KONA No.20 (2002) 9

1. Introduction

Motionless or static mixers are widely known andapplied in process technologies for the mixing of liq-uids, especially for highly viscous materials, and tocontact different phases to enhance heat and masstransfer. Producing dispersions in two- and multi-phase systems such as emulsions, suspensions,foams, etc., is also the common aim of using motion-less mixers. Far less information is known on theirbehavior, capabilities and applications in bulk solidstreatments. Although investigations started morethan thirty years ago in this field, research and devel-opment is still under way even now. Recent studiesand applications gave evidence on the beneficial fea-tures of such devices in powder technology for mix-ing and other treatments of bulk solids.

Motionless or static mixers are f low-modifyinginserts, built into a tube, duct or vessel. These toolsdo not move themselves, but using the pressure dif-ference or the kinetic and potential energy of thetreated materials, create predetermined f low patternsand/or random movements, causing velocity differ-ences and thus relative displacements of various partsof the moving material. In this way, motionless mixerscan considerably improve the process to be carriedout. In f luids, motionless mixers work efficientlyboth in turbulent and laminar regions. Splitting, shift-ing, shearing, rotating, accelerating, decelerating and

recombining of different parts of materials are com-mon mechanisms in this respect, both in f luids andbulk solids.

Motionless mixers eliminate the need for mechani-cal stirrers and therefore have a number of benefits:No direct motive power, driving motor and electricalconnections are necessary. The f low of materials(even particulate f low) through them may be inducedeither by gravity, pressure difference or by utilizingthe existing potential or kinetic energy. The spacerequirement is small, allowing a compact design ofequipment in bulk solids treatments. Installation iseasy and quick, e.g. by simple replacement of a sec-tion of tube or by fixing inserts into a tube or vessel.Set-up and operating costs are much lower than thoseof mechanical mixers, while maintenance is practi-cally superf luous. Motionless mixers are available ina number of different types, shapes and geometries,made from a great variety of materials. The mixer cantherefore easily be matched to process requirementsand to the features of the processed materials. Phys-ical properties, e.g. f low behavior, particle size,mechanical strength, abrasive effects, safe prescrip-tions. e.g. for food and pharmaceutical industries, canbe taken into account by the proper design of mixers.Applications in powder technology are equally feasi-ble in gravity and pneumatic conveying tubes, inchutes, hoppers and silos, or even in rotating, vi-brated or shaken containers.

The greatest advantages of motionless mixers inbulk solids treatment are: high performance, continu-ous operation, energy and manpower savings, mini-mum space requirement, low maintenance costs,

J. GyenisUniversity of KaposvarResearch Institute of Chemical and Process Engineering*

Motionless Mixers in Bulk Solids Treatments – A Review†

Abstract

In this paper the general features, behavior and application possibilities of motionless mixers inmixing and treatments of bulk solids are overviewed, summarizing the results published during thelast three decades. Working principles, mechanisms, performance, modeling and applications ofthese devices are described. Related topics, such as use in particle coating, pneumatic conveying,contacting, f low improvement, bulk volume reduction, and dust separation are also summarized.

* Veszprem, Egyetem u. 2, Hungary† Accepted: June 28, 2002

trouble-free operation, easy measurement and con-trol, and improvement of product quality.

There are a number of different types of motionlessmixers available from a number of manufacturers,most of them are applicable for bulk solids, too. Themost widely known types are, e.g. Sulzer SMX andSMF mixers, Ross ISG and LPD mixers, Komaxmixer, Kenics and FixMix mixers, etc. Fig. 1 showssome examples of these devices.

