–274 (2010)

Aguiar, R., Cunha, R.L., Cunha, E.F.M., Rego, J.Y.N.: Chemico-physical characterization ofmandiocaba roots. In: Proceedings of the Scientific Initiation Seminar and 2nd Post-graduationSeminar of Embrapa East Amazon, pp. 1–4, Embrapa, Belém (2014). (In Portuguese)

Aires, J.E.F., Silva, W.P., Aires, K.L.C.A.F., Júnior, A.F.S., Castro, D.S., Silva, C.M.D.P.S.: Guavaosmotic dehydration: description by two-dimensional diffusion models considering shrinkageand variations in process parameters. Int. J. Food Eng. 12(6), 527–536 (2016)

Aires, J.E.F., Silva, W.P., Aires, K.L.C.A.F., Júnior, A.F.S., Silva, C.M.D.P.S.: Convective dryingof osmo-dehydrated apple slices: kinetics and spatial behavior of effective mass diffusivity andmoisture contente. Heat Mass Transfer 54(4), 1121–1134 (2018)

Akoy, E.O.M.: Experimental characterization and modeling of thin-layer drying of mango slices.Int. Food Res. J. 21(5), 1911–1917 (2014)

Alam,M.M., Islam,M.N., Islam,M.N.: Effect of process parameters on the effectiveness of osmoticdehydration of summer onion. Int. Food Res. J. 20(1), 391–396 (2013)

Allali, H., Marchal, L., Vorobiev, E.: Blanching of strawberries by ohmic heating: effects on thekinetics of mass transfer during osmotic dehydration. Food Bioproc, Technol. 3, 406–414 (2008)

Andrés, A., Fito, P., Heredia, A., Rosa, E.M.: Combined technologies for development of high-quality shelf-stable mango products. Dry. Technol. 25(11), 1857–1866 (2007)

AOAC (Association of Official Analytical Chemists): Official Methods of Analysis. 16th edn.Washington, USA (1995)

Araújo, P.M., Fonseca, J.R.L., Magalhães, M.M.A., Medeiros, M.F.D.: Drying of carrosts in sliceswith osmotic dehydration. Afr. J. Biotechnol. 13(30), 3061–3067 (2014)

Arias, L., Perea, Y., Zapata, J.E.: Kinetic of the mass transfer process in the osmotic dehydration ofmango (Mangifera indica L.) var. TommyAtkins as function of the temperature. Inform. Tecnoló.28(3), 47–58 (2017)

Assis, F.R.,Morais, R.M.S.C.,Moraes, A.M.M.B.:Mathematical modelling of osmotic dehydrationkinetics of apple cubes. J. Food Process. Preserv. 41(3), 1–16 (2017)

Assis, F.R., Morais, R.M.S.C., Morais, A.M.M.B.: Osmotic Dehydration combined with freeze-drying of apple cubes and comparison with microwave drying and hot air drying. Adv. Food Sci.Eng. 2(1), 39–47 (2018)

Azarpazhooh, E., Ramaswamy, H.S.: Modeling and optimization of microwave osmotic dehydra-tion of apple cylinders under continuous-flow spray mode processing conditions. Food Bioproc.Technol. 5, 1486–1501 (2012)


Azoubel, P.M., Da Silva, F.O.: Optimisation of osmotic dehydration of “Tommy Atkins” mangofruit. Int. J. Food Sci. Technol. 43(7), 1276–1280 (2008)

Azoubel, P.M., El-Aouar, A.A., Tonon, R.V., Kurozawa, L.E., Antonio, G.C., Murr, F.E.X., Park,K.J.: Effect of osmotic dehydration on the drying kinetics and quality of cashew apple. Int. J.Food Sci. Technol. 44(5), 980–986 (2009)

Azuara, E., Beristain, C.I., Garcia, H.S.: Development of a mathematical model to predict kineticsof osmotic dehydration. J. Food Sci. Technol. 29(4), 239–242 (1992)

Babalis, J.S., Belessiotis, G.V.: Influence of drying condition on the drying constants and moisturediffusivity during the thin layer drying of figs. J. Food Eng. 65(6), 449–458 (2004)

Borsato, D., Moreira, I., Silva, R.S.S.F., Bona, E., Nóbrega, M.M., Pina, M.V.R., Moreira, M.B.:Simulation of the multicomponent diffusion during the osmotic dehydration of apple: determi-nation of the diffusion coefficients by the simplex method, Semina: Ciências Agrárias, 31(2),391–404(2010). (In Portuguese)

Brandão, M.C.C., Maia, G.A., Lima, D.P., Parente, E.J., Campello, C.C., Nassu, R.T., Feitosa, T.,Sousa, P.H.M.: Physical and chemical, microbiological and sensorial analysis of mango fruitssubmitted to osmotic-solar dehydration. Rev. Braz. Frutic. 25(1), 38–41 (2003). (In Portuguese)

Brazil. Ministry of Agriculture, Livestock and Supply. Normative Instruction n° 23, December 14,2005. Approves the Technical Regulation on Identity and Quality of Starchy Products derivedfrom cassava root. Official Journal of the Federative Republic of Brazil, Brasília, p. 5 Section 1(2005). (In Portuguese)

Brazil. Ministry of Health. National Health Surveillance Agency. Standard no. 360, December 23,2003. Technical regulation on nutritional labeling of packaged foods, 9 p. Ministry of Health,National Health Surveillance Agency, Brasília (2003)

Cabrera, E., Sanjuán, N., Panadés, G., Cruz, L.: Influence of osmotic pretreatment on the convectivedrying of guava. Int. Food Res. J. 23(4), 1623–1628 (2016)

Carmo, A.S., Alves, T.C.O., Martins, P.C.: Study of the kinetics of osmotic dehydration of maniocslices. Rev. Braz. Agrotecnol. 7(2), 266–272 (2017). (In Portuguese)

Castiglioni, G.L., Silva, F.A., Caliari, M., Soares Júnior, M.S.: Mathematical modeling of dryingprocess of fibrousmass of cassava.Rev.Braz. deEngenhariaAgrícola eAmbiental 17(9), 987–994(2013). (In Portuguese)

Castro, D.S., Nunes, JS., Júnior, A.F.S., Aires, J.E.F.A., Silva, W.P., Gomes, J. P.: Influence oftemperature on the process of dehydration osmotic pieces of guava, Rev. Geintec 4(5)1413–1423(2014). (In Portuguese)

Castro, D.S., Silva, W.P., Gomes, J.P., Aires, J.E.F., Aires, K.L.C.A.F., Junior, A.F.S.: Developmentand sensory evaluation of osmotically dehydrated guava. Braz. J. Food Technol. 21(e2016013),1–8 (2018). (In Portuguese)

Chicherchio, C.L.S.: Cassava and major derivatives. In: CONAB. Perspectives for Agriculture:Crop Data 2014/15, pp. 106–117. CONAB, Brasília (2014)

Chirife, J., Favetto, G.J.: Some physico-chemical basis of food preservation by combined methods,Food Res. Int., Oxford 25(5), 389–396 (1992)

Corrêa, J.L.G., Rasiab, M.C., Muletc, A., Cárcelc, J.A.: Influence of ultrasound application onboth the osmotic pretreatment and subsequent convective drying of pineapple (Ananas comosus).Innovative Food Sci. Emerg. Technol. 41, 284–291 (2017)

Corzo, O., Bracho, N., Alvarez, C.: Water effective diffusion coefficient of mango slices at differentmaturity stages during air drying. J. Food Eng. 87(4), 479–484 (2008)

Couto, E.M.: Characterization of Cassava cultivars from the semi-arid region of Minas Gerais infour harvest seasons. Doctoral Thesis in Food Sciences, Federal University of Lavras, Lavras,Brazil (2013). (In Portuguese)

Crank, J.: The Mathematics of Diffusion, 2nd edn. Clarendon, Oxford (1975)Dehghannya, J., Gorbani, R., Ghanbarzadeh, B.: Effect of ultrasound-assisted osmotic dehydrationpretreatment on drying kinetics and effective moisture diffusivity of Mirabelle plum. J. FoodProces. Preserv. 39(6), 2710–2717 (2015)


Dehghannya, J., Bozorghi, S., Heshmati, M.K.: Low temperature hot air drying of potatocubes subjected to osmotic dehydration and intermittent microwave: drying kinetics, energyconsumption and product quality indexes. Heat Mass Transf. 54(4), 929–954 (2018)

Dionello, R.G., Berbert, P.A., Molina, M.A.B., Pereira, R.C., Viana, A.P., Carlesso, V.O.: Assess-ment of convective drying models for fresh and osmo-dehydrated pineapple rings. Food Sci.Technol. 29(1), 232–240 (2009). (In Portuguese)

Escobar, M.P., Galindo, F.G., Wadso, L., Najera, J.R., Sjoholm, I.: Effect of long-term storage andblanching pre-treatments on the osmotic dehydration kinetics of carrots (Daucus carota L. cv.Nerac). J. Food Eng. 81(2), 313–317 (2007)

Feng, L., Zhang, M., Adhikari, B.: Effect of water on the quality of dehydrated products: a review ofnovel characterizationmethods and hybrid drying technologies. Dry. Technol. 32(15), 1872–1884(2014)

Fialho, J.F., Vieira, E.A.: Cassava in the Cerrado: Technical Guidelines/Technical Editors, 2 edn.Embrapa Cerrados, Planaltina, Brazil (2011)

