powder technology handbook

Third Edition

2006 by Taylor & Francis Group, LLC

www.pharmatechbd.blogspot.com

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edited by

Hiroaki MasudaKo HigashitaniHideto Yoshida

Third Edition

A CRC title, part of the Taylor & Francis imprint, a member of theTaylor & Francis Group, the academic division of T&F Informa plc.

Boca Raton London New York



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Published in 2006 byCRC PressTaylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300Boca Raton, FL 33487-2742

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Preface to the Third Edition Powders and particles are extending their applications in recent developing fields such as the information market, including mobile phones, copy machines, and electronic displays, as well as pharmaceuticals, cosmetics, foods, chemicals, and many other fundamental engineering fields. Nanoparticles are also promising research subjects for the development of more effective applica-tions of various particles. They need powder technology in their preparation, characterization, mea-surement, and functional treatment and for totally systematic handling.

Since the first edition published in 1988 and the second edition in 1997, the Powder Technology Handbook has been accepted in many fields of engineering. Because of this acceptance and the encouragement of Russell Dekker, we agreed to update the book and present this third edition.

This new edition has been substantially revised and expanded. The content has been updated, not only by adding newly developed areas such as simulations, surface analysis, and nanoparticles, but also by introducing new young authors. Some sections are combined, so that the readers can easily refer to the subject.

We hope this handbook will serve as a strong guide to the field of powder and particle technology. Special acknowledgment is given to all contributors and also to all the original authors whose

valuable work is cited in this handbook. We also extend acknowledgment to Dr. Matsusaka, associ-ate professor of Kyoto University, for his collaboration on the editing work.

With this, our third edition, we thank our new editorial staff: Kari Budyk, Tao Woolfe, and others at Taylor & Francis Books (formerly Marcel Dekker) for their laborious editing and produc-tion work.

HIROAKI MASUDA

KO HIGASHITANI

HIDETO YOSHIDA

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Preface to the Second Edition Since first published in 1988, the Powder Technology Handbook has been accepted as a reference in many areas of engineering. Because of this acceptance and the support of Russell Dekker, the Chief Publishing Officer of our publisher, we agreed to update the book and present this second edition.

This entire book has been substantially revised. American and European authors have been invited to join the Japanese authors who participated in writing the first edition, giving the book a wider viewpoint. In response to reviews for the first edition, the contents have been reorganized. New sections have been added to treat the recent advances in computer simulation (V.19) and work-ing atmospheres and hazards (VII.1VII.3). This second edition contains a more detailed table of contents so that readers can understand the whole range of the handbook.

It is hoped that this handbook will serve as a strong guide to the field of particle technology. Special acknowledgment is given to Dr. Koichi Iinoya, professor emeritus of Kyoto University,

for his advisory work. This second edition is dedicated to him on the occasion of his 80th year of age. We are indebted to Joseph Stubenrauch and others at Marcel Dekker, Inc., for their laborious editing work.

KEISHI GOTOH

HIROAKI MASUDA

KO HIGASHITANI

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Preface to the First Edition Particulate or powder technology deals with a variety of particles, from submicrometer to large grains and gravels and from liquid mist or droplets to bubbles, as well as solid particles and aggre-gates. It also deals with two-phase (solidgas, solidliquid, and liquidgas) and three-phase (solidliquidgas) mixtures and is related to work in the medical, biological, pharmaceutical, chemical, mining, metallurgical, mechanical, civil, food and agricultural science, and engineering fields. Many natural and artificial phenomena encountered in our daily lives may be explained by knowledge of powder technology.

The first book on particle technology in general was probably Micromeritics by J. M. Dalavalle, published in 1943; the second may be Particulate Technology by C. Orr, published in 1966. There are also various books on specific fields in powder technology. In Japan, the first handbook was published in 1965 and the second appeared in 1986.

Particulate or powder technology is a fundamental engineering field involving newly developed high or evolutionary technology. Submicrometer particles, for example, are a focus of practical applications.

This handbook has been developed from the second Japanese handbook, although the contents have been revised and updated. It provides a comprehensive understanding of powder technology. Although many investigators have contributed, the various manuscripts have, as much possible, been edited in a unified fashion, so as not to become a mere collection of monographs: Keishi Gotoh has edited the sections on dry powders and Ko Higashitani those on wet powders. Koichi Iinoya assumes the entire responsibility as editor in chief.

Special acknowledgment is given to all contributors who prepared their manuscripts on time. The editors also acknowledge all original authors whose valuable work is cited in this handbook. We are indebted to Nikkan Kougyo Shimbunsha Publishers, who kindly supplied us with the original drawings of all figures used in the Japanese edition. The work of a number of students in relettering the artwork is gratefully acknowledged.

Once again, this handbook provides a comprehensive understanding of powder technology as a sort of encyclopedia and it is hoped that it will be valuable as a guide to this invaluable engineer-ing field. We are indebted to Ms. Lila Harris and others at Marcel Dekker, Inc., for their laborious editing work.

KOICHI IINOYA

KEISHI GOTOH

KO HIGASHITANI

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Editors Hiroaki Masuda is a professor in the Department of Chemical Engineering at Kyoto University, Japan. He is a member of the Society of Chemical Engineers, Japan and the Institute of Electrostatics (Japan), among other organizations, and is the president of the Society of Powder Technology, Japan. His research interests include electrostatic characterization, adhesion and reentrainment, dry dispersion of powder, and fine particle classification. Dr. Masuda received his Ph.D. degree (1973) in chemical engineering from Kyoto University, Japan.

Ko Higashitani graduated from the Department of Chemical Engineering, Kyoto University, Japan in 1968. He worked on hole pressure errors of viscoelastic fluids as a Ph.D. student under the supervi-sion of Professor A. S. Lodge in the Department of Chemical Engineering, University of WisconsinMadison, USA. After he received his Ph.D. degree in 1973, he moved to the Department of Applied Chemistry, Kyushu Institute of Technology, Japan, as an assistant professor, and then became a full professor in 1983. He joined the Department of Chemical Engineering, Kyoto University, in 1992. His major research interests now are the kinetic stability of colloidal particles in solutions, such as coagulation, breakup, adhesion, detachment of particles in fluids, and slurry kinetics. In particular, he is interested in measurements of particle surfaces in solution by the atomic force microscope and how the surface microstructure is correlated with interaction forces between particles and macroscopic behavior of particles and suspensions.

Hideto Yoshida is a professor in the Department of Chemical Engineering at Hiroshima University, Japan. He is a member of the Society of Chemical Engineers, Japan and the Society of Powder Technology, Japan. His research interests include fine particle classification by use of high-performance dry and wet cyclones, standard reference particles, particle size measurement by the automatic-type sedimentation balance method, and the recycling process of fly-ash particles. Dr. Yoshida received his Ph.D. degree (1979) in chemical engineering from Kyoto University, Japan.

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Contributors

Motoaki Adachi Department of Chemical Engineering Frontier Science Innovation CenterOsaka Prefecture University Sakai, Osaka, Japan

Charles S. Campbell School of Engineering, Aerospace and Mechanical Engineering University of Southern California Los Angeles, California, USA

Masatoshi Chikazawa Division of Applied Chemistry Graduate School of Engineering Tokyo Metropolitan University Hachioji, Tokyo, Japan

Reg Davies E. I. Du Pont de Nemours, Inc. Wilmington, Delaware, USA

Shigehisa Endoh National Institute of Advanced Industrial Science and Technology Tsukuba, Japan

Yoshiyuki Endo Process and Production Technology Center Sumitomo Chemical Co., Ltd. Osaka, Japan

Richard C. Flagan Division of Chemistry and Chemical Engineering California Institute of Technology Pasadena, California, USA

Masayoshi Fuji Ceramics Research Laboratory Nagoya Institute of Technology Tajimi, Gifu, Japan

Toyohisa Fujita Department of Geosystem Engineering Graduate School of Engineering University of Tokyo Tokyo, Japan

Yoshinobu Fukumori Faculty of Pharmaceutical SciencesKobe Gakuin University Kobe, Japan

Mojtaba Ghadiri Institute of Particle Science and Engineering School of Process, Environmental and Materials Engineering University of Leeds Leeds, United Kingdom

Kuniaki Gotoh Department of Applied Chemistry Okayama University Okayama, Japan

Jusuke Hidaka Department of Chemical Engineering and Materials Science Faculty of Engineering Doshisha University Kyotanabe, Kyoto, Japan

Ko Higashitani Department of Chemical Engineering Kyoto University Katsura, Kyoto, Japan

Hajime Hori Department of Environmental Health Engineering University of Occupational and Environmental Health Kitakyushu, Fukuoka, Japan

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Hideki Ichikawa Faculty of Pharmaceutical Sciences Kobe Gakuin University Kobe, Japan