The Sulzer SMX mixer (Fig. 1a) is a typical formof lamellar mixer, composed of narrow strips or lamel-las placed side by side within a tube section. Thesestrips decline from axial direction alternately by posi-tive and negative angles, crossing the planes of eachother, and thus constituting a 3-D series of X forms.During f low, the material is split into several streamsor layers corresponding to the number of strips,shifted to opposite directions relative to each other.Flow cross-sections contract along its up-f low sidesand expand at the down-f low sides. Thus, the materialis forced laterally from the contracting to the neigh-boring expanding channels. One SMX element, i.e.one series of crossing strips, mixes principally in twodimensions along the plane of the X forms. Therefore,the next series of X forms is aligned at 90° to ensurethree-dimensional mixing. Sulzer SMX is thus charac-terized by excellent cross-sectional (transversal) mix-ing and a high dispersing effect with a small space

requirement and a narrow residence time distribu-tion. In multiphase f lows no deposits and blockagesoccur, due to the high turbulence caused by the sharpedges and crossings. But, a drawback of this mixeralso comes from this, because sharp edges and thesudden changes in f low directions increases pressuredrop. In bulk solids f low, troubles can arise, especiallyfor cohesive materials, for larger particles or broadsize distributions.

Fig. 1b shows the Ross LPD mixer which consistsof a series of slanted semi-elliptical plates positionedin a discriminatory manner in a tubular housing.When the material f lows through this mixer, the inputstream is split and diverted repeatedly in differentdirections along the cross-section of the tube, untila homogeneous mixture is achieved. This type ofmotionless mixer is generally used for the turbulentf low of low-viscosity liquids to enhance macro- andmicro-mixing and/or to improve the heat transfercoefficient in heat exchangers. It is also feasible forparticulate f lows. But, since the f low at a given tubesection is divided into two streams only, shear andmaterial exchange takes place in one plane onlybetween the two half-tube cross-sections, thus themixing effect along a given length is weaker than inSMX mixers, especially for viscous materials or bulksolids. Naturally, the pressure drop is also less. Forbulk solids, the maximal throughput in a Ross LPD

10 KONA No.20 (2002)

Fig. 1 Examples for motionless mixers also applicable for bulk solids(a) lamellar (Sulzer SMX) mixer, (b) Ross LPD mixer, (c) Komax mixer, (d ) Kenics static mixer, (e) FixMix mixer, ( f ) a - taper and(g) b - skewness of a FixMix element

(a) (b) (c) (d) (e) ( g)

a

( f )

b

b

mixer is higher than in SMX, and the risk of pluggingfor cohesive powders or large particle sizes is consid-erably reduced. Another difference is that, due to thenon-uniform axial velocity profile, the longitudinalmixing effect of the LPD mixer may be higher thanthat of the SMX mixer.

The Komax mixer (see Fig. 1c) consists of f latplates arranged essentially in axial direction in a tube,but at both ends of these plates they are hatched,rounded and bent in opposite directions. The neigh-boring mixer plates are arranged at 90° in radialdirection, touching each other with the tips of thebent f laps. This mixer is also called a “Triple-ActionMixer”, because it provides (i) two-by-two division,(ii) cross-current mixing and (iii) back mixing ofcounter-rotating vortices. Each mixing element set incombination sweeps approximately two-thirds of thecircumference of the pipe and directs the f low to theopposite side, providing very strong wall-to-wall radialtransfer. Between the sets of generally four mixer ele-ments, inter-set cavities provide space for intensivecontacting of the sub-streams of material by strongmomentum reversal and f low impingement. For mul-tiphase f low, this mixer is resistant to fouling or clog-ging, because the f lips of the mixer elements aresmoothly contoured with a large radius. Intersectionsbetween the element ends with the wall are alloblique angles, eliminating corners that can trap solidor fibrous materials and promote material accumula-tion. Momentum reversal and f low impingement pro-vide a self-cleaning environment.