Garcia-Noguera, J., Oliveira, F.I.P., Gallão, M.I., Weller, C.L., Rodrigues, S., Fernandes, F.A.N.:Ultrasound-assisted osmotic dehydration of strawberries: effect of pretreatment time andultrasonic frequency. Dry. Technol. 28(2), 294–303 (2010)

Góis, J.L.C.X., Costa, A.K.L., Filho, R.S.F.: Study of osmotic dehydration of banana apple (Musaacuminata Colla×Musa balbisiana Colla, AAB Group), Instituto Federal de Educação, Ciênciae Tecnologia do Rio Grande do Norte, IFRN, pp. 1–8 (2010). (In Portuguese)

Guiné, R.P.F.: Moisture diffusivity in pears: Experimental determination and derivation of amathematical prediction model. Int. J. Food Sci. Technol. 41(10), 1177–1181 (2006)

Gupta, S.V., Patil, B.N.: Convective drying of osmo-dehydrated sapota slices. Int. J. Agricult. FoodSci. Technol. 5(4), 219–226 (2014)

Hadipernata, M., Ogawa, M.: Mass transfer and diffusion coefficient of d-Allulose during osmoticdehydration. J. Appl. Food Technol. 3(2), 6–10 (2016)

Hamedi, F., Mohebbi, M., Shahidi, F., Azarpazhooh, E.: Ultrasound-assisted osmotic treatment ofmodel food impregnated with pomegranate peel phenolic compounds: mass transfer, texture, andphenolic evaluations. Food Bioproc. Technol. 11(5), 1061–1074 (2018)

He, J.F., Macgregor, G.A.: Reducing population salt intake worldwide: from evidence to imple-mentation. Prog. Cardiovasc. Dis. 52(5), 363–382 (2010)

Hills, B.P., Takaca, S.F., Belton, P.S.: A new interpretation of proton NMR relaxation timemeasurements of water in food. Food Chem. 37(2), 95–111 (1990)

Isquierdo, E.P., Borém, F.M., Andrade, E.T., Corrêa, J.L.G., Oliveira, P.D., Alves, G.E.: Dryingkinetics and quality of natural coffee. Trans. ASABE 56(3), 1003–1010 (2013)

Jeffery, G.H., Basset, J., Mendham, J., Denney, R.C.: Vogel’s textbook of Quantitative ChemicalAnalysis, 5th edn. Longman Scientific & Technical, England (1989)

Junqueira, J.R.J., Correa, J.L.G.,Mendonça,K.S.: Evaluation of the shrinkage effect of sweet potato.J. Food Process. Preserv. 41(3), 1–10 (2017)

Kaya, A., Aydin, O., Kolayli, S.: Influence of osmotic dehydration on drying kinetics of carrot. J.Thermal Sci. Technol. 36(2), 155–162 (2016)

Kek, S.P., Chin, N.L., Yusof, Y.A.: Simultaneous time-temperature-thickness superposition theo-retical and statistical modelling of convective drying of guava. J. Food Sci. Technol. 51(12),3609–3622 (2013)

Korsrilabut, J., Borompichaichartkul, C., Duangmal, K.: Effect of invert sugar on the drying kineticsand water mobility of osmosed-air dried cantalupe. Int. J. Food Sci. Technol. 45(7), 1524–1531(2010)

Kowalski, S., Łechtanska, J.M.: Drying of red beetroot after osmotic pretreatment: kinetics andquality considerations. Chem. Process Eng. 36(3), 345–354 (2015)

Kowalski, S.J., Mierzwa, D.: Influence of preliminary osmotic of carrot (Daucus Carota L.). Chem.Process Eng. 32(3), 185–194 (2011)

Koyuncu, T., Tosun, I., Pinar, Y.: Drying characteristics and heat energy requirement of corneliancherry fruits (Cornus mas L.). J. Food Eng. 78(2), 735–739 (2007)


Kudra, T.: Energy aspects in drying. Dry. Technol. 22(5), 917–932 (2004)Kumar, A., Islam, S., Dash, K.K., Sarkar, S.: Optimization of process parameters for osmoticdehydration of chayote cubes by response surface methodology. Int. J. Agr. Environ. Biotechnol.10(6), 725–737 (2017)

Lane,H., Eynon, L.:Determination of reducing sugar bymeans of Fehling’s solutionwithmethyleneblue as internal indicatior. J. Soc. Chem. Ind., London 42, 32T–37T (1923)

Lewicki, P.P.: Water as the determinant of food engineering properties: a review. J. Food Eng. 61(4),483–495 (2004)

Li, S., Dickinson, L.C., Chinachoti, P.: Mobility of “unfreezable” and “freezable” water in waxycorn starch by 2H and 1H NMR. J. Agr. Food Chemistry 46(1), 62–71 (1998)

Lugo, P.J.M., Padilla,K.A.M.,Gallo,R.T., Fandiño, J.M.M.,Vasquez,R.D.G.: Experimental evalua-tion of venezuelan cassava drying by using a hybrid air heating system. Rev. Chilena de Ingeniería26(2), 329–338 (2018)

Luna, A.T., Rodrigues, F.F.G., Costa, J.G.M., Pereira, A.O.B.: Physical-chemical study, microbialand bromatological of Manihot esculenta Crantz (mandioca). Rev. Inter.: Saúde, Humanas eTecnolo 1(3), 1–11(2013). (In Portuguese)

Maieves, H.A.: Physical, physical chemical and technological potential of new Cassava cultivars.Master’s dissertation in FoodEngineering, FoodEngineeringCollege, FederalUniversity of SantaCatarina, Florianópolis, Brazil (2010). (In Portuguese)

Maldonado, S., Santapaola, J.E., Singh, J., Torrez, M., Garay, A.: Cinética de la transferencia demasa durante la deshidratación osmótica de yacón (Smallanthus sonchifolius). Food Sci. Technol.28(1), 251–256 (2008)

Mayor, L., Moreira, R., Chenlo, F., Sereno, A.M.: Kinectcs of osmotic dehydration of pumpkinwith sodium chloride solutions. J. Food Eng. 74(2), 253–262 (2006)

Mercali, G.D.: Study of mass transfer in banana osmotic dehydration (Musa sapientum, shum.).Master’s dissertation in Chemical Engineering, Federal University of the Rio Grande do Sul,Porto Alegre, Brazil (2009). (In Portuguese)

Mercali, G.D., Kechinski, C.P., Coelho, J.A., Tessaro, I.C., Marczak, L.D.F.: Study of mass transferduring the osmotic dehydration of blueberry. Braz. J. Food Tecnol. 13(2), 91–97 (2010). (InPortuguese)

Mercali, G.D., Kechinski, C.P., Coelho, J.A., Tessaro, I.C., Marczak, L.D.F.: Study of mass transferduring the osmotic dehydration of blueberry. Braz. J. Food Technol. 13(2), 91–97 (2011). (InPortuguese)

Mierzwa, D., Kowalski, S.J.: Ultrasound-assisted osmotic dehydration and convective drying ofapples: process kinetics and quality issues. Chem. Process Eng. 37(3), 383–391 (2016)

Montgomery, D.E.: Introduction to Statistical Quality Control, Sixt edn. Wiley, New York (2008)Moreno, A., León, D., Giraldo, G., Rios, E.: Estudio de la cinética fisicoquímica del mango(Mangiferia indica L. Var. tommy Atkins) tratado por métodos combinados de secado, DYNA,77(162), 75–84 (2010)

Moyers, C.G., Baldwin, G.W.: Psychrometry, evaporative cooling and solids drying. In: Perry,R.H., Green, D.W. (eds.) Perry’s Chemical Engineers’ Handbook, 7 th edn, pp. 12-1–12-90, MacGraw-Hill, Nova York (1999). (CD-ROM)

Nogueira, M.C.S.: Agronomic Experimentation I-Concepts, Planning and Statistical Analysis.Esalq, Piracicaba (2007). (In Portuguese)

Osidacz,R.C.,Ambrosio-Ugri,M.C.B.: Physicochemical quality of eggplant dehydratedwith variedpretreatments. Acta Scient. Technol. 35(1), 175–179 (2013)

Park, K.J., Bin, A., Pedro, R.B.F.: Drying of pear dAnjou with and without osmotic dehydration. J.Food Eng. 56(1), 97–103 (2002)

Pavkov, I., Babic, L., Babic, M., Radojcin, M., Stojanovic, C.: Effects of osmotic pre-treatment onconvective drying kinetics of nectarines halves (Pyrus persica L.). J. Process. Energy Agr. 15(4),217–222 (2011)


Pereira, L.M., Ferrari, C.C., Mastrantonio, S.D.S., Rodrigues, A.C.C., Hubinger, M.D.: Kineticaspects, texture, and color evaluation of some tropical fruits during osmotic dehydration. Dry.Technol. 24(4), 475–484 (2006)

Pereira, L.M., Carmello-Guerreiro, S.M., Hubinger, M.D.: Microscopic features, mechanical andthermal properties of osmotically dehydrated guavas. LWT Food Sci. Technol. 42(1), 378–384(2009)

Pessoa, T., Amaral, D.S., Duarte,M.E.M., CavalcantiMata,M.E.R.M.,Gurjão, F.F.: Sensory assess-ment of passed guavas obtained by combined techniques of osmotic dehydration anddrying.Holos4(27), 137–147 (2011). (In Portuguese)

Pessoa, T., Silva, D.R.S., Duarte, M.E.M., Cavalcanti Mata, M.E.M.R., Gurjão, F.F., Miranda,D.S.A.: Physical and physicochemical yam sticks of submitted to osmotic dehydration in saline.Holos 7(33), 30–38 (2017)