Kengo Ichiki Department of Mechanical EngineeringThe Johns Hopkins University Baltimore, Maryland, USA

Hironobu Imakoma Department of Chemical Science and EngineeringKobe University Kobe, Japan

Eiji Iritani Department of Chemical EngineeringNagoya University Nagoya, Chikusa-ku, Japan

Chikao Kanaoka Ishikawa National College of Technology Tsubata, Ishikawa, Japan

Yoichi Kanda Department of Chemical EngineeringKyoto University Katsura, Kyoto, Japan

Yoshiteru Kanda Department of Chemistry and Chemical Engineering Yamagata University Yonezawa, Yamagata, Japan

Yoshiaki Kawashima Gifu Pharmaceutical University Mitahora-Higashi, Gifu, Japan

Yasuo Kousaka Department of Chemical EngineeringOsaka Prefecture University Sakai, Osaka, Japan

Ryoichi Kurose Central Research Institute of Electric Power Industry Yokosuka, Kanagawa, Japan

Hisao Makino Central Research Institute of Electric Power Industry Yokosuka, Kanagawa, Japan

Matsuoka Masakuni Department of Chemical EngineeringTokyo University of Agriculture and Technology Koganei, Tokyo, Japan

Hiroaki Masuda Department of Chemical EngineeringKyoto University Katsura, Kyoto, Japan

Shuji Matsusaka Department of Chemical EngineeringKyoto University Katsura, Kyoto, Japan

Minoru Miyahara Surface Control Engineering Laboratory Department of Chemical EngineeringKyoto University Katsura, Kyoto, Japan

Kei Miyanami Department of Chemical EngineeringOsaka Prefecture University Sakai, Osaka, Japan

Yasushige Mori Department of Chemical Engineering and Materials Science Doshisha University Kyotanabe, Kyoto, Japan

Makio Naito Joining and Welding Research InstituteOsaka University Ibaraki, Osaka, Japan

Yoshio Ohtani Department of Chemistry and Chemical EngineeringKanazawa University Kanazawa, Ishikawa, Japan

Morio Okazaki Department of Chemical EngineeringKyoto University Kyoto, Japan

Kikuo Okuyama Department of Chemical Engineering Hiroshima University Higashi-Hiroshima, Japan

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Jun Oshitani Department of Applied Chemistry Okayama University Okayama, Japan

Yasufumi Otsubo Center of Cooperative ReserchChiba University Image-ku, Chiba, Japan

Isao Sekiguchi Department of Applied Chemistry Chuo University Bunkyo-ku, Tokyo, Japan

Mamoru Senna Faculty of Science and TechnologyKeio University Yokohama, Kanagawa, Japan

Manabu Shimada Department of Chemical EngineeringDivision of Chemistry and Chemical Engineering Hiroshima University Higashi-Hiroshima, Japan

Kunio Shinohara Materials Chemical Engineering, Lab. Division of Chemical Process EngineeringHokkaido University Sapporo, Japan

Yoshiyuki ShirakawaDepartment of Chemical Engineering and Materials ScienceDoshisha UniversityKyotanabe, Kyoto, Japan

Minoru Sugita Ohsaki Research Institute, Inc. Tokyo, Japan

Michitaka Suzuki Department of Mechanical System EngineeringUniversity of Hyogo Himeji, Japan

Hiroshi Takahashi Department of Mechanical Systems EngineeringMuroran Institute of Technology Muroran, Hokkaido, Japan

Minoru Takahashi Ceramics Research LaboratoryNagoya Institute of Technology Tajimi, Aichi, Japan

Takashi Takei Faculty of Urban Environmental ScienceTokyo Metropolitan University Hachioji, Tokyo, Japan

Isamu Tanaka Department of Environmental Health EngineeringUniversity of Occupational and Environmental Health Kitakyushu, Fukuoka, Japan

Tatsuo Tanaka Hokkaido University Sapporo, Japan

Toshitsugu Tanaka Department of Mechanical Engineering Osaka University Suita, Osaka, Japan

Ken-ichiro Tanoue Yamaguchi University Ube, Yamaguchi, Japan

Yuji Tomita Department of Mechanical and Control EngineeringKyushu Institute of Technology Kitakyushu, Fukuoka, Japan

Shigeki Toyama Nagoya University Nagoya, Japan

JunIchiro Tsubaki Department of Molecular Design and Engineering Nagoya University, Nagoya, Japan

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Hirofumi Tsuji Central Research Institute of Electric Power Industry Yokosuka, Kanagawa, Japan

Yutaka Tsuji Department of Mechanical Engineering Osaka University Suita, Osaka, Japan

Hiromoto Usui Department of Chemical Science and EngineeringKobe University Kobe, Japan

Satoru Watano Department of Chemical EngineeringOsaka Prefecture University Sakai, Osaka, Japan

Richard A. Williams Institute of Particle Science and Engineering School of Process, Environmental, and Materials EngineeringUniversity of Leeds Leeds, United Kingdom

Hiroshi Yamato Department of Environmental Health EngineeringUniversity of Occupational and Environmental Health Kitakyushu, Fukuoka, Japan

Toyokazu Yokoyama Hosokawa Powder Technology Research Institute Hirakata, Osaka, Japan

Hideto Yoshida Department of Chemical EngineeringHiroshima University Higashi-Hiroshima, Japan

Hiroki Yotsumoto National Institute of Advanced Industrial Science and Technology Tsukuba, Ibaraki, Japan

Shinichi Yuu Ootake R. & D. Consultant Office Fukuoka, Japan

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Contents

PART I Particle Characterization and Measurement

Chapter 1.1 Particle Size 3

1.1.1 Definition of Particle Diameter 3 1.1.2 Particle Size Distribution 3 1.1.3 Average Particle Size 6

Chapter 1.2 Size Measurement 13

1.2.1 Introduction 13 1.2.2 The Approach 14 1.2.3 Particle Size Analysis Methods and

Instrumentation 15

Chapter 1.3 Particle Shape Characterization 33

1.3.1 Introduction 33 1.3.2 Representative Size 34 1.3.3 Geometrical Shape Descriptors 35 1.3.4 Dynamic Equivalent Shape 45 1.3.5 Concluding Remarks 47

Chapter 1.4 Particle Density 49

1.4.1 Definitions 49 1.4.2 Measurement Method for Particle Density 50

Chapter 1.5 Hardness, Stiffness and Toughness of Particles 53

1.5.1 Indentation Hardness 53 1.5.2 Measurement of Hardness 56 1.5.3 Measurement of Stiffness 59 1.5.4 Measurement of Toughness 60

Chapter 1.6 Surface Properties and Analysis 67

1.6.1 Surface Structures and Properties 67 1.6.2 Surface Characterization 76 1.6.3 Atomic Force Microscopy 93

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PART II Fundamental Properties of Particles

Chapter 2.1 Diffusion of Particles 103

2.1.1 Thermal Diffusion 103 2.1.2 Turbulent Diffusion 109

Chapter 2.2 Optical Properties 115

2.2.1 Definitions 115 2.2.2 Light Scattering 116 2.2.3 Light Extinction 119 2.2.4 Dynamic Light Scattering 122 2.2.5 Photophoresis 123

Chapter 2.3 Particle Motion in Fluid 125

2.3.1 Introduction 125 2.3.2 Motion of a Single Particle 125 2.3.3 Particle Motion in Shear Fields 130

Chapter 2.4 Particle Sedimentation 133

2.4.1 Introduction 133 2.4.2 Terminal Settling Velocity 133 2.4.3 Settling of Two Spherical Particles 138 2.4.4 Rate of Sedimentation in Concentrated

Suspension 139

Chapter 2.5 Particle Electrification and Electrophoresis 143

2.5.1 In Gaseous State 143 2.5.2 In Liquid State 147

Chapter 2.6 Adhesive Force of a Single Particle 157

2.6.1 Van der Waals Force 157 2.6.2 In Gaseous State 159 2.6.3 In Liquid State 162 2.6.4 Measurement of Adhesive Force 163

Chapter 2.7 Particle Deposition and Reentrainment 171

2.7.1 Particle Deposition 171 2.7.2 Particle Reentrainment 174

Chapter 2.8 Agglomeration (Coagulation) 183 2.8.1 In Gaseous State 183 2.8.2 In Liquid State 190

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Chapter 2.9 Viscosity of Slurry 199

2.9.1 Introduction 199 2.9.2 Basic Flow Characteristics 199 2.9.3 Time-Dependent Flow Characteristics 200 2.9.4 Viscosity Equations for Suspensions of Spherical

Particles of Narrow Particle Size Distribution 200 2.9.5 Effect of Particle Size Distribution on Slurry