The Kenics static mixer shown in Fig. 1d pos-sesses almost all the advantages of the Komax mixer.It consists of a long cylindrical pipe containing a num-ber of helical elements twisted by 180° alternately inleft-hand and right-hand directions, perpendicular tof low direction. The adjacent elements are set by 90°in radial direction, therefore the outlet edge of a givenelement and the inlet edge of the next one are perpen-dicular to each other. The smooth helical surfacedirects the f low of material towards the pipe wall andback to the center, due to secondary vortices inducedby the spiral-form twist of the f low channels. Addi-tional velocity reversal and f low division results fromshearing of the material along the tube cross-sectionbetween the adjacent elements. The systematic divi-sion of streams and their recombination in anotherway enhance the mixing effect proportionally to 2n,where n is the number of the applied mixer elements.For f luids or in multiphase f lows, a relatively narrowresidence time is ensured, in addition to excellentradial mixing. Due to the smooth and mildly bending

surfaces of the helices, the pressure drop along aKenics mixer is very low, while it provides continuousand complete mixing and eliminates radial gradientsin temperature, velocity and composition. For bulksolids, because of the non-uniform axial velocity pro-file, a certain degree of longitudinal mixing also takesplace. Due to the smooth surfaces and relatively widef low channels, the risk of plugging or blockage isvery limited.

The FixMix motionless mixer shown in Fig. 1e isvery similar to the Kenics static mixer, with the essen-tial difference that the individual elements are slantedrelative to the tube axis and are tapered along theirlength. It results in several benefits: the slightlyincreasing gap between the mixer element and thetube wall eliminates the corners or contact pointsbetween them. Therefore, there are no dead zones,and deposition or blockage cannot occur. On theother hand, the cross-section of the f low channels onthe two sides of a mixer element changes continu-ously along its length: the cross-sectional area on oneside expands while on the other side it contracts. Dueto the tangential f low at the wall and the pressure dif-ference between the two sides, an intensive cross-f low takes place between the neighboring f lowchannels. These features provide improved mixingefficiency, lower pressure drop with suitable cross-sectional turbulence, and more uniform radial andtangential velocity fields. The higher velocity and theturbulence close to the tube wall results in higherheat transfer coefficients and a cleaner surface. Inaddition to this self-cleaning effect, the lack of cor-ners makes the cleaning easier for difficult materials.This mixer provides higher mixing efficiency per unitmixer length and reduces the risk of blockage in bulksolids treatment.

During the past three decades, quite a number ofpapers were published on the application of motion-less mixers in this latter field, and it is worth survey-ing these results to initialize further studies andpractical applications.

2. Motionless Mixers in Bulk Solids Mixing

The mixing of bulk solids is an important operationin many industries, such as in the chemical and phar-maceutical industries, mineral processing, food in-dustry and for treatments of agricultural materials.Uniform composition in these processes is of primaryimportance, as well as to eliminate segregation. Be-sides mechanical mixers and silo blenders, motion-less mixers represent a viable solution for this task,

KONA No.20 (2002) 11

especially if continuous operation is possible or nec-essary. The application to homogenize solids wasalready envisaged as early as in 1969 by Pattison [1].

A crucial condition of such an application is thetrouble-free f low of the bulk solids to be treated.Therefore, motionless mixers can only be used forfree-f lowing particles, but cohesiveness to some ex-tent is tolerable even in gravity f low of such materials.

In addition to the devices conventionally known asmotionless mixers, any other tools inserted into atube or vessel or the intentional changes of tube orchute cross-sections can modify the f low pattern ofsolids. Therefore, they may also be considered assome kind of motionless mixer. Various inserts insilos or hoppers, or cascade chute assemblies causingthe multiple division and recombination or modifica-tion of bulk solids f lows can also be ranked here.

2.1 Mixing Mechanisms of Motionless MixersSeveral workers investigated the mixing mecha-

nisms of particulate solids in motionless mixers act-ing in transversal [2] and longitudinal directions [3].Observing the interactions between the particles andmixer elements, four kinds of mixing actions weredistinguished [3, 4]. Namely: (a) multiple division andrecombination of the particle f low, (b) interaction ofparticles with other particles, with the surface ofmixer elements and the tube wall, (c) changes in f lowdirection, and (d) differences in velocity profile.Three main mechanisms, namely diffusive, convec-tive and shear mixing were attributed to theseactions. Shear: certain particle regions are shearedduring particle f low, creating velocity differencesbetween the adjacent layers. Convection: multiple divi-sion and recombination of the particle f low, as it issplit into sub-streams and diverted to different ductsor directions, and then unified with other sub-streams. Dispersive or dif fusive-type mixing: stochasticmovements with interchanges of different particles. Agreat deal of experience accumulated in the lastdecades indicates that these mixing mechanisms actmore or less together in any type of motionless mixer,and therefore they are hardly separable from eachother.