Pornpraipech, P., Khusakul, M., Singklin, R., Sarabhorn, P., Areeprasert, C.: Effect of temperatureand shape on drying performance of cassava chips. Agr. Nat. Resour. 51(5), 402–409 (2017)

Ramya, H.G., Kumar, S., Kumar, M.: Mass exchange evaluation during optimization of osmoticdehydration for oyster mushrooms (Pleurotus sajor-caju) in salt-sugar solution. J. Appl. Nat. Sci.6(1), 110–116 (2014)

Rayaguru, K., Routray, W.: Mathematical modeling of thin layer drying kinetics of stone appleslices. Int. Food Res. J. 19(4), 1503–1510 (2012)

Rinaldi, M.M., Vieira, E.A., Fialho, J.F., Malaquias, J.V.: Effect of different freezing forms oncassava roots. Braz. J. Food Thechnol. 18(2), 93–101 (2015). (In Portuguese)

Riva, M., Campolongo, S., Leva, A.A., Maestrelli, A., Torreggiani, D.: Structure-propertyrelationships in osmo-air dehydrated apricot cubes. Food Res. Int. 38(5), 533–542 (2005)

Rodríguez, M.M., Arballo, J.R., Campañone, L.A., Cocconi, M.B., Pagano, A.M., Mascheroni,R.H.: Osmotic dehydration of nectarines: influence of the operating conditions and determinationof the effective diffusion coefficients. Food Bioproc. Technol. 6(10), 2708–2720 (2013)

Rodríguez, M.M., Arballo, J.R., Campañone, L.A., Mascheroni, R.H.: Analysis of operating condi-tions on osmotic dehydration of plums (PrunusDomesticaL.) and 3D-numerical determination ofeffective diffusion coefficientsAnalysis of operating conditions on osmotic dehydration of plums(Prunus Domestica L.) and 3D-numerical determination of effective diffusion coefficients. Int.J. Food Eng. 13(11), 1–13 (2017)

Ruiz-López, I.I., Huerta-Mora, I.R., Vivar-Vera, M.A., Martínez-Sánchez, C.E., Herman-Lara, E.:Effect of osmotic dehydration on air-drying characteristics of chayote. Dry. Technol. 28(10),1201–1212 (2010)

Ruiz-López, I.I., Ruiz-Espinosa, H., Herman-Lara, E., Zárate-Castillo, G.: Modeling of kinetics,equilibrium and distribution data of osmotically dehydration carambola (Averrhoa carambolaL.) in sugar solutions. J. Food Eng. 104(2), 218–226 (2011)

Sacilik, K., Elicin, A.K.: The thin layer drying characteristics of organic apple slices. J. Food Eng.73(3), 281–289 (2006)

Sanjinez-Argandoña, E.J., Cunha, R.L., Menegalli, F.C., Hubinger, M.D.: Evaluation of totalcarotenoids and ascorbic acid in osmotic pretreated guavas during convective drying. ItalianJ. Food Sci. 17(3), 305–314 (2005)

Sankat, C.K., Castaigne, F., Maharaj, R.: The air drying behaviour of fresh and osmoticallydehydrated banana slices. Int. J. Food Sci. Technol. 3(2), 123–135 (1996)

Sarno, R.M., Levy, R.B., Bandoni, D.H., Monteiro, C.A.: Estimated sodium intake for the Brazilianpopulation, 2008-2009. Rev. Saúde Pública 47(3), 571–578 (2013)

Silva Júnior, A.F., Aires, J.E.F., Cleide, K.LC.A.F.A., Silva, M.D.P.S., Farias, V.S.O.: Effects of saltconcentration on osmotic dehydration of green bean. J. Agr. Stud. 3(1), 60–78 (2015)

Silva, M.A.C., Silva, Z.E., Mariani, V.C., Darche, S.: Mass transfer during the osmotic dehydrationof West Indian cherry. LWT, Food Sci. Technol. 45(2), 246–252(2012)

Silva, P.A., Cunha, R.L., Lopes, A.S., Pena, R.S.: Characterization of tapioca flour obtained in Parástate, Brazil. Ciencia Rural 43(1), 185–191 (2013). (In Portuguese)


Singh, B., Gupta, A.K.: Mass transfer kinetics and determination of effective diffusivity duringconvective dehydration of pre-osmosed carrot cubes. J. Food Eng. 79(2), 459–470 (2007)

Singh, B., Singh Hathan, B.: Convective dehydration kinetics and quality evaluation of osmo-convective dried beetroot candy. Italian J. Food Sci. 28(4), 669–682 (2016)

Singh, B., Panesar, P.S., Nanda, V.: Osmotic dehydration kinetics of carrot cubes in sodium chloridesolution. Int. J. Food Sci. Technol. 43(8), 1361–1370 (2008)

Sritongtae, B., Mahawanich, T., Duangmal, K.: Drying of osmosed cantaloupe: effect of polyols ondrying and water mobility. Dry. Technol. 29(5), 527–535 (2011)

STATSOFT. Statistica for Windows, Tulsa, USA (1997)Sutar, P.P., Prasad, S.: Modeling mass transfer kinetics and mass diffusivity during osmoticdehydration of blanched carrots. Int. J. Food Eng. 7(4), 1–20 (2011)

Togrul, H.: Simple modeling of infrared drying of fresh apple slices. J. Food Eng. 71, 311–323(2005)

Udomkun, P., Argyropoulos, D., Nagle, M., Mahayothee, B., Müller, J.: Sorption behaviour ofpapayas as affected by compositional and structural alterations from osmotic pretreatment anddrying. J. Food Eng. 157, 14–23 (2015)

Valduga, E., Tomicki, L., Witschinski, F., Colet, R., Peruzzolo, M., Ceni, G.C.: Evaluation ofacceptability and mineral components of different cassava cultivars (Manihot esculenta Crantz)after cooking. Alimentos e Nutrição Araraquara 22(2), 205–210 (2011). (In Portuguese)

Vázquez-Vila, M.J., Chenlo-Romero, F., Moreira-Martínez, R., Pacios-Penelas, B.: Dehydrationkinetics of carrots (Daucus carota L.) in osmotic and air convective drying processes. Span. J.Agr. Res. 7(4), 869–875 (2009)

Vieira, J.C., Montenegro, F.M., Lopes, A.S., Pena, R.S.: Physical and sensorial quality of sweetcookies with cassava starch. Ciência Rural 40(12), 2574–2579 (2010)

Yadav, A.K., Singh, S.V.: Osmotic dehydration of fruits and vegetables: a review. J. Food Sci.Technol. 51(9), 1654–1673 (2014)

Zúñiga, R.N., Pedreschi, F.: Study of the pseudo-equilibrium during osmotic dehydration of applesand its effect on the estimation of water and sucrose effective diffusivity coefficients. FoodBioproc. Technol. 5(7), 2717–2727 (2012)

Chapter 7Heat Transfer in a Packed-Bed EllipticCylindrical Reactor: Theory,Heterogeneous Transient Modeling,and Applications

A. S. Pereira, R. M. da Silva, R. S. Santos, A. G. Barbosa de Lima,R. O. de Andrade, W. M. P. B. de Lima, and G. S. de Lima

Abstract This chapter focuses on the study of heat transfer in packed-bed ellipticcylindrical reactor. Based on the local thermal non-equilibrium, a heterogeneousmathematical model was developed. The transient model is composed for one solidphase and another fluid phase, in which the balance equation for each constituent,written in elliptic cylindrical coordinates, is applied separately, and the proposedmodel includes different phenomena such as geometry of the particles and reactor,bed porosity, fluid velocity, conduction, and convection heat transfer between thesolid particles and fluid flowing inside the bed, and heat generations in the involved

A. S. Pereira (B)Federal Institute of Education, Science and Technology Baiano - IFBaiano, Highway BR 420,Rural Zone, Santa Inês, BA Zip Code: 45320-000, Brazile-mail: [email protected]

R. M. da SilvaFederal Institute of Education, Science and Technology of Paraíba, IFPB, R. Tranqüilino CoelhoLemos, 671, Dinamérica, Campina Grande, PB Zip Code: 58432-300, Brazile-mail: [email protected]

R. S. SantosRural Federal University of the Semi-Arid, Av. Francisco Mota, 572, Mossoró, RN Zip Code:59625-900, Brazile-mail: [email protected]

A. G. B. de Lima (B) · R. O. de Andrade · W. M. P. B. de Lima · G. S. de LimaDepartment of Mechanical Engineering, Federal University of Campina Grande, Av. AprígioVeloso, 882, Bodocongó, Campina Grande, PB Zip Code: 58429-900, Brazile-mail: [email protected]

R. O. de Andradee-mail: [email protected]

W. M. P. B. de Limae-mail: [email protected]

G. S. de Limae-mail: [email protected]


185









https://doi.org/10.1007/978-3-030-47856-8_7

186 A. S. Pereira et al.

phases. Application has been done to a specific geometry of the reactor with aspectratio 2.

Keywords Heat transfer · Fixed-bed reactor · Two-phase model · Simulation

7.1 Introduction

The study of heat transfer in porous media (structure composed by connected andfor unconnected voids and solid material) has been an important topic of researchesaround the world. This morphology is present both in nature, as in most of theChemical Engineering unitary operations, such as filtration, distillation, absorptionand adsorption, drying and catalytic reactions in fixed and fluidized beds (Freire2004). On catalytic reactions, fixed-bed tubular reactors are often used in industry topromote such highly exothermic or endothermic heterogeneous gas-solid reactions.However, in order to have a realistic and safety design of such equipment, theoreticaland experimental studies, and the development of accurate mathematical models,based on cold (or heated) flow experiments, must be performed.