Viscosity 202 2.9.6 Measurement of Slurry Viscosity by a

Capillary Viscometer 202 2.9.7 Measurement of Slurry Viscosity by a Rotating Viscometer 203

Chapter 2.10 Particle Impact Breakage 205

2.10.1 Impact Force 205 2.10.2 Mode of Breakage 206 2.10.3 Analysis of Breakage for the Semibrittle

Failure Mode 208 2.10.4 Analysis of Breakage of Agglomerates 210

Chapter 2.11 Sintering 213

2.11.1 Mechanisms of Solid-Phase Sintering 213 2.11.2 Modeling of Sintering of Agglomerates 214 2.11.3 Sintering Process of Packed Powder 216

Chapter 2.12 Ignition and Combustion Reaction 219

2.12.1 Combustion Profile 219 2.12.2 Devolatilization and Ignition 219 2.12.3 Gaseous Combustion 221 2.12.4 Solid Combustion 222

Chapter 2.13 Solubility and Dissolution Rate 225

2.13.1 Solubility of Fine Particles 225 2.13.2 Factors to Increase Solubility 225 2.13.3 Theories of Dissolution 226 2.13.4 Measurement of Dissolution Rate 230 2.13.5 Methods to Increase the Dissolution Rate 230

Chapter 2.14 Mechanochemistry 239

2.14.1 Terminology and Concept 239 2.14.2 Phenomenology of Mechanochemistry 239 2.14.3 Theoretical Background 240 2.14.4 Structural Change of Solids under

Mechanical Stress 240 2.14.5 Mechanochemical Solid-State Reaction and

Mechanical Alloying 242

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2.14.6 Soft Mechanochemical Processes and Their Application 242

2.14.7 Recent Developments and Future Outlook 244

PART III Fundamental Properties of Powder Beds

Chapter 3.1 Adsorption Characteristics 249

3.1.1 Introduction 249 3.1.2 Adsorption Measurement 249 3.1.3 Theory of Adsorption Isotherms 250 3.1.4 Adsorption Velocity 255 3.1.5 Adsorbed State of Adsorbate 256 3.1.6 Estimation of Surface Properties by

Adsorption Method 259

Chapter 3.2 Moisture Content 265

3.2.1 Bound Water and Free Water 265 3.2.2 Methods for Determining Moisture

Content in a Particulate System 267

Chapter 3.3 Electrical Properties 269

3.3.1 In Gaseous State 269 3.3.2 In Nonaqueous Solution 275

Chapter 3.4 Magnetic Properties 283

3.4.1 Magnetic Force on a Particle 283 3.4.2 Ferromagnetic Properties of Small Particles 286 3.4.3 Magnetism of Various Materials 288

Chapter 3.5 Packing Properties 293

3.5.1 Packing of Equal Spheres 293 3.5.2 Packing of Multisized Particles 299

Chapter 3.6 Capillarity of Porous Media 309

3.6.1 Common Phenomenon: Young-Laplace Effect 309 3.6.2 Nitrogen Adsorption Method 310 3.6.3 Mercury Intrusion Method

(Mercury Porosimetry) 313 3.6.4 Other Techniques of Interest 314

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Chapter 3.7 Permeation (Flow through Porous Medium) 317 3.7.1 Resistance to Flow through a Porous Medium 317 3.7.2 Pressure Drop across a Fibrous Mat 321

Chapter 3.8 Specific Surface Area 325

3.8.1 Definition of Specific Surface Area 325 3.8.2 Adsorption Method 326 3.8.3 Heat of Immersion 330 3.8.4 Permeametry 332

Chapter 3.9 Mechanical Properties of a Powder Bed 335

3.9.1 Shearing Strength of a Powder Bed 335 3.9.2 Adhesion of a Powder Bed 338 3.9.3 Yielding Characteristics of a Powder Bed 341

Chapter 3.10 Fluidity of Powder 349

3.10.1 Definition of Fluidity 349 3.10.2 Measurement of Fluidity 349 3.10.3 Factors Affecting Fluidity 357 3.10.4 Improvement of Fluidity 357

Chapter 3.11 Blockage of Storage Vessels 361

3.11.1 Phenomena and Factors 361 3.11.2 Mechanisms and Flow Criteria 361 3.11.3 Methods of Preventing Blockage 368

Chapter 3.12 Segregation of Particles 371

3.12.1 Definition and Importance 371 3.12.2 Related Operations 371 3.12.3 Fundamental Mechanisms 372 3.12.4 Patterns and Degrees 376 3.12.5 Minimizing Methods 380

Chapter 3.13 Vibrational and Acoustic Characteristics 383

3.13.1 Behavior of a Particle on a Vibrating Plate 383 3.13.2 Behavior of a Vibrating Particle Bed 385 3.13.3 Generating Mechanism of Impact Sound

between Two Particles 386 3.13.4 Frictional Sound from a Granular Bed 390 3.13.5 Vibration of a Small Particle in a Sound Wave 394 3.13.6 Attenuation of Sound in a Suspension of Particles 396

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PART IV Particle Generation and Fundamentals

Chapter 4.1 Aerosol Particle Generation 401

4.1.1 Condensation Methods 401 4.1.2 Liquid Atomization 404 4.1.3 Powder Dispersion 407 4.1.4 Generation of Monodisperse Particles 408

Chapter 4.2 Generation of Particles by Reaction 413

4.2.1 Gas-Phase Techniques 413 4.2.2 Liquid-Phase Techniques 418

Chapter 4.3 Crystallization 425

4.3.1 Crystallization Phenomena and Kinetics 425 4.3.2 Operation and Design of Crystallizers 428

Chapter 4.4 Design and Formation of Composite Particles 435

4.4.1 Composite Particle Formation in the Fluid Bed Process 436

4.4.2 Particle Design in the Emulsifying Process 443 4.4.3 Summary 445

Chapter 4.5 Dispersion of Particles 449

4.5.1 Particle Dispersion in Gaseous State 449 4.5.2 Particle Dispersion in Liquid State 456

Chapter 4.6 Electrical Charge Control 465

4.6.1 In Gaseous State 465 4.6.2 Charge Control by Contact Electrification

in Gaseous State 473 4.6.3 In Liquid State 474

Chapter 4.7 Surface Modification 485

4.7.1 Purpose of Surface Modification 485 4.7.2 Methods of Surface Modification 485 4.7.3 Conventional Treatments with Surfactants,

Coupling Agents, and Simple Heating 486 4.7.4 Microencapsulation and Nanocoating 486 4.7.5 Polymerization and Precipitation In Situ 488 4.7.6 Mechanical Routes and Apparatus 488 4.7.7 Characterization of Coated Particles 488 4.7.8 Remarks and Recent Developments 490

Chapter 4.8 Standard Powders and Particles 493

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PART V Powder Handling and Operations

Chapter 5.1 Crushing and Grinding 503

5.1.1 Introduction 503 5.1.2 Comminution Energy 503 5.1.3 Crushing of Single Particles 504 5.1.4 Kinetics of Comminution 512 5.1.5 Grinding Operations 515 5.1.6 Crushing and Grinding Equipment 517

Chapter 5.2 Classification 527

5.2.1 Basis of Classification 527 5.2.2 Dry Classification 530 5.2.3 Wet Classification 532 5.2.4 Screening 546

Chapter 5.3 Storage (Silo) 551 5.3.1 General Characteristics of Silos 551 5.3.2 Classification of Silos 551 5.3.3 Planning Silos 552 5.3.4 Design Load 554 5.3.5 Load due to Bulk Materials 554 5.3.6 Calculation of Static Powder Pressure 556 5.3.7 Design Pressures 559

Chapter 5.4 Feeding 561

5.4.1 Introduction 561 5.4.2 Various Feeders 562

Chapter 5.5 Transportation 567

5.5.1 Transportation in the Gaseous State 567 5.5.2 Transportation in the Liquid State 573

Chapter 5.6 Mixing 577

5.6.1 Introduction 577 5.6.2 Powder Mixers 577 5.6.3 Mixing Mechanisms 581 5.6.4 Power Requirement for Mixing 584 5.6.5 Selection of Mixers 587

Chapter 5.7 Slurry Conditioning 591

5.7.1 Slurry Characterization 591 5.7.2 Slurry Preparation 594

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Chapter 5.8 Granulation 599

5.8.1 Granulation Mechanisms 599 5.8.2 Granulators 607

Chapter 5.9 Kneading and Plastic Forming 615

5.9.1 Kneading 615 5.9.2 Plastic Forming 618

Chapter 5.10 Drying 621

5.10.1 Drying Characteristics of Wet Particulate and Powdered Materials 621

5.10.2 Dryer Selection and Design 623

Chapter 5.11 Combustion 629

5.11.1 Introduction 629 5.11.2 Control of the Combustion Process 629 5.11.3 Combustion Burner 629 5.11.4 Furnace and Kiln 633