The models of porous media heat transfer can be divided into two groups: (a)pseudo-homogeneous—where there is no distinction between the phases, and thesolid–fluid mixture heat transfer occurs in the same temperature at each locationof the bed (local thermal equilibrium) and (b) heterogeneous model—where eachphase has its own heat transfer dynamics, and there is a parameter that couplingthe heat transfer between the phases (local thermal non-equilibrium). These modelscan be further subdivided into 1D, 2D, or 3D models according to the analyzedgeometry. Each model may present variations due to the considered simplifyingassumptions; however, the heterogeneous model is the most accurate and realisticunder the physical point of view.

Heat transfer studies in fixed-bed reactors are still limited to simple cylindricalgeometries, pseudo-homogeneous model, and variations in some system thermo-physical properties of the involved materials. Therefore, this chapter aims to realizea study of the heat transfer in a fixed-bed reactor with elliptic cylindrical geometryand applying a two-phase mathematical model (heterogeneous model).

7.2 Porous Media and Packed-Bed Reactors

7.2.1 Porous Media

For a material to be considered as a porous medium it must be checked whether itcontains relatively small voids, generally called pores, within the solid or semi-solidmatrix. The pores usually are filled by a fluid, such as air, water, or a fluid mixture,moreover, theymust be permeable, i.e., these fluidsmay penetrate the porousmedium

7 Heat Transfer in a Packed-Bed Elliptic … 187

Fig. 7.1 Particle filling state, initial (left) and final (right), after compression sintering and /orheating

through one face and emerge on another face, or migrate from the volume interior tosurface due to the action of someexternal agent, such as heat pressure or concentrationgradients.

Porous media can be classified according to structure as granular or fibrous. Gran-ules are usually formed by a set of particles or grains, spherical or not, arrangedregularly or randomly, and represent the vast majority of porous media. Fibers areformed by a set of very long inclusions, called fibers, that can be natural or synthetic,straight or curved, being randomly arranged or in regular distributions. Examplesof porous media are particle beds, porous rocks, fibrous cluster such as tissues andfilters, and extremely smallmicrospore-containing catalytic particles (Mendes 1997).Figure 7.1 illustrates a porous medium consisting of particles with different shapesand dimensions, uncompressed, and compressed by pressure and/or heating.

Except for metal structures, dense rocks, and some plastics, on a microscopicscale, solids can be considered porous media materials (Dullien 1992). Havingadequate models to predict the behavior of the momentum, mass, and heat transportphenomena inside of porous media can be fundamental in the scientific, technolog-ical, and industrial areas, such as the fixed-bed reactors. The ability to model theporous medium behavior under different conditions allows to accelerate the devel-opment and to improve the efficiency of processes involving porous media and thus,to allow economic and environmental gains.

It is difficult to precisely describe the porous media geometry due to its complexstructure. In theory, this material can be specified by analytical equations thatdefine the shape and pores dimensions. For practical purposes, it is impossible tofully describe these equations and, therefore, some geometric approximations areconsidered, obtaining characteristics very close to the real ones.

As described in Eq. (7.1), the porosity is the ratio of void volume (V v), whichare the zones not occupied by the solid material and the total volume of the porousmedium (VT) which is the sum of the void volume and the solid particle volumes(Dullien 1992).

ϕ = VV

VT(7.1)


Fig. 7.2 Distribution ofparticles in a porous bed

Thus, porosity indicates the void volumepercentage in relation to the total volume;Fig. 7.2 can assist in the understanding of these parameters.

The Eq. (7.2) shows a relationship between porosity and density of the bed (bulkdensity) that contain particle and fluid:

ρbed = m total

Vtotal(7.2)

where the total mass is the sum of solid and fluid mass, as follows:

m total = (1 − ϕ)(SH)ρs + ϕ(SH)ρf (7.3)

where ρs and ρf are, respectively, the particle and fluid densities, and

Vtotal = (SH)Vtotal = (SH) (7.4)

Inserting Eqs. (7.3) and (7.4) in Eq. (7.2), the available volume to flow is definedas

ϕ = ρbed − ρs

ρf − ρs(7.5)

Another way to determine the porous medium is by using the packing factor (PF),which represents the actual fraction occupied by the particles. The mathematicalexpression for this purpose is


ϕ = 1 − (PF) = 1 −(N · VP

Vtotal

)(7.6)

where N is the effective particle number, V p is the particle volume, and V total is theunit cell volume (porous media).

The particle geometric characteristics: shape, size, and distribution influence thebehavior of the unconsolidated porous media. The bed porosity increases as theparticle shape is very different from a spherical shape, thus, the sphericity is lessthan 1. Given this, many works report the use of an equivalent diameter for theparticles.

The equivalent diameter (dp) is defined as the sphere diameter with the sameparticle volume (McCabe et al. 1985). It can be determined by the ratio dp = 6/Ap,if the specific surface area (Ap), particle surface area divided by particle volume, isknown. The Ap represents the contact area between the solid and the fluid phase,which is a very important parameter in some processes. An equivalent nominaldiameter may also be obtained by sieving if an equivalent diameter measurement isnot available. This mathematical expression for the diameter is most commonly usedfor particles with shape closer to the spherical. For particles with regular or irregulargeometry, a sphericity factor β is defined by

β =(VP

Vsc

)1/3

(7.7)

where the values of this factor differ for particles of different shapes. In Eq. (7.7),V p and V sc, respectively, represent the particle and circumscribed sphere volumes,as shown in Fig. 7.3 (Curray and Griffiths 1955).

In many applications, the bed particles do not have a uniform diameter, but asize distribution. Thus, it is common to determine an average value for the particlediameter (equivalent particle diameter). The consequence of this approach is that a

Fig. 7.3 Relationshipbetween particle volume andcircumscribed sphere volume


Fig. 7.4 Scheme of anunconventional fixed-bedreactor

real bed with various particle sizes distribution will be represented by a bed formedby spherical particles with the same equivalent diameter.

7.2.2 Chemical Reactors

7.2.2.1 Reactor Fundamentals

Chemical reactors are equipment in which chemical reactions occur. They can befound in two basic types, tanks or tubes, aiming to maximize the generation ofdesired productswith higher added value; produce the highest yield at the lowest cost;generate intermediates chemical products for new processes, and to generate profits,operating within pre-established safety (controlled), according to environmentallegislation (Fábrega 2012).

The ideal reactors (for which a specific mathematical model is developed frompre-established conditions and predict properly the physical phenomena behaviorwhen realistic conditions are applied) and non-ideal reactors (for which treatmentand specific mathematical function due to reaction and/or reactor peculiarities arerequired) have been reported in the literature. Batch, tubular, andmixing are the threemain types of ideal reactors. Figure 7.4 illustrates a schematic of a fixed-bed reactorwith fluid inlet and outlet, the particle packing, and the fluid flow direction in thebed.

7.2.2.2 Reactors Modeling

Due to the development of computers and the availability of industrial simulators, it isnot recommended to expand the reactor scale without first developing any modelingas simple as it may be, to have a better knowledge of the equipment and processbehavior.Modeling canvary from the fundamental,which canuse simpler differential


equations by separately evaluating each mechanism that influences the process, tolater add more information from the same mechanisms to the model, providing amore complex reactor simulation, or it can be based on pilot experimentation toadjust the model effective parameters (Froment and Hofmann 1987).

The reactor to be adequately controlled must be very well known and, therefore,a model that describes its behavior as operating with great accuracy is necessary.On the other hand, applications involving a dynamic model usually require a largecomputational effort with direct impact on the processing time. In addition, to thedevelopment of models with high prediction potential, it is necessary to consider thedifficulty in their solution, both in computational terms and in the availability of thenecessary (Bunnell et al. 1949).

The simulation of chemical reactors had large use in recent years. These simula-tions have served several purposes: reactor design, reactor start and stop strategies,determination of desired and hazardous operating conditions for process control, andoptimization, using sometimes detailed and heterogeneous models.

The heat transfer related catalytic bed models can be divided into heteroge-neous model (solid phase + fluid phase) also known as two-phase model and singlemodel (pseudo-homogeneous). Each model may also present variations due to theused assumptions. For example, in a tubular reactor, one-dimensional models donot consider radial gradients of temperature or concentration, grouping all resis-tance to heat transport on the wall. The two-dimensional consider the existence of anon-planar radial profile of temperatures and concentrations, which presupposes theknowledge of the effective radial thermal conductivity, and the film coefficient onthe wall (Giordano 1991).

Performance analyses of different two-dimensional models (pseudo-homogeneous and heterogeneous) show that the pseudo-homogeneous modelis consistent having a simpler computational solution and programming thanthe other models. In the two-phase model (solid + fluid), each phase has itsown dynamics of heat transfer, which is physically more realistic. Nevertheless,few scientists have studied this model for inherent modeling reasons, which areconsiderably more complicated solution of the energy equations for the solid andfluid phases, experimental difficulty in determining the solid–fluid heat transfercoefficient required for heterogeneous model, and the difficulty in spot temperaturemeasurement for each phase.

7.3 Heat Transfer in Fixed-Bed Elliptical Reactorvia Two-Phase Model

7.3.1 Physical Problem and Geometry

The packed-bed elliptical reactor studied in this research is illustrated in Fig. 7.5.The reactor bed is percolated by a heated fluid (fluid 1), which exchanges heat with


Fig. 7.5 Scheme of a packed-bed elliptical cylindrical reactor

the particles, and the system is cooled at the wall by fluid 2 which has a temperatureless than the inlet fluid temperature. Fluid 1 flows in the laminar regime.

This physical problem with the use of pseudo-homogeneous model has beenstudied by Oliveira et al. (2004), Silva Filho et al. (2013), Silva et al. (2017, 2018);however, based on the heterogeneous model no works have been reported in theliterature.

The system geometric shape proposed in this chapter suggests the use of a partic-ular coordinate system that best fits this geometry and, consequently, will lead togreater efficiency and confidence of the results (Lima 1999). In this case, the ellipticcylindrical coordinate system is most appropriate.

Thus, a change of variables is a natural requirement. The general relations betweenthe Cartesian coordinate system (x, y, z) and the elliptical cylindric coordinate system(τ , φ, z) are given as follows (Magnus et al. 1966):


x = L cosh τ cosφ (7.8)

y = L senh τ senφ (7.9)

z = z (7.10)

where L is the ellipse focal length, mathematically calculated by the expression

L =√L22 − L2

1, where L1 and L2 are the ellipse minor and major axes, respectively(Fig. 7.5). To obtain the desired transformation, consider the following variables:

ξ = cosh τ (7.11)

η = cosφ (7.12)

Thus, the substitution of these variables ξ and η in Eqs. (7.8)–(7.9) providesthe direct relationships between the two coordinate systems. Thus, the followingrelationships are obtained for x, y, and z, in terms of ξ and η:

x = Lξη (7.13)

y = L√(

1 − η2)(

ξ 2 − 1)

(7.14)

z = z (7.15)

The domain of validity of variables ξ, η, and z in the elliptic cylindrical systemare 1 ≤ ξ ≤ L2/L , 0 ≤ η ≤ 1, and 0 ≤ z ≤ H .

The elimination of variable φ, in the Eqs. (7.8) and (7.9), generating the xy plancurves (Fig. 7.6), characterized by the parameters ξ = ξ0 (constant). The surfaces

Fig. 7.6 Representativescheme of the ellipticcylindrical coordinatesystem in ξη and xy planes


ξ0 > 1 are revolution ellipsoids with center in origin. The generated ellipses havethe same focus. The two-ellipse focus are located along the x-axis at the points (x =±L, y = 0). The surface ξ = 1 it is a straight line that joins the origin (z = 0) andthe focal point (z = +L).

According to Figs. 7.5 and 7.6, when L2 → L1, the elliptic cylinder tends to acircular cylinder with diameter of 2L1. Thus, at the limit when the interfocal distancetends to zero, the elliptical coordinate system is reduced to the cylindrical: Lξ → rand η → cos θ, when ξ → ∞, where r and θ are the cylindrical coordinates.

7.3.2 Governing Equations

The transient energy equations (in terms of temperature) for the fluid and solid phasesin the Cartesian coordinate system are, respectively (Nield and Bejan 1992):

• Fluid phase

ϕ(ρcp)f∂Tf∂t

+ (ρcp)fv · ∇Tf = DP

Dt+ ϕ∇ · (Kf∇Tf) + μψ + ϕqf + h(Ts − Tf) (7.16)

• Solid phase

(1 − ϕ)(ρc)s∂Ts∂t

= (1 − ϕ)∇ · (Ks∇Ts) + (1 − ϕ)qs + h(Tf − Ts) (7.17)

where f and s refer to the fluid and solid phases, respectively, T is the temperature,t is the time, v is the fluid average velocity, ϕ is the media porosity, ρ is the density,cp is the specific heat at constant pressure, K is the thermal conductivity, μψ is theviscous dissipation term, P is the pressure, q internal energy generation per volumeunit, and h is the specific heat transfer coefficient by convection, between the solidand fluid phases.

The first term of Eq. (7.16) represents the transient transfer of energy; and thesecond term, the convective heat transport, and where the relation of Dupuit–Forch-heimer v = ϕV,V the fluid velocity was used. The third term represents the substan-tive derivative of pressure, the fourth term is the conduction heat transport, the fifthterm corresponds to viscous dissipation, the sixth term is the internal energy gener-ation, and the seventh term represents the convection heat exchange between thesolid and fluid phases. The first term of Eq. (7.17) represents the transient transferof energy and the second term represents the conductive heat flux through the solid.The third term represents the heat generation inside the solid, and the fourth termrefers to the heat exchange between the solid and fluid phases, by convection.

Some values of h can be obtained indirectly (Polyaev et al. 1996). One of thecorrelations for a porous particle bed is given by Dixon and Cresswell (1979):


h = asfhsf (7.18)

where hsf is the convective heat transfer coefficient to both phases and afs is thespecific surface area, given by the relationships between the total area to heat transferand the particle bed volume. For example, to a spherical particle bed this parameteris given as follows:

asf = 6(1 − ϕ)/dP (7.19)

where dP is the particle diameter and the parameter hsf is given as follows:

1

hsf= dP

Nusf Kf+ dP

βKs(7.20)

where β is the sphericity of the porous bed particles obtained by (see Eq. 7.7):

β =(a2

b2

)1/3

(7.21)

being a and b positive real numbers that determine the particle dimensions and shape(see Fig. 7.3). The Nusselt number Nusf can be obtained by the following expression(Handley and Heggs 1968):

Nusf = (0.225/ϕ)Pr13 Re

13p (7.22)

valid for particle Reynolds numbers ReP > 100. In this equation, Pr is the Prandtlnumber. Another correlation for Nusselt number is given as follows (Wakao andKaguei 1982):

Nusf = 2.0 + 1.1Pr13 Re0.6p (7.23)

Equation (7.23) is valid for low values of ReP. In this case, predictions of Nusfvary between 0.1 and 12.4 (Miyauchi et al. 1981; Wakao et al. 1976; Wakao andKaguei 1979). Several other authors, such as Alazami and Vafai (2000), Grangeotet al. (1994), Saito and Lemos (2005), Quintard et al. (1997), Quintard andWhitaken(2000) and Nield (2002) have reported alternative expressions for determining theparameters hsf and asf.

Considering viscous dissipation and the substantive derivative of pressure negli-gible, the general conservation equation applied for the fluid and solid phases for ageneric variable Φ and writing in any coordinate system (Maliska 1995) are givenby

∂

∂t

[ϕ(ρcP)f

Φ

J

]+ ∂

∂ξ

[(ρcP)fU

Φ

J

]+ ∂

∂η

[(ρcP)fV

Φ

J

]+ ∂

∂z

[(ρcP)fW

Φ

J

]=


∂

∂ξ

[α11ϕ JΓ Φ ∂Φ

∂ξ+ α12ϕ JΓ Φ ∂Φ

∂η+ α13ϕ JΓ Φ ∂Φ

∂z

]

+ ∂

∂η




∂z

]

+ ∂

∂z




∂z

]+ ϕ

qfJ

+ h(Φs − Φf)

(7.24)

and

∂

∂z

[α31(1 − ϕ)JΓ Φ ∂Φ

∂ξ+ α32(1 − ϕ)JΓ Φ ∂Φ

∂η+ α33(1 − ϕ)JΓ Φ ∂Φ

∂z

]

+(1 − ϕ)qsJ

+ h

J(Φf − Φs) (7.25)

where J represents the Jacobian, determined mathematically as follows:

J−1 =

∣∣∣∣∣∣∣

∂x∂ξ

∂x∂η

∂x∂z

∂y∂ξ

∂y∂η

∂y∂z

∂z∂ξ

∂z∂η

∂z∂z

∣∣∣∣∣∣∣(7.26)

The coefficients αij, on the Eqs. (7.24) and (7.25) are determined by the followingrelations:

α11 = a′

J 2(7.27)

α12 = α21 = d ′

J 2(7.28)

α22 = b′

J 2(7.29)

α13 = α31 = e′

J 2(7.30)

α33 = c′

J 2(7.31)

α23 = α32 = f ′

J 2(7.32)

where


a′ =(

∂ξ

∂x

)2

+(

∂ξ

∂y

)2

+(

∂ξ

∂z

)2

(7.33)

b′ =(

∂η

∂x

)2

+(

∂η

∂y

)2

+(

∂η

∂z

)2

(7.34)

c′ =(

∂z

∂x

)2

+(

∂z

∂y

)2

+(

∂z

∂z

)2

(7.35)

d ′ =(

∂ξ

∂x

∂η

∂x

)+(

∂ξ

∂y

∂η

∂y

)+(

∂ξ

∂z

∂η

∂z

)(7.36)

e′ =(

∂z

∂x

∂ξ

∂x

)+(

∂z

∂y

∂ξ

∂y

)+(

∂z

∂z

∂ξ

∂z

)(7.37)

f ′ =(

∂z

∂x

∂η

∂x

)+(

∂z

∂y

∂η

∂y

)+(

∂z

∂z

∂η

∂z

)(7.38)

For the elliptic cylindrical coordinate system, the determination of the Jacobianinverse provides as a result:

J−1 = − L2(ξ 2 − η2

)√(

ξ 2 − 1)(1 − η2

) (7.39)

In the general equation (Eqs. 7.24 and 7.25), the terms containing αij with i �= j arethe diffusive terms referring to the non-orthogonality of themesh. Thus, checking theorthogonality of the adopted coordinate system becomes an important requirement.In this case, the necessary and sufficient conditions for a coordinate system to beorthogonal are (McRobert 1967):

(∂x

∂ξ

∂x

∂η

)+(

∂y

∂ξ

∂y

∂η

)+(

∂z

∂ξ

∂z

∂η

)= 0 (7.40)

(∂x

∂η

∂x

∂z

)+(

∂y

∂η

∂y

∂z

)+(

∂z

∂η

∂z

∂z

)= 0 (7.41)