Chapter 5.12 Dust Collection 637

5.12.1 Flow-Through-Type Dust Collectors 637 5.12.2 Obstacle-Type Dust Collectors 644 5.12.3 Barrier-Type Dust Collectors 649 5.12.4 Miscellaneous 651

Chapter 5.13 Electrostatic Separation 653

5.13.1 Separation Mechanism 653 5.13.2 Separation Machines 656

Chapter 5.14 Magnetic Separation 661

5.14.1 Classification of Magnetic Separators 661 5.14.2 Static Magnetic Field Separators 663 5.14.3 Magnetohydrostatic Separation 668 5.14.4 Electromagnetic-Induction-Type

Separation 670

Chapter 5.15 Gravity Thickening 673

5.15.1 Pretreatment 673 5.15.2 Ideal Settling Basin 673 5.15.3 Settling Curve 675 5.15.4 Kynch Theory 676 5.15.5 Design of a Continuous Thickener 678

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Chapter 5.16 Filtration 683

5.16.1 Basis of Cake Filtration Theory 684 5.16.2 Constant-Pressure and Constant-Rate

Filtration 688 5.16.3 Internal Structure of Filter Cake 690 5.16.4 Non-Newtonian Filtration 692 5.16.5 Filtration Equipment 693

Chapter 5.17 Expression 697

5.17.1 Basis of Expression 697 5.17.2 Modified Terzaghi Model 697 5.17.3 Secondary Consolidation 701 5.17.4 Simplified Analysis 703 5.17.5 Expression Equipment 703

Chapter 5.18 Flotation 705

5.18.1 Principles of Flotation 705 5.18.2 Classification of Minerals according to

Their Flotation Behavior 707 5.18.3 Flotation Reagents 708 5.18.4 Flotation Machines 710 5.18.5 Differential Flotation 714 5.18.6 Plant Practice of Differential Flotation 714

Chapter 5.19 Electrostatic Powder Coating 717

5.19.1 Coating Machines 717 5.19.2 Powder Feeding Machine 719 5.19.3 Powder Coating Booth 720 5.19.4 Numerical Simulation for Electrostatic

Powder Coating 721

Chapter 5.20 Multipurpose Equipment 725

5.20.1 Fluidized Beds 725 5.20.2 Moving Beds 727 5.20.3 Rotary Kiln 731

Chapter 5.21 Simulation 737

5.21.1 Computer Simulation of Powder Flows 737 5.21.2 Breakage of Aggregates 748 5.21.3 Particle Motion in Fluids 754 5.21.4 Particle Methods in Powder Beds 756 5.21.5 Transport Properties 760 5.21.6 Electrical Properties of Powder Beds 764

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PART VI Process Instrumentation

Chapter 6.1 Powder Sampling 771

6.1.1 Sampling Equipment 771 6.1.2 Analysis of Sampling 774

Chapter 6.2 Particle Sampling in Gas Flow 779

6.2.1 Anisokinetic Sampling Error 779 6.2.2 Sampling in Stationary Air 780 6.2.3 Practical Applications of Particle Sampling 783

Chapter 6.3 Concentration and Flow Rate Measurement 795

6.3.1 Particle Concentration in Suspensions 795 6.3.2 Powder Flow Rate 799

Chapter 6.4 Level Measurement of a Powder Bed 805

6.4.1 Level Meters and Level Switches 805 6.4.2 Mechanical Method 806 6.4.3 Electrical Method 808 6.4.4 Ultrasonic Wave Level Meters 809 6.4.5 Radiometric Method 809 6.4.6 Pneumatic Method and Others 810

Chapter 6.5 Temperature Measurement of Powder 813

6.5.1 Thermal Contact Thermometers 813 6.5.2 Radiation Thermometers 814

Chapter 6.6 On-Line Measurement of Moisture Content 817

6.6.1 Introduction 817 6.6.2 Electrical methods 817 6.6.3 Infrared Moisture Sensor 821 6.6.4 Application of Moisture Control to

Powder-Handling Processes 823

Chapter 6.7 Tomography 827

6.7.1 Introduction 827 6.7.2 Sensor Selection and Specification 829 6.7.3 Examples of Powder-Processing Applications 830

PART VII Working Atmospheres and Hazards

Chapter 7.1 Health Effects Due to Particle Matter 837

7.1.1 Introduction 837

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7.1.2 Respiratory System 837 7.1.3 Penetration and Deposition of Particles in

the Respiratory Tract 838 7.1.4 Fate of Deposited Particles 839 7.1.5 Health Effects of Inhaled Particles 840 7.1.6 Threshold Limit Value 841

Chapter 7.2 Respiratory Protective Devices for Particulate Matter 843

7.2.1 Introduction 843 7.2.2 Types of Respirators 843 7.2.3 Air-Purifying Respirators 843 7.2.4 Atmosphere-Supplying Respirators 845 7.2.5 Protection Factor 846 7.2.6 Notes for Using Respirators 847

Chapter 7.3 Spontaneous Ignition and Dust Explosion 849

7.3.1 Spontaneous Ignition of Powder Deposits 849 7.3.2 Dust Explosion Mechanism and Prevention 861

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Part I Particle Characterization and Measurement

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3Particle Size JunIchiro Tsubaki Nagoya University, Nagoya, Japan

1.1.1 DEFINITION OF PARTICLE DIAMETER

Particle size data are essential to anyone treating powders. Expressing the size of a single particle is not a simple task when the particle is nonspherical. Expressions of individual particle size and a

of variously defined characteristic diameters. When a particle is circumscribed by a rectangular prism with length l , width w, and height t , its

size is expressed by the diameter, obtained from the three dimensions. l, w , and t are measured with a microscope. Feret and Martin diameter are statistical diameters, which are affected by the particle orientation or measuring direction. The mean values of them are often defined as characteristic diameters. Unrolled diameter is the mean value of a statistical diameter.

The equivalent diameters are the diameters of spheres having the same geometric or physical properties as those of nonspherical particles.

1.1.2 PARTICLE SIZE DISTRIBUTION

Size Distribution

When a certain characteristic diameter, shown in Table 1.1, is measured for N particles, and the number of particles, dN, having diameters between x and x + dx, is counted, the density size distri-

q xdNN dxo

( ) 1

(1.1)

where

q x dx0 0

1 ( )

(1.2)

The cumulative distribution Q 0 (x) is given as

Q x q x dx0 0( ) ( ) 0x (1.3) Therefore,

dQ xdx

q x00 ( ) ( )

(1.4)

1.1



hypothetical equivalent sphere with regard to some properties. Table 1.1 lists the physical meaning

bution q 0 (x) is defined as


4 Powder Technology Handbook

TABLE 1.1 Expression of Particle Size

Definition of characteristic diameters Physical meaning and corresponding measuring method

Geometric size

Breadth: b Length: l Thickness: t

b b bb

b b

12 3

31 1

2 2 26

1 3 1 2

, , ,

/ /,

/ /l tt l

l l bt lt

Feret diameter Distance between pairs of parallel tangents to the particle silhouette in some fixed direction

Martin diameter Length of a chord dividing the particle silhouette into two equal areas in some fixed direction

Unrolled diameter Chord length through the centroid of the particle silhouette

Sieve diameter

12 1 2 1 2

a a a a( ) ora1, a2: Openings of sieves

Volume: v Equivalent diameter

Equivalent projection area diameter (Heywood diameter)

Diameter of the circle having same area as projection area of particle, corresponding to diameter obtained by light extinction

Surface: s Equivalent surface area diameter (specific surface diameter) (s/p)1/2

Diameter of the sphere having the same surface as that of a particle

Equivalent volume diameter (6v/p)1/3

Diameter of the sphere having the same volume as that of a particle, corresponding to diameter obtained by (electrical sensing zone method)

Stokes diameter Diameter of the sphere having the same gravitational settling velocity as that of particle obtained by gravitational or centrifugal sedimentation and impactor

Aerodynamic diameter Diameter of the sphere having unity in specific gravity and the same gravitational settling velocity as that of a particle obtained by the same methods as above

Equivalent light-scattering diameter

Diameter of the sphere giving the same intensity of light scattering as that of a particle, obtained by the light-scattering method






Particle Size 5

The size distributions thus defined are on a number basis. In the case of mass or volume basis, total mass M and fractional mass dM are used instead of N and dN, respectively, and also the sub-script value is changed from 0 to 3, so that q

3 ( x ), Q 3( x ) should be used. In general the subscript is described as r, and r 0, 1, 2, 3 corresponds to number, length, area, and mass or volume basis, respectively. Density distribution q

r ( x ) can be transformed to another basis distribution q

r ( x ) by

q xx q x dx

x q x dxs

s r

r

s r

r

( ) ( )( )

0

(1.5)

When particle size distributes widely, the distributions are plotted versus ln x instead of x and defined as

Q x Q xr

ln ( ) ( ) r (1.6)

q xdQ xd x

xq xr

r

r

(ln ) ( )ln

( )

(1.7)

The density distribution in a representation with a logarithmic abscissa is distinguished by superscript *.