(∂x

∂z

∂x

∂ξ

)+(

∂y

∂z

∂y

∂ξ

)+(

∂z

∂z

∂z

∂ξ

)= 0 (7.42)

It can be verified that all these conditions are satisfactory for the elliptic cylindricalcoordinate system. Then, the coefficients d′, e′ and f ′ are null, and Eq. (7.24) will bereduced as follows:

∂

∂t

[ϕ(ρcP)f

Φ

J

]+ ∂

∂ξ

[(ρcP)fuξ

Φ

J

]+ ∂

∂η

[(ρcP)fuη

Φ

J

]+ ∂

∂z

[(ρcP)fuz

Φ

J

]=


∂

∂ξ


∂ξ

]+ ∂

∂η


∂η

]+ ∂

∂z


∂z

]+ ϕ

qfJ

+ h

J(Φs − Φf) (7.43)

Substituting Eqs. (7.27), (7.29), (7.31), and (7.39) in Eq. (7.24) and rearrangingthe terms, whereΦ = T and Γ Φ = K f , we obtain for the fluid phase, the followingequation:

∂

∂t

⎡⎣ ϕ(ρcp)fL

2(ξ2 − η2

)Tf√(

ξ2 − 1)(1 − η2

)⎤⎦+ ∂

∂ξ

⎡⎣(ρcp)fL

2(ξ2 − η2

)uξ Tf√(

ξ2 − 1)(1 − η2

)⎤⎦+ ∂

∂η

⎡⎣(ρcp)fL

2(ξ2 − η2

)uηTf√(

ξ2 − 1)(1 − η2

)⎤⎦

+ ∂

∂z

⎡⎣(ρcp)fL

2(ξ2 − η2

)uzTf√(

ξ2 − 1)(1 − η2

)⎤⎦ = ∂

∂ξ

[√ (ξ2 − 1

)(1 − η2

) ϕKf∂T f

∂ξ

]+ ∂

∂η

[√ (1 − η2

)(ξ2 − 1

) ϕKf∂T f

∂η

]

+ ∂

∂z

⎡⎣ L2

(ξ2 − η2

)√(

ξ2 − 1)(1 − η2

) ϕKf∂Tf∂z

⎤⎦+

L2(ξ2 − η2

)√(

ξ2 − 1)(1 − η2

) [ϕqf + h(Ts − Tf)] (7.44)

Considering uz � uξ and uz � uη, the Eq. (7.44) assumes the way:

∂

∂t

⎡⎣ϕ(ρcp)fL

2(ξ 2 − η2

)Tf√(

ξ 2 − 1)(1 − η2

)⎤⎦+ ∂

∂z

⎡⎣(ρcp)fL

2(ξ 2 − η2

)uzTf√(

ξ 2 − 1)(1 − η2

)⎤⎦ =

∂

∂ξ

[√(ξ 2 − 1

)(1 − η2

)ϕKf∂Tf∂ξ

]+ ∂

∂η

[√(1 − η2

)(ξ 2 − 1

)ϕKf∂Tf∂η

]

+ ∂

∂z

⎡⎣ L2

(ξ 2 − η2

)√(

ξ 2 − 1)(1 − η2

)ϕKf∂Tf∂z

⎤⎦+ L2

(ξ 2 − η2

)√(

ξ 2 − 1)(1 − η2

) [ϕqf + h(Ts − Tf)]

(7.45)

Similarly, for the energy equation applied to the solid phase, and substitutingΦ = T and Γ φ = Ks, we obtain

∂

∂t

⎡⎣ (1 − ϕ)

(ρcp)sL

2(ξ 2 − η2

)Ts√(

ξ 2 − 1)(1 − η2

)⎤⎦ = ∂

∂ξ

[√(ξ 2 − 1

)(1 − η2

) (1 − ϕ)Ks∂Ts∂ξ

]

+ ∂

∂η

[√(1 − η2

)(ξ 2 − 1

) (1 − ϕ)Ks∂Ts∂η

]+ ∂

∂z

⎡⎣ L2

(ξ 2 − η2

)√(

ξ 2 − 1)(1 − η2

) (1 − ϕ)Ks∂Ts∂z

⎤⎦

+ L2(ξ 2 − η2

)√(

ξ 2 − 1)(1 − η2

) [(1 − ϕ)qs + h(Tf − Ts)]

(7.46)


Fig. 7.7 Scheme showingthe heat exchangesconsidered in the boundaryfor the solid and fluid phases

Since Eqs. (7.45) and (7.46) are second order in space and first order in timedifferential equations, their solution requires at least two boundary conditions foreach direction and one initial condition.Moreover, it is an elliptical equation, makingit necessary to define these boundary conditions along the entire boundary of theconsidered domain. Thus, considering Fig. 7.7, the following initial and boundaryconditions are given:

(a) Prescribed temperature condition at the reactor inlet:

T (ξ, η, z = 0, t) = T0 (7.47)

(b) Parabolic condition at reactor output:

∂T

∂z(ξ, η, z = H, t) = 0 (7.48)

(c) Symmetry conditions:

∂T

∂ξ(ξ = 1, η, z, t) = 0 (7.49)

∂T

∂η(ξ, η = 0, z, t) = 0 (7.50)

∂T

∂η(ξ, η = 1, z, t) = 0 (7.51)

(d) Reactor wall conditions


It is considered that in the reactor wall heat diffusive and convective fluxes (only forthe fluid phase) occur on the inner side of the wall that equals the diffusive heat fluxat the reactor wall, which is equal to the convective heat flux, at the external side ofthe reactor wall. Thus, can be written as

q ′′ = − k

L

√ (ξ 2 − 1

)(ξ 2 − η2

) ∂T

∂ξ

∣∣∣∣∣(ξ=ξin)

+ hwin(TP − Twin) = hwext(Twext − Tm) =

− kwrL

√ (ξ 2 − 1

)(ξ 2 − η2

) ∂T

∂ξ

∣∣∣∣∣(ξ=ξext)

(7.52)

where ξ in = L2/L on the surface (Fig. 7.5) and the subscript wr means the reactorwall location.

7.3.3 Numerical Treatment of Heat Transport Equations

It is well known by the scientific community that physical problems related to trans-port phenomena (energy, linear momentum, and mass) have a high complexity andinevitably are governing by partial differential equations. To obtain an analyticalsolution to problems of this insignificance, when it is achieved, will require labo-rious and rigorous mathematical treatment, with severe considerations. Thus, the useof numerical techniques emerges as an alternative for the interpretation and solutionof the physical problem with great consistence and realism.

The advance in the study of physical problems involving computer simulation,as well as the speed of computer processing today, has significantly increased thesearch for the analysis of such problems through numerical solutions. There areseveral numerical methods that are being used by the scientific community. In thischapter, we will use the finite-volume method, which has as its basic principle thetransformation of partial differential equations into elementary algebraic equations.The fundamental concept of the finite-volumemethod is that any continuous quantitycan be approximated by a discrete model, consisting of a set of continuous functions,defined in a finite number of subdomains, so-called control-volumes, with nodalpoints located in the centroid of them (Patankar 1980; Maliska 1995).

Figure 7.8 illustrates the computational domain used to represent the physicaldomain in the fixed-bed elliptic cylindrical reactor, where there is symmetry in thefour quadrants (see Figs. 7.5 and 7.6). In Fig. 7.8, the control-volume is associatedwith the nodal point P and the lines ξ and η constants defining the contour. The pointsF, T, N, S, E, and W are the neighboring nodal points (top, bottom, north, south,east, and west, respectively).

Considering the control-volume outlined in Fig. 7.8, it is possible to make thediscretization of Eqs. (7.45) (fluid phase) and (7.46) (solid phase) by integratingeach term in volume and time. Assuming a fully implicit formulation and theWUDS


Fig. 7.8 Numerical mesh control-volume in the elliptical cylindric coordinate system

scheme as a spatial interpolation function for the convective and diffusive fluxesover the control-volume, after rigorous mathematical treatment we obtain the energyequations for both phases in the discretized form, as follows.

• Fluid phase

APfTPf = AEfTEf + AWfTWf + AN f TNf + ASfTSf + AFfTFf + ATfTTf + A0PfT

0Pf + Bf

(7.53)

where

AFf = L2(ξ 2f − η2

f

)√(

ξ 2f − 1

)(1 − η2

f

)[ϕKffβff

δzf− (0.5 − αf)ρffcPffuz

]�ξ�η (7.54)

ATf = L2(ξ 2t − η2

t

)√(

ξ 2t − 1

)(1 − η2

t

)[ϕKtfβtf

δzt+ (0.5 + αt)ρtfcPtfuz

]�ξ�η (7.55)


AEf =√(

1 − η2e

)(ξ 2e − 1

) ϕKefβef

δηe�ξ�z (7.56)

AWf =√(

1 − η2w

)(ξ 2w − 1

) ϕKwfβwf

δηw�ξ�z (7.57)

ANf =⎧⎨⎩√

(ξ 2n −1)

(1−η2n)

ϕKnfβnf

δηn�η�z, Internal points.

0,Boundary points.(7.58)

ASf =√(

ξ 2s − 1

)(1 − η2

s

) ϕKsfβsf

δηs�η�z (7.59)

A0Pf = L2

(ξ 2 − η2

)√(

1 − η2)(

ξ 2 − 1) ϕ0ρ0

f c0Pf�ξ�η�z

�t(7.60)

APf = AEf + Awf + ANf + ASf

+ L2(ξ 2f − η2

f

)√(

ξ 2f − 1

)(1 − η2

f

)[ϕKffβff

δzf+ (0.5 + αf)ρffcPffuz

]�ξ�η

+ L2(ξ 2t − η2

t

)√(

ξ 2t − 1

)(1 − η2

t

)[ϕKtfβtf

δzt− (0.5 − αt)ρtfcPtfuz

]�ξ�η + SMf

+ L2(ξ 2 − η2

)√(

1 − η2)(

ξ 2 − 1)[ϕρfcPf

�t+ asfhsf

]�ξ�η�z (7.61)

SMf =

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

L�η�z

√(ξ 2

n −η2P)

(1−η2P)⎡

⎢⎢⎣

⎛⎝1+ Kf

Kwr+ hwinf

hwextf+ KfU

∧

hwextfδξn+ hwinfδξn

KwrU∧

⎞⎠

⎛⎝hwinf+ K fU

∧

δξn

⎞⎠

⎤⎥⎥⎦

, Boundary points.

0, Internal points

(7.62)


Bf =

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

L

√(ξ 2

n −η2P)

(1−η2P)

�η�z

⎡⎢⎢⎣

⎛⎝1+ Kf

Kwr+ hwinf

hwextf+ KfU

∧

hwextfδξn+ hwinfδξn

KwrU∧

⎞⎠

⎛⎝hwinf+ KfU

∧

δξn

⎞⎠

⎤⎥⎥⎦

, Boundary points.

L2(ξ 2 − η2

)√(

1 − η2)(

ξ 2 − 1) [ϕqf + asfhsfTS)]�ξ�η�z, Internal points.

(7.63)

• Solid phase

APsTPs = AEsTEs + AwsTws + ANsTNs + ASsTSs + AFsTFs + ATsTTs + A0PsT

0Ps + Bs

(7.64)

where

AEs =√(

1 − η2e

)(ξ 2e − 1

) (1 − ϕ)Kesβes

δηe�ξ�z (7.65)

Aws =√(

1 − η2w

)(ξ 2w − 1

) (1 − ϕ)Kwsβws

δηw�ξ�z (7.66)

ANs =⎧⎨⎩

0, Internal points.√(ξ 2

n −1)(1−η2

n)(1−ϕ)Knsβns

δηn�η�z, Boundary points.

(7.67)

ASs =√(

ξ 2s − 1

)(1 − η2

s

) (1 − ϕ)Kssβss

δξs�η�z (7.68)

AFs = L2(ξ 2f − η2

f

)√(

ξ 2f − 1

)(1 − η2

f

) (1 − ϕ)Kfsβfs

δzf�ξ�η (7.69)

ATs = L2(ξ 2t − η2

t

)√(

ξ 2t − 1

)(1 − η2

t

) (1 − ϕ)Ktsβts

δzt�ξ�η (7.70)

A0Ps = L2

(ξ 2 − η2

)√(

1 − η2)(

ξ 2 − 1)(1 − ϕ0

)ρ0s c

0Ps�ξ�η�z

�t(7.71)

APs = AEs + Aws + ANs + ASs + AFs + ATs +L2(ξ2 − η2

)√(

1 − η2)(

ξ2 − 1)[

(1 − ϕ)ρscPs�t

+ asfhsf

]+ SMs (7.72)


SMs =

⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩

L�η�z

√(ξ2n −η2P)(1−η2P)⎡

⎢⎢⎢⎢⎣

⎛⎜⎝1+ Ks

Kwr+ KsU

∧

hwextsδξn

⎞⎟⎠

⎛⎜⎝ KsU∧

δξn

⎞⎟⎠

⎤⎥⎥⎥⎥⎦

, Boundary points.

0, Internal points.

(7.73)

Bs =

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

L

√(ξ 2

n −η2P)

(1−η2P)

�η�z

⎡⎢⎣(1+ Ks

Kwr+ KsU

∧

hwextsδξn

)

(KsU∧

δξn

)

⎤⎥⎦

, Boundary points.

L2(ξ 2 − η2

)√(

1 − η2)(

ξ 2 − 1) [(1 − ϕ)qs + asfhsfTf)]�ξ�η�z, Internal points.

(7.74)

The coefficients AK ,K �= P, represent the components of diffusive and convectiveheat transfer from the neighboring points toward the P point. The effects of the vari-able T in on previous time its value in the present time are computed in the coefficientA0P . These effects are gradually reduced as the process tends to steady-state condi-

tion. The applications of Eqs. (7.53) and (7.64) are restricted to the computationaldomain.

Nodal points on the domain contour are not into the set of linear algebra equationsto solve. After the system of equations has been solved, the estimation of the variableT is performed in these nodal points. For example, for symmetry axes, it is assumedthat the conduction heat flux leaving the point adjacent to the symmetry point is equalto the conduction heat flux arriving at these points, as illustrated in Fig. 7.9.

These points can be mathematically expressed for the fluid phase, for example,as follows.

(−K f

L

√ (1 − η2

)(ξ 2 − η2

) ∂T

∂η

)∣∣∣∣∣e

=(

−K f

L

√ (1 − η2

)(ξ 2 − η2

) ∂T

∂η

)∣∣∣∣∣w

(7.75)

Thus, by discretizing Eq. (7.75) and rearranging the common terms, thetemperature at the nodal points in η = 0, is given by

TEf =

⎡⎢⎢⎣1 +

⎛⎜⎜⎝

Kfwδηw

√(1−η2

w)(ξ 2

P−η2w)

KfPδηe

√(1−η2

e)(ξ 2

P−η2e)

⎞⎟⎟⎠⎤⎥⎥⎦TPf −

⎛⎜⎜⎝

Kfwδηw

√(1−η2

w)(ξ 2

P−η2w)

KfPδηe

√(1−η2

e)(ξ 2

P−η2e)

⎞⎟⎟⎠TWf (7.76)


Fig. 7.9 Schematicrepresentation of a symmetrypoint on face η = 0

The representative equation for determining the fluid phase temperature in theinner wall of the porous bed (see Fig. 7.7) is given by

Twinf =Tm + TPf

(KfKwr

+ hwinhwext

+ KfU∧

hwextδξn+ hwinδξn

KwrU∧

)(1 + Kf

Kwr+ hwin

hwext+ KfU

∧

hwextδξn+ hwinδξn

KwrU∧

) (7.77)

7.4 Application: Heat Transfer in an Elliptic CylindricalReactor Filled with Spheroidal Particles

In this chapter, as an application will be considered the heated air flow percolating abed of prolate spheroidal particles in the local thermal equilibrium condition and insteady state. The reactor wall is cooled by water at room temperature Tm.

The thermophysical and geometrical parameters used in the simulation can beseen in Table 7.1.

In the software Mathematica® a computational code was developed to solvethe set of discretized equations, using Gauss–Seidel solution method, considering aconvergence criterion of 10−9. All results were obtained using a mesh with 20 × 20×20 control-volumes obtained after some refinements.


Table 7.1 Thermophysical and geometrical parameters used in the simulation

Reactor Air (fluid phase) Particles (solid phase)

L1 (m) L2 (m) kf (W/mK)

hwext (W/m2 K) ρf (kg/m3) ks (W/mK) b (m) a (m)

0.05 0.10 2.47 ×10−3

2.69 1.09488 5.64 2.5 ×10−3

2.0 ×10−3

H (m) Kwr (W/mK) uz (m/s) cpf (J/kg K) μf (kg/ms)

ρs (kg/m3) cps (J/kgK)

ϕ

0.20 401 0.10 1000 2.025 ×10−5

487 5500 0.44

Tm (°C) T0 (°C) β

30 70 0.85

The results presented here take into account the dimensionless temperatureprofiles (T − Tm)/(T 0 − Tm) in different xy planes (z/H = 0.0833, 0.5277 and0. 9722) and on the yz(x/L = 0.0) and xz(y/L = 0.0) planes. Percolating fluid has theconvection heat transfer coefficient (hwint) calculated by correlations involving theparticle Reynolds number (Beek 1975), as follows:

Rep = 2ρuzϕdp3μ(1 − ϕ)

(7.78)

The Colburn factor (JH) and the Stanton number (St) both for heat transfer aregiven as follows (Incropera and De Witt 1992):

JH = 2.06Re−0.575p (7.79)

and

St = JHPr2/3

(7.80)

Since that the Stanton number is defined by

St = h

ρVcP(7.81)

we can write

hwint = Stρuzϕcp (7.82)

Figures 7.10, 7.11, 7.12 illustrate the dimensionless temperature distribution inthe xy plane at different axial positions for the solid and fluid phases. Figures 7.13,


(a) Fluid phase, z/H= 0.0833. (b) Solid phase z/H = 0.0833.

(c) Fluid phase, z/H = 0.5277. (d) Solid phase, z/H = 0.5277.

(e) Fluid phase, z/H = 0.9722. (f) Solid phase, z/H = 0.9722.

Fig. 7.10 Dimensionless temperature distribution within a fixed-bed elliptic cylindrical reactorfilled with prolate spheroidal particles (hwint = 1.03 × 10−4 W/m2 K)

7.14, 7.15 illustrate the dimensionless temperature distribution in the xz and yz planesfor the solid and fluid phases.

Considering the inner wall of the reactor, it can be observed that an increase inthe heat transfer coefficient on the inner wall of the reactor (hwint) from 1.03 × 10−4

W/m2 K to 40 W/m2 K does not cause significant changes in the temperature fieldfor both phases inside the reactor. Major changes can be seen in the region near theoutlet (z/H = 0.9722) on the surface (x = L2).