The discrete expression, which gives the size distribution histogram, q r , i, q

* r , i , becomes

qQx

Q x Q xx x

r,ii

r i r i

i i

r i

, ( ) ( )11

(1.8)

qQ

x

Q x Q xx x

r ir i

i

r i r i

i i,

,

ln( ) ( )ln( )

1

1

(1.9)

Normal Distribution

The normal or Gaussian distribution function is defined as

q xx x

r( ) exp 1

2 250

2

2s p s

( )

(1.10)

where x 50 is the 50% or median diameter defined as Qr (x50 ) 0.5 and is the standard deviation

expressing the dispersion of the distribution.

s x x x x84 13 50 50 15 87. . (1.11)

Log-Normal Distribution

The log-normal distribution function is given by substituting ln x and ln g , respectively, for x and

in Equation 1.10 as follows:

q xx x

r

( )

(ln ) ln exp

ln lnln

1

2 250

2

2s sg gp

(1.12) www.pharmatechbd.blogspot.com


where g is the geometric standard deviation given as

sg x

x

x

x

84 13

50

50

15 87

.

.

(1.13)

If a size distribution obeys the log-normal form, the other distribution converted by Equation 1.5 also obeys the log-normal form. The geometric standard deviation of any distribution is the same value; meanwhile, the median diameters are different but can convert each other. In the case of the volume and number distribution the median diameters, x

50,3 , x 50,0, , can convert each other by Hatchs equation.

ln ln ln, ,

x x50 3 50 023 sg (1.14)

RosinRammler (Weibull) Distribution

The RosinRammler or Weibull distribution function is written as

Q x bxr

n( ) exp 1 ( )

or

Q x xx

r

n

( ) exp 1e

(1.15)

where b is a constant equal to x e n

and x

e x

63.2 . n is the distribution constant expressing the dispersion of particle sizes. The density distribution is written as

q x nbx bxr

n n( ) exp( ) 1

or

q xx

x

x

x

xr

n n

( ) exp 1e e

(1.16)

Graphical Representation

abscissa. Q

3, i in Table 1.2 is plotted on log-normal and RosinRammler probability paper, as shown in

distribution obeys the log-normal function of which x 50 1.0 mm and x 84.13 2.2 mm. If we read the

two values of x 15.87 , x 50 or x 84.13 , g can be calculated. From Figure 1.3 x 50 1.0 mm and x 84.13 2.2 mm,

then g 2.2. The dotted line in Figure 1.3 is the number distribution converted from measured volume

distribution by Hatchs equation. ISO 9276-1 (JIS Z 8819-1) standardizes the graphical representation of particle size analysis data.

1.1.3 AVERAGE PARTICLE SIZE

x MMM

MM

k r k rk k r

r

k k r

r

k,,

,

,

,

,

0

0

3 3

3 3 (1.17)



tributions are illustrated in Figure 1.1 with a general abscissa and Figure 1.2 with a logarithmic

Figure 1.3. Since the plots are on a straight line on a log-normal probability graph, the particle size

As an example, a set of data obtained by a sieving test is illustrated in Table 1.2, and the size dis-

and x e is an absolute size constant defined as x e x 63.2 , that is,

All average particle diameters except the geometric mean diameter are defined by


Particle Size 7

Where M k,r is complete k th moment of a q r ( x ) -distribution.

M x q x dxk rk

r,

0

( )

ln ln,x x q x dxr rgeo ( )0 (1.19)

If a density distribution is given as a histogram, M k,r is calculated by the following equations.

Equation 1.18 is rewritten as follows if k 1.

M q x dxk

q x x

k

k r r ii

mk

x

x

r i ik

ik

i

m

i

i

, , ,

1

111

11

11

1

( )

11

111

11

Q

x x

x xr i

ik

ik

i ii

m

,

(1.20)

TABLE 1.2 Calculation of the Histogram and the Cumulative Distribution

1 2 3 4 5 6 7 8i xi Mi Q3,i xi q

3,i lnxi (q

3,i)

(mm) (103kg) (%) (mm) (%mm1) (%)0 0.063 0

1 0.09 0.1 0.1 0.027 3.7 0.357 0.3

2 0.125 0.27 0.37 0.035 7.7 0.329 0.8

3 0.18 1.03 1.4 0.055 18.7 0.365 2.8

4 0.25 2.2 3.6 0.07 31.4 0.329 6.7

5 0.355 5.4 9 0.105 51.4 0.351 15.4

6 0.5 9.3 18.3 0.145 64.1 0.342 27.2

7 0.71 13.7 32 0.21 65.2 0.351 39.1

8 1 17 49 0.29 58.6 0.342 49.6

9 1.4 17 66 0.4 42.5 0.336 50.5

10 2 14.6 80.6 0.6 24.3 0.357 40.9

11 2.8 9.9 90.5 0.8 12.4 0.336 29.4

12 4 5.6 96.1 1.2 4.7 0.357 15.7

13 5.6 2.4 98.5 1.6 1.5 0.336 7.1

14 8 1.1 99.6 2.4 0.5 0.357 3.1

15 11.2 0.3 99.9 3.2 0.1 0.336 0.9

16 16 0.1 100 4.8 0.0 0.357 0.3



Although a lot of average diameters can be defined, the several listed in Table 1.3 are generally used.

(1.18)

Geometric mean diameter is defined as



If k 1,

.

M qx

xQ

x

x

x xr r i

i

mi

ir i

i

i

i ii

m

11 1

1

11, , ,

lnln

(1.21)

Equation 1.19 is rewritten as follows:

ln ln,,

, ,

x q xdxq

x x

Qx x

geo r r ii

m

x

x

r i

i ii

mr i

i ii

i

1 111

1

21 ( )i

m

(1.22)

The calculation results are illustrated in Table 1.3. The spread of a size distribution is represented by its variance, which represents the square of the

standard deviation,

2

10

2

2 1

2x x q x dx M M

r r r r, , ,( )( ) ( )

(1.23)

0.1 1 100

20

40

60

80

100

[mm]

q* [%

], q*

[%

], Q

3 [%

]3

3 q3

q3

Q3

x

FIGURE 1.1 A graphical representation of particle size distribution with a linear abscissa.



The values of the average diameters listed in Table 1.3 can be calculated from the data in Table 1.2.

. The variance, 2 , of a q r ( x ) -distribution is defi ned as


Particle Size 9

From a histogram,

2 3 3

1

2 2

1

13

141 1

q x x q x xr i

i

m

r ii

m

i i i i, ,( ) ( )

2

3 3

11

13

14

1

Q x xx x

Q xr i

i ii

m

r i ii i

, ,xxi

i

m

11

2

( )

(1.24)

The standard deEquation 1.24.

ISO 92762 (JIS Z 8819-2) standardizes the calculation of average particle sizes.

Notation

i number of the size class with upper particle size x i

k power of x m total number of size classes M

k,r complete k th moment of a q r ( x ) -distribution n distribution constant

FIGURE 1.2 A graphical representation of particle size distribution with a logarithmic abscissa.

00

20

40

60

80

100

2 4 6 8 10x [mm]

q* [%

mm1 ],

q* [%

mm1 ],

Q3

[%]

33

q3

q3

Q3



viation of the particle sizes illustrated in Table 1.2 is calculated as 1.29 mm by



FIGURE 1.3 Cumulative distributions on a log-normal and RosinRammler distribution graph.

0.01 0.1 0.1

1

510

2030

7090

9999.9

50

0.1

1

510

2030

7090

9999.9

50

1 10

Q 3 [%

]

Q 0 .Q 3

[%

]

x [mm]

TABLE 1.3 Average Diameters

Average diameters Symbols Defi nition Examples of

q0(x) q3(x) Table 1.2 [mm]

from from

Arithmetic average length diameter Weighted average number diameter

x

1,0 0.228

Arithmetic average surface diameter x2,0 0.303

Arithmetic average volume diameter x3,0 0.410

Weighted average length diameter x1,1 0.402

Weighted average surface diameter, Sauter-diameter

x

1,2 0.749

Weighted average volume diameter x1,3 1.40

Harmonic mean diameter x1,r 0.147 (r0)0.749 (r3)

Geometric mean diameter xgeo,r 3.98 (r3)




Particle Size 11

N particle number q

r ( x ) density distribution

q r

q r ( x )

q r

* ( ln x ) density distribution in a representation with a logarithmic abscissa q

r

* q

r

* ( x ) q

r,i average density distribution of the class x i , histogram q

r,i average density distribution of the class In x i , histogram Q

r ( x ) cumulative distribution

Q r Q

r ( x )

Q r,i Q r ( x i) Q r ( x i1 )

x particle size, diameter of a sphere x

e absolute size constant

x i upper size of a particle size interval

x i1 lower size of a particle size interval

x i x i x i1 , width of the particle size interval

x 15.87

,

x 50,

x 63.2,

x 84.13 defi ned as Q r ( x 15.87 ) 0.1587, Q r ( x 50 ) 0.5 , Q r ( x 63.2 ) 0.632 Q r ( x 84.13 ) 0.8413

x 50,3 median particle size of a cumulative volume distribution

x 50,0 median particle size of a cumulative number distribution

r, s type of quantity of a distribution, r, s 0, 1, 2, 3 s standard deviation s

g geometrical standard deviation of log-normal distribution




13

Size Measurement Reg Davies E. I. Du Pont de Nemours, Inc., Wilmington, Delaware , USA

1.2.1 INTRODUCTION

The particle size distribution has been usefully defined as the state of subdivision of a material.For a smooth dense sphere, size ( X ) is equivalent to diameter ( D

). In most industrial applications,

however, size ( X ) is equivalent to diameter ( D ) only through the use of an adjustment factor ( F ), where

D

= FX

F can be a shape factor or, in the case of optical methods, a combined shape and extinction coefficient. Unless F is known, accurate particle size measurement of irregular particles is impossible. In these instances, size will be a function of the direction of linear measurement. It will be a function of the physical principle by which it is detected and a function of the instrument by which it is measured. Hence, an average size calculated from data obtained via an envelopevolume diameter of a powder in an electrolyte, a light-scattering measurement of the powder in suspension, or a permeability mea-surement of dry powder in airwill not be the same. The resulting differences will provide a valuable fingerprint of shape/optical variations and can be used advantageously for this purpose.

six of these are obtained from microscopy and image analysis: the sieve diameter from sieving meth-ods, specific surface diameter from permeability measurements, surface diameter from gas adsorp-tion; Stokes diameter from sedimentation methods, volume diameter from electrical sensing zone methods, and optical diameters from instruments using optical sensing detectors. Again, for most industrial powders, all these diameters will be different. This is not necessarily a disadvantage if one is aware of the reasons for the differences and is able to convert one equivalent diameter to another. It is used to advantage when one wishes to increase the sensitivity of detection of a change in size distribution of a powder during a processing step. For example, if one is concerned with breakage and the reduction of mass, then a volume-sensitive (e.g., electrical sensing zone instrument or X-ray sensing) instrument will be most useful. Whereas in attrition, where volume is conserved but large numbers of very fine particles are abraded from the surfaces of large particles, number counting or surface methods will have the highest sensitivity to the change.

Such considerations lead one to conclude that one should always choose the most suitable method and instrument for the job in hand. No sample should ever be submitted to or analyzed by a physical resting laboratory simply with a request for particle size analysis. Neither should one use an instrument because it is conveniently located near ones workplace. Several hundred instruments are documented in the literature for the measurement of particle size distribution and, their range of application spans six orders of magnitude. The most comprehensive treatise that discusses size measurement and the instruments available is given by Allen. 1 At the time of writing this chapter, Allens book had just been submitted for its fifth edition. Allens treatment combines historical size measurement with in-depth theory. Many of the older techniques are described, but many of these are now almost obsolete. In this chapter, theory will be minimal and only modern instruments will be discussed. For information on other methods, theory and detail, simply read the work by Allen.

1.2



Table 2.1 shows many common methods of experiencing the size of irregular particles. The first





1.2.2 THE APPROACH

There are several basic steps that might have to be followed from the initial thought that size distri-bution data are required. Some of these could be the following:

1. Define the particle-processing problem. What is the hypothesis? What are you expecting to find? Why are you measuring size?

2. Define the type and extent of the size distribution data requiredif any! 3. Acquire a reproducible sample of the test material. 4. Prepare (disperse) the sample for analysis. 5. Check the approximate upper and lower sizes and the state of dispersion in the sample by

microscopy. 6. Select the most relevant (sensitive) physical principle to measure this range of size pres-

ent. In some instances, this could require more than one principle. 7. Select an instrument that uses this principle. Again, in some instances this could require

more than one instrument. 8. Calibrate the instrument(s) against international standards. 9. Conduct the analysis as per international (ISO) or national standards. 10. Select the most relevant data-handling method, calculate the most relevant distribution,

and display it as per ISO or national standards.

This chapter will provide information to assist the reader with steps 6 and 7 onlyselection of a method/instrument for size measurement. Information on other steps is provided elsewhere.

TABLE 2.1 Several Methods of Expressing the Size of Irregular Particles

Average thickness The average diameter between the upper and lower surfaces of a particle in its most stable position of rest

Average length The average diameter of the longest chords measured along the upper surface of a particle in the position of rest

Average breadth The average diameter at right angles to the diameter of average length along the upper surface of a particle in its position of rest

Ferets diameter The diameter between the tangents at right angles to the direction of scan, which touch the two extremities of the particle profile in its position of rest

Martins diameter The diameter which divides the particles profile into two equal areas measured in the direction of scan when the particle is in a position of rest

Projected area diameter The diameter of the sphere having the same projected area as the particle profile in the position of rest

Particle sieve diameter The width of the minimum square aperture through which the particle will pass

Specific surface diameter The diameter of the sphere having the same ratio of external surface area to volume as the particle

Surface diameter The diameter of the sphere having the same surface area as the particle

Stokes diameter The diameter of the sphere having the same terminal velocity as the particle

Volume diameter The diameter of the sphere having the same volume as the particle

Optical diameter The diameter of the sphere having the same optical (e.g., backscattering or forward scattering) cross section as the particle; these will be different.




Size Measurement 15

1.2.3 PARTICLE SIZE ANALYSIS METHODS AND INSTRUMENTATION

For simplicity, the methods and instruments have been loosely classified into six groups:

1. Visual methods (e.g., optical, electron, and scanning electron microscopy and image analysis)

2. Separation methods (e.g., sieving, classification, impaction, electrostatic differential mobility)

3. Stream scanning methods (e.g., electrical resistance zone, and optical sensing zone measurements)

4. Field scanning methods (e.g., laser diffraction, acoustic attenuation, photon correlation spectroscopy)

5. Sedimentation 6. Surface methods (e.g., permeability, adsorption)

Discussion will not be uniform across these classes. Class 6 will have minimum discussion, as the methods are not widely used for measuring distributions; classes 1, 2, and 5 will have moderate discussion, as they receive widespread use in laboratories where high-cost instruments are not common; classes 3 and 4 will receive the most discussion, as many of the instruments in these classes are being used for on-line, in-process measurement and in todays industrial environment are being implemented into process measurement and control schemes. Use for powders, suspensions, and aerosol will be treated simul-taneously; that is, aerosol will not be treated separately, as in previous versions.

Visual Methods: Microscopy

Use of a microscope should always accompany size analysis by any method because it permits an estimate to be made of the range of sizes present and the degree of dispersion. In most instances, particle size measurement rarely follows, as other procedures are faster and less stressful to the operator. Microscope size analysis is used primarily as an absolute method of size analysis, as it is the only one in which individual particles are seen. It is used more widely in aerosol analysis, as airborne particles are more often deposited onto surfaces [e.g., by impactors, thermal precipitators (i.e., in a state more conducive to visual examination)]. It is used perhaps more for shape/ morphology analysis than size analysis and for beneficiation studies of minerals when combined with x-rays analysis. It is also used when other methods are not possible (e.g., inclusions in steel, porosity in ceramics).

Clearly, the range of sizes and their degree of dispersion strongly influence the ease and reli-ability of size measurement. For instances where particles are not already deposited on surfaces, sample preparation is a critical step. This is discussed in detail by Allen 1 . Typically, samples can be extracted from an agitated well-dispersed suspension, but dry, temporary, or permanent mounts also possible. For dry mounts, particles can be dusted onto a surface; for temporary slides, powder can be dispersed-held in viscous media. For permanent slides, a 2% solution of collodion in amylacetate or other similar systems can be used to fix the particles permanently in place for later examination.

In transmission electron microscopy (TEM), particles are deposited on a very thin film that is transparent to the electron beam. This film is supported on metal grids or frames. For scanning elec-tron microscopy (SEM) backscatter measurements, the powder is dispersed onto a metal substrate and made conductive by coating with a thin layer of carbon from a vacuum evaporator.

It cannot be stressed enough that preparation of the sample for visual examination is one critical step and the fact that it receives little space in this chapter does not reflect on its importance.