Radial dimensionless temperature gradients are high at the reactor inlet due to thethermal inlet effects. As the axial position increases along the reactor, these radialgradients decrease. It can be seen at any axial position along the bed that the radialdimensionless temperature gradients are slightly most affected by larger for the fluidphase than the solid phase, and that the region near the reactor surface ismore affectedby the cold wall.


(a) Fluid phase, z/H = 0.0833. (b) Solid phase z/H = 0.0833.


(e) Fluid phase, z/H = 0.9722 (f) Solid phase, z/H = 0.9722.

Fig. 7.11 Dimensionless temperature distribution within fixed-bed elliptical cylindric reactor filledwith prolate spheroidal particles (hwint = 2.0 W/m2 K)


In this chapter, the physical problem of heat transfer and fluid flow in a particle-filledfixed-bed has been studied. Emphasis is given to elliptical cross-sectional reactors.

A transient mathematical modeling written in elliptic cylindrical coordinatesapplied to the particulate and fluid phases was proposed, and its numerical solution,which is based on the finite-volume method, is presented.

Results of temperature distribution within the reactor at different planes have beenpresented and discussed. From the results obtained, the following conclusions aregiven:

(a) Under the physical point of view the heterogeneous mathematical model provedto be satisfactory for the study of heat transfer in fixed-bed reactorwith an ellipticcylindrical geometry;

(b) The temperature distribution of the phases indicates that heat flux occurs fromthe center toward the reactor wall (angular and radial directions) and in the axialdirection from the inlet to the outlet region;


(a) Fluid phase, z/H = 0.0833. (b) Solid phase z/H = 0.0833.


(e) Fluid phase, z/H = 0.9722. (f) Solid phase, z/H = 0.9722.

Fig. 7.12 Dimensionless temperature distribution within fixed-bed elliptic cylindrical reactor filledwith prolate spheroidal particles (hwint = 40 W/m2 K)

(c) Axial temperature gradients aremost relevant in the region near the reactor inlet;(d) Radial temperature gradients are larger near the reactor wall;(e) The temperature distribution within the reactor was higher for solid phase as

compared to the fluid phase;


a) Fluid phase (y/L=0.0). b) Fluid phase (x/L=0.0).

c) Solid phase (y/L=0.0). d) Solid phase (x/L=0.0).

Fig. 7.13 Dimensionless temperature distribution of the fluid and solid phases inside the ellipticcylindrical reactor (hwint = 1.03 × 10−4 W/m2 K)




Fig. 7.14 Dimensionless temperature distribution of the fluid and solid phases inside the ellipticcylindrical reactor (hwint = 2.0 W/m2 K)




Fig. 7.15 Dimensionless temperature distribution of the fluid and solid phases inside the ellipticcylindrical reactor (hwint = 40 W/m2K)


Acknowledgments The authors thank to FINEP,CAPES andCNPq (BrazilianResearchAgencies)for financial support to this research, and also to the researchers for their referenced studies whichhelped in improving the quality of this work.

References

Alazmi, B., Vafai, K.: Analysis of variants within the porous media transport models. J. Heat Transf.122(2), 303–326 (2000)

Beek, W.J., Muttzall, K.M.K.: Transport Phenomena. Wiley, London (1975).Bunnell, D.G., Irvin, H.B., Olson, R.W., Smith, J.M.: Effective thermal conductivities in gas-solidsystems. Ind. Eng. Chem. Res. Dev. 41(9), 1977–1981 (1949)

Curray, J.K., Griffiths, J.C.: Sphericity and roundness of quartz grains in sediments. Bull. Geol.Soc. Am. 66, 1075–1096 (1955)

Dixon, A.G., Cresswell, D.L.: Theoretical prediction of effective heat transfer parameters in packedbeds. AIChE J. 25(4), 663–676 (1979)

Dullien, F.A.L.: Porous Media: Fluid Transport and Pore Structure, 2nd edn. Academic Press, SanDiego, USA (1992)

Freire, J.T.: Heat andmass dispersion in flows through porousmedia. J. PorousMedia 7(2), 143–153(2004)

Froment, G.F., Hofmann, H.P.K.: Design of fixed-bed gas-solid catalytic reactors. In: Carberry, J.J.,Varma, A. (eds.) Chemical Reaction and Reactor Engineering. Marcel Dekker, Inc., New York(1987)

Fábrega, F.M.: Calculus of Reactor I. Report. Pitágoras de Jundiaí College, 1st ed. Jundiaí, Brazil(2012)

Giordano, R.C.: Modeling and optimization of natural gas steam reforming. Doctoural Thesis,Escola Politécnica, University of São Paulo, São Paulo, Brazil (1991). (In Portuguese)

Grangeot, G., Quintard,M.,Whitaker, S.: Heat transfer in packed beds: interpretation of experimentsin terms of one- and two-equation models. Heat Transfer 1994. Inst. Chem. Eng., Rugby, 5,291–296 (1994)

HandleyD, Heggs P.J.:Momentum and heat transfermechanisms in regular shaped packings, Trans.Inst. Chem E, 46: paper T251 (1968)

Incropera, F.P., De Witt, D.P.: Fundamentals of Heat and Mass Transfer, 3 edn. LTC—LivrosTécnicos e Científicos Editora S.A., Rio de Janeiro (1992). (In Portuguese)

Lima, A.G.B.: Diffusion Phenomena in Prolate Spheroidal Solids. Studied Case: Drying of Banana.Doctoral thesis in Mechanical Engineering, State University of Campinas, Campinas, Brazil(1999). (In Portuguese)

Magnus, W., Oberhettinger, F., Soni, R.P.: Formulas and Theorems for the Special Functions ofMathematical Physics, 3rd edn. Springer, Berlin (1966)

Maliska, C.R.: Heat Transfer and Computational Fluid Mechanics. LCT-Livros Técnicos eCientíficos Editora S. A, Rio de Janeiro (1995). (In Portuguese)

McCabe,W.L., Smith, J.C., Harriot, P.: Unit Operations of Chemical Engineering, 4th edn.McGraw- Hill International Editions, New York, USA (1985)

McRobert, T.M.: Spherical Harmonics: An Elementary Treatise on Harmonic Functions withApplications. Pergamon Press, Oxford (1967)

Mendes, N.: Heat and moisture prediction models for building porous elements. Doctoral Thesis,Federal University of Santa Catarina, Florianópolis, Brazil (1997). (In Portuguse)

Miyauchi, T.S., Furusaki, S., Morooka, S., Ikeda, Y.: Transport Phenomena and Reaction in CatalystBeds. In: Drew, T.B., Cokelet, G.R., Hoopes Jr., J.W., Vermeulen, T. (eds.) Advances in ChemicalEngineering, vol. 11, 276–449. Academic Press, New York (1981)


Nield,D.A.:Anote on themodeling of local thermal non-equilibrium in a structured porousmedium.Int. J. Heat Mass Transf. 45(21), 4367–4368 (2002)

Nield, D.A., Bejan, A.: Convection in Porous Media. Springer, New York (1992)Oliveira, L.G.: Heat transfer in packed bed cylindrical-elliptical reactor: thermal-fluid dynamicsand geometric aspects. Doctoral thesis in Process Engineering, Federal University of CampinaGrande, Campina Grande, Brazil (2004). (In Portuguese)

Patankar, S.V.: Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing Corporation, NewYork (1980)

Polyaev, V.M., Mozhaev, A.P., Galitseysky, B.A., Lozhkin, A.L.: A study of internal heat transferin nonuniform porous structures. Expt. Therm. Fluid Sci. 12, 426–432 (1996)

Quintard, M., Kaviany, M., Whitaker, S.: Two-medium treatment of heat transfer in porous media:numerical results for effective properties. Adv. Water Resour. 20, 77–94 (1997)

Quintard, M. Whitaker, S.: Theorical Analysis of Transport in Porous Media. In: Vafai, K. (ed.)Handbook of Heat Transfer in Porous Media, pp. 1–52. Marcel Dekker, Inc., New York (2000)

Saito, M.B., de Lemos, M.J.S.: Interfacial heat transfer coefficient in nonequilibrium convectivetransport in porous media. Int. Comm. Heat Mass Transf. 32(5), 666–676 (2005)

Silva, R.M., Lima, A.G.L., Oliveira, L.G., Araújo, M.V., Santos, R.S.: Transient heat transfer in apacked-bed elliptic cylindrical reactor: a finite-volume approach. Def. Diff. Forum 380, 79–85(2017)

Silva, R.M., Lima, A.G.B., Pereira, A.S., Machado, M.C.N., Santos, R.S.: Unsteady state heattransfer in packed-bed elliptic cylindrical reactor: theory, advanced modeling and applications.In: Delgado, J.M.P.Q, Lima, A.G.B (eds.) Transport Phenomena in Multiphase Systems, vol. 93,pp. 139–179. Springer International Publishing AG, Cham (2018)

Silva Filho, A.A., Silva de Almeida, J.P., Lima, A.G.B.: Heat transfer inside elliptic cylindricalreactor: effect of bed porosity. Def. Diff. Forum, 336, 97–102 (2013)

Wakao, N., Kaguei, S.: Effect of fluid dispersion coefficients on particle-to-fluid heat transfercoefficients in packed beds. Chem. Eng. Sci. 34, 325–336 (1979)

Wakao, N., Kaguei, S.: Heat and Mass Transfer in Packed Beds. Gordon and Breach SciencePublishers, New York (1982)

Wakao, N., Tanaka, K., Nagai, H.: Measurement of particle-to-gas mass transfer coefficients fromchromatographic adsorption experiments. Chem. Eng. Sci. 31, 1109–1113 (1976)

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