When a satisfactory dispersion of particles on a relevant substrate has been achieved, parti-cle size analysis can follow. Points to consider are resolution, the total number of particles to be counted, the choice of size distribution (whether number or mass distribution is required), and the



effect of material properties. The limit of resolution (i.e., the distance at which two particles in close proximity appear as a single particle) is proportional to the wavelength of the illuminating source and inversely proportional to both the refractive index of the immersion medium and the sine of the angular aperture of the objective. Although absolute limits of resolution exceed the following, the more common ranges of measurement are 3-1000m for optical microscopy, 2 nm to 1m for TEM, and 20 nm to 1000m for SEM.

For manual counting and operator comfort, the total number of particles should be typically below 800, and procedures have been developed to attain acceptable statistical accuracy with this constraint. Counting particles by number is easier than by mass, as statistical reliability does not rely on the omission of one particle, whereas counting by mass (e.g., of a distribution containing 999 particles of diameter 1m and one 10 mm particle), the omission of the one 10mm particle removes approximately 50% of the mass. Hence, very accurate assessment of the largest particles in the sample is essential for mass distribution measurement.

Allen 1 shows the expected standard error S(P r ) of the percentage P

r by number in each size

class, out of the total number in all size classes, to be

Sm

r

r r

r

( ) ( )P P P 100S

(2.1)

where m r is the total number of particles of all size classes. The standard error is a maximum when

Pr=50 ; hence, S ( P

r ) will always be less than 2%an acceptable error for most instancesif M

r

625 particles. For mass counting, if S( M

g ) is the standard deviation experienced as a percentage of the total by weight, M

g is the percentage by weight in a given size range, and M r is the number of particles counted in the size range, then

S MMMg

g

r

( )

(2.2)

So if 10% by weight of particles lie in the upper or top size range for a similar acceptable accu-racy of 2%, it is absolutely necessary to count 25 particles in the top size range. Without special procedures, the total number count to achieve this accuracy would be many thousands and beyond the endurance of an operator. Two approaches can be taken: count the thousands using automatic microscopes/image analyses or maintain the count below 800 by reducing the area examined for the smaller sizes. This procedure is beyond the scope of this chapter, but it is described in British Standard 3406 2 and by Allen 1 .

Furthermore, for most purpose, a choice is made to count on a projected area basis rather than a linear basis. Although this requires an estimate of a circle of equivalent area to the irregular particle, the law of compensating errors generally results in lower errors than by manipulation of any of the possible linear measurements.

root-2 progression of sizes and five different geometric areas. The importance of a well-dispersed and nonsegregated sample becomes clear when the geometric areas of this reticule are examined. Spatial variations can be minimized by using opposite quadrants.

Materials properties affect the procedure depending on particle strength, wettability, and particle refractive index, to name three factors. Others can be similarly important. Strength and wettability will certainly influence the method of dispersion and the mounting of the sample. The refractive index will influence resolution. With image analysis, gray value discrimination and edge defini-tion is an acute problem for automatic counting. These latter instruments vary widely in cost, and cost generally correlates with the ability to enhance the image electronically. Allen 1 discusses the



Figure 2.1 shows a typical reticule given in British Standard 3406 showing seven circles in a


Size Measurement 17

commercially available instruments today. Typically, manufacturers are sensitive to cost and offer lines of expensive instruments with full image enhancement capability and color representation, moderately priced instruments for generalpurpose analysis and lower-cost instruments for applica-tions where resolution, gray value discrimination, and edge detaching are not a problem. Software packages are also appearing whereby images can be analyzed by a personal computer with software interactive capability on a routine basis.

Size analysis by microscopy is performed in our laboratory in less than 2% of size measurement cases, but it is significantly higher when shape information is required.

Separation Methods

These methods are typified by procedures which permit the extraction of a certain size class from the feed sample followed by a measurement of the percentage by number or mass of the removed size class relative to the feed concentration. Sieving is perhaps the oldest of these methods, although classification by winnowing was widely used to separate grain in ancient Egypt. Sieving is very well known, but perhaps at the same time the least well known for potential errors in the analysis. Because it appears to be a simple and low-cost process, errors are commonplace.

Sieving consists of placing a powder on a surface (e.g., a plate with numerous openings of a fixed size) or a mesh of intersecting wires with numerous openings of a fixed size, and agitating the surface (sieve) so that particles of size smaller than the holes pass through. To speed up the analysis, several sieves are placed on top of each other, the coarsest at the top and the rest shaken until the residue on each sieve contains particles which cannot pass through the lower sieve. This is a well-known

FIGURE 2.1 The British Standard Graticule (Graticules Ltd). From British Standard 3406 (1963) .





procedure; what is not always appreciated are the errors involved in the process. For the sake of this discussion, only wire-woven sieves will be discussed, as these generally pose the greatest problems and are the most commonly used.

Separation of sizes on the sieve depends on the maximum breath and maximum thickness of a particle. Length affects the separation only when it becomes excessive. The sieve surface contains apertures with a range of sizes and a range of shapes. They are classified internationally by their mesh sizes and percentage of open area.

The first error arises in the assumption that this classification is accurate for all sieves both new and old. Apertures vary widely and the standard deviation of apertures is smaller (e.g., 35% for large aperture sieves of nominal aperture widths of 630 m and larger, 10% for small aperture widths of 40 m 3 ). Leschonski 4 examined eight 50-m sieves and the median aperture varied from 47.3 to 63.2 m. Hence, sieve calibration is necessary at frequent intervals of use if size analysis is to be accurate. Several approaches have been used, including microscopy and sieving with standard pow-ders. The latter is more tedious, but for woven sieves, it gives a better measure of three-dimensional aperture sizes and calibrates the sieve in terms of volume diameter using the actual procedure used for size measurement. Leschonski recommends a counting and weighing technique similar to that of Andreasen 5 applied to the fraction of particles passing the sieve just prior to the completion of the analysis. These are usually of narrow size range and are typical of the cut size of the sieve.

As sieving is a rate process and the passage of a particle through an aperture a statistical proce-dure, sieving accuracy (i.e., the time of sieving) depends also on the size distribution spread of sizes, the number and mass of particles on the sieve surface, the particle shape, the method of shaking, and the percentage of open area. Agglomeration and strength of particles affect the outcome. For highly agglomerated dry powders, agglomeration effects can be overcome by wet sieving; hence, wet sieving is recommended often for particle sizes less than 200 mesh. Friability strongly influences the choice of the sieving procedure and, again, wet sieving is less aggressive. Sieve wear with time influences aperture size and requires recalibration at frequent intervals. Sieve cleaning is sometimes the primary source of aperture distortion. Sieving machines are numerous and use different methods of agitating the particles on the surface, thus assisting them to pass through the sieve. A Ro-tap machine with horizontal rotary and vertical tapping motion is aggressive, but for strong particles, it is highly effective.

Air-swept sieves (e.g., Hosokawa Alpine and Allan Bradley sonic sifters) can be equally aggres-sive on the particle, whereas wet sieving is gentler (e.g., Retsch, Hosokawa, Alpine). Automatic ver-sions such as the Gradex Size Analyzer simultaneously reduce analytical times and operator error. The sieving process is simple but probably experiences the most inaccuracy of all sizing methods.

Classifications in liquid and air can be used to separate size classes but is not commonly used for size analysis. Online analyzers have been developed using air classification (e.g., the Humboldt size analyzer), but perhaps the more recent applications have been in classification/fractionation methods using hydrodynamic chromatography (HDC) and field flow fractionation (FFF) for col-loidal suspensions.

in a dilute suspension are separated by injecting them into a nonporous packing of large particles in a laminar flow of clean fluid . Particle separation occurs due to the hydrodynamic interaction of the laminar flow profile and the cross section of the particle. Large particles whose diameters inter-act with the higher-velocity central stream lines of the parabolic laminar flow profile move faster through the column, whereas small particles whose diameters interact only with the slower profiles near the packing surfaces move slower. Size analysis is obtained by measuring the concentration of particles existing the column with time using an ultraviolet detector. Size resolution and size discrimination are not generally as good as FFF. Here, a similar injection of particles is made into a long channel under laminar flow, but this time a field is applied across the channel. In centrifu-gal fields typified by the DuPont SFFF, shear-induced hydrodynamic lift forces oppose the driving force of the field. Because of diffusional effects, finer particles diffuse nearer the higher velocity central portion of the laminar flow field and are eluted first, whereas larger particles pushed by the



Figures 2.2 and 2.3 shows the essential differences between the two. In HDC, colloidal particles


Size Measurement 19

centrifugal field nearer to the outer wall and away from the higher-velocity portions of the flow profile are retarded. Again, concentration exiting the channel is measured by an ultraviolet (UV) detector and size distribution calculated. In the DuPont SFFF, a time-delayed exponential centrifu-gal field is used. Although a constant force field provides high resolution of particles, an exponential force field in which the centrifugal field is allowed to decay exponentially speeds up the analysis, particularly for wide size distributions. Alternate types of fields have been reported in the literature. These include magnetic, thermal, and steric designs.

For aerosols, typical devices that fractionate feed distributions in gases include impactors and electrostatic differential mobility analyzers.

In impactors, the particles in gas are passed through a nozzle and made to interact normally with a plane surface. The resulting particle trajectories can be calculated using the equation of motion of a particle in a flow field. Above a certain size of particle termed the cut size, particles will strike the surface with the potential for collection. Particles smaller than the cut size will follow the flow of gas, not touch the surface, and so have low potential for collection. The collection efficiency at the impaction surface is expressed in terms of the Stokes number (Stk) where

StkC D U

Wp c p o

r

m

2

18 12( )

(2.3)

FIGURE 2.2 Capillary model of hydrodynamic chromatography separation.

FIGURE 2.3 Centrifugal sedimentation field flow fractionation.





Where p p density of the particle and D p its diameter, C c is the Cunningham correction, U o is the

velocity of the gas, is the gas viscosity, and W the diameter/width of the nozzle. Impaction surfaces are calibrated by determining the collection effiency as a function of the Stokes number. For a given impactor geometry and operating condition, the Stokes number at the 50% collection efficiency is estimated and used to determine the cut size D

p for those conditions. Thus, by reducing the value of W , the nozzle diameter for the identical gas flow, the impaction

velocity. U p increases and the cut size is reduced. In this way, multiple impaction stages can be

designed within an instrument to collect a variety of sizes. These instruments are termed cascade impactors. By weighing or otherwise estimating (microscopy) the weight of particles on each sur-face, a size distribution can be measured.

Impactors suffer from errors in that there is some interaction between neighboring surfaces, deposition occurs inside the impactor by other mechanisms (e.g., eddy diffusion, thermal, or elec-trostatic). More importantly, particles rebound from the collection surfaces and are recollected on later stages. To minimize rebound, surfaces can be made tacky. Agglomeration is another concern in that it broadens the size distribution and the collected mass on any impactor stage. The mass of the agglomerate will determine its collection efficiency, and agglomerates will be collected as if they were large particles. Upon impact however, they may mechanically disperse into their smaller com-ponents on the collection surface. The mass loading of any stage influences the collection efficiencyand impactors are used with low concentrations of particles in gas and are operated for short sam-pling times. Solids concentrations and sampling times can be increased by redesign of the collection surface (e.g., in the Lundgren impactor, the collection stage is held on a slowly rotating drum). The lower size of collection can be extended by other designs (i.e., high-flow-rate systems, the use of microjets, and low pressure). Impactors are generally used for particles sizes in excess of 1 m with cyclone or sedimentation pre-stages for sizes greater than 10 m. They have found widespread use in health and biological studies, including respiratory/lung deposition studies. Typical of these is the

For fine particles in gases (e.g., 1m and smaller), electrical mobility analyzers have become e of a charged spherical

particle in an electric field is given by

VpeC E

DB E

e

c

pe

3pm

(2.4)

where E is the strength of the electric field, e the elementary charge, P the number of elementary charges carried by the particle, C

c the Cunningham correction, the gas viscosity, and D p the par-

ticle diameter. Be , the electrical mobility, is inversely proportional to diameter and can be varied by changing the electrical voltage applied to the central collection rod and other parameter values remaining unchanged. Hence, particles are collected on the center rod according to their mobility. Particles larger than a critical size determined by a critical electrical mobility do not reach the rod and pass through the analyzer. Their concentration is detected by either an electrometer or a con-densation nuclei counter.

Thermosystems manufacture both types of instrument: TSI 3071 is a differential mobility analyzer (DMA) fitted with an impactor to preclassify particles coarser than 1 m, and a condensation nuclei counter to measure number concentration. Two DMA are sometimes used in tandem to study kinet-ics and growth, where the first acts as a generation and classification stage to present a narrow size distribution to the second. A conditioner between the DMAs can apply humidity or gases (e.g.. SO

3,

NH 3 , etc.) for interaction studies. The TSI 3030 electrical aerosol analyzer uses an electrometer and

employs 11 voltage steps which span the range 0.0031 m. Automatic and manual modes are available at an aerosol flow rate of 4 L/min.



Andersen impactor, Figure. 2.4.

common. Figure 2.5 shows two types of systems in which the velocity V


Size Measurement 21

Stream Scanning Methods

tion with an external field is taken as a measure of their size. Such methods are usually limited to measurements at low particle concentrations and are most suitable for particle number counting. They have found widespread use in air quality and contamination monitoring. For the determination of mass distributions, many thousands of particles typically have to be counted. They are used for both particles in liquid and particles in gases.

The Coulter principle is used for particles in liquids only. Patented in 1949 and published in 1956 for blood cell counting, the principle has found widespread use in all branches of particle science.

aperture of known size is inserted into the suspension. By placing an electrode both inside and outside the tube and initiating the flow of an electrical current through the orifice, an electric field of known

the immersed tube, particles in suspension flow singly through the orifice, and momentary changes in impedance give rise to voltage pulses, the heights of which are proportional to particle volume. Theses pulses are amplified, sized, and counted and expressed as a size distribution. Size ranges from 0.6 to 1200 m are typical, but several apertures/tubes have to be used to achieve this. This is because

FIGURE 2.4 Anderson impactor .



characteristics becomes a sensing zone. When suspension flow is initiated by applying vacuum on

Figure 2.6 shows the basic principle. Particles are dispersed in an electrolyte and a tube containing an

Stream scanning methods are those in which particles are examined one at a time, and their interac-



FIGURE 2.5 Electrical mobility analyzer.

FIGURE 2.6 Coulter counter.




Size Measurement 23

each orifice can sense particles from 2% to 60% of the orifice diameter. Problems can arise due to the necessity to use and match multiple aperture tubes, due to aperture blockage by large particles, by the passage of more than one particle through the sensing zone at a time (coincidence), by the nondetection of particles smaller than the lower detection limit of an aperture, and by the evolution of erroneous pulses due to abnormal interactions with the electric field.

The first problem is easily overcome by trial and error and by calibration. The second is simply overcome by preclassifying the sample. Coincidence errors are routinely overcome by the applica-tion of simple formulas supplied by the manufacturer.

Abnormal pulses arise due to the fact that the electric field is not uniform and that the field is dense near the inlet and outlet edges of the orifice. Passage of particles through these regions or interaction of extreme particle shapes with these regions can generate nonuniform electrical pulses. These can be eliminated by the use of mechanical focusing of particles through the orifice center or by electronic editing of abnormal pulses by the electronic data analyzer. The latter is more common today.

The nondetection of particles due to each orifice having a lower detection limit of 2% of its diameter is overcome by the performance of a mass balance. This is discussed at length by Allen 1 .

Accurate particle size analysis is best performed on dilute suspensions in which particles pass through the center of the orifice and mass balances are performed. In addition to Coulter, the principle is also applied in the Elzone electrozone counter manufactured by Particle Data. One special use of the Coulter principle is for the determination of oversize counts in coating slurries. As there are very few, a precision transparent sieve with a 2% tolerance is used in combination with a Coulter mass balance procedure to prefill the few oversize particles and examine them by microscopy to determine their nature, count them by, size and recombine the data into the total mass balance. Allen describes this procedure on precision sieves manufactured by Collimated Holes Inc.

The primary value of the Coulter principle is that it can be used to measure both mass and popu-lation distributions accurately, and as volume diameter is one typical size representation, this agrees closely with most sedimentation analysis and with sieve analyses when calibrated, as discussed earlier in this section.

Of more widespread use are optical sensing zones which operate according to the following principles:

1. Collecting and measuring the light intensity in a forward direction 2. Collecting and measuring the light intensity in other directions (e.g., 90 or backscatter) 3. Light blockage or geometric shadowing 4. The measurement of phase shift

The most common types of instruments fall under class 1. They are available in various degrees of sophistication and wide variations in design. Particle size response is a function of the size, the shape, the orientation of the particle, the flow rate, and the relative refractive index between the particle and its surroundings.

Instrumentation cost and lower measurement limit are determined by the light source, the light collection system, and the efficiency of the detector. White-light sources are cheaper but give rise to a lower detection limit of 0.5 m. Extension below this limit demands the use of lasers or laser diodes and highly efficient light collection systems. It is a balance among the intensity of the light source, the particle response, and the collection optics.

The relationship between particle size and scattered light intensity at any angle can be obtained for spheres with Mie theory. For a monotonic increase in scattering cross section with size, forward scattering at small angles is used. This has been dependence on particle refractive index, but extraneous light scattered from instrument internals is more of a problem than with




24 Powder Technology

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