The majority of experimental studies carried outuntil now used helical mixer elements such as Kenicsor FixMix-type devices. In a few works, other types ofmotionless mixers such as Sulzer (Koch) mixers andmixer grids composed of helices, rods or lamellas,were investigated.

For certain types of mixers, the mixing mecha-nisms inf luence the characteristic direction of mixing.

There is a general belief that motionless mixers per-form mainly radial (transversal) mixing, and that axial(longitudinal) mixing is negligible. But, according toour experience, also seen from the results of otherworkers, this is not entirely valid even for viscous liq-uids or plastic materials, due to non-uniform axialvelocity profiles. Depending on their shape, arrange-ment and operational conditions, and in addition to ahigh radial dispersion [2], motionless mixers maycause effective axial mixing [3, 4], too. This latter fea-ture is of crucial importance in equalizing concen-tration variations in time and space in continuousparticle f lows caused either by segregation or by non-uniform feeding.

2.2 Mixing Kinetics and PerformanceThe performance of a bulk solids mixer is charac-

terized by its throughput, i.e. the treatable mass perunit volume and time, and by the degree of homo-geneity achieved. These features are in close relationwith the mixing kinetics, i.e. with the rate of homo-geneity improvement, characterizing how fast theconcentration uniformity is getting better as a func-tion of time or mixer length. The mixing kineticsdetermines the number of motionless mixers neces-sary to achieve a given degree of homogeneity or itsequilibrium. The latter may be the result of two com-peting processes: mixing and segregation. In otherwords: whilst the mixing mechanism tells us in whatmanner, the mixing kinetics characterizes by whichrate and how far the process is going on.

From a practical point of view, the performance of amixer is the most important feature, if we disregardthe actual mechanism of mixing. However, the mech-anism gives an explanation of the mixing kineticsexperienced, thus also serving as a starting point forfurther improvements. Therefore, almost all studiescarried out in this field aimed at determining the rateof process [5-14], and only a few works dealt with themechanism. The kinetics of the mixing and segrega-tion processes competing with each other can becharacterized by the equation [14]:

�Km(1�M)�KsΦ (1)

where M denotes the actual degree of mixedness, Km

and Ks are the kinetic constants of mixing and segre-gation, respectively, while Φ is the so-called segrega-tion potential [14]. Although there are a number ofvarious definitions for the degree of mixedness [15],the most simple and well applicable one was definedby Rose [16] as

dMdt

12 KONA No.20 (2002)

M�1� (2)

where s and s0 are the estimated standard deviationsof the sample concentrations taken from the actualmixture and in a totally segregated state, respectively.

Among the earliest works carried out in this field,the mixing performance of the Kenics [2-4, 8] andSulzer (Koch) motionless mixers [6, 7] was reportedby the team of L. T. Fan. In some studies, the mixingof wheat, sorghum grains and f lour was determinedboth in axial and radial directions. Among differentexperimental methods, the radioactive tracer tech-nique was used to observe the rate of the process.The practical purpose of these investigations was toupgrade low-quality products by adding high-qualityones during continuous blending. Motionless mixerswere proposed, e.g. to feed mills with a controlledquality of raw material. The kinetics of simultaneousmixing and segregation processes was investigatedexperimentally with free-f lowing particles which dif-fered in particle size or in particle density, or both.Under given conditions, comparison showed thatdifferences both in particle size and density gavesubstantially faster mixing and segregation ratescompared to systems where differences took place ineither particle size or particle density alone [8].

The mixing of materials of different particle sizes,shapes and densities is generally accompanied bysegregation. After quite a long mixing time, theseconcurrent processes result in a balanced degree ofmixedness which is lower than it would be in a totallyrandom distribution of the component particles.Depending on the initial positions of the components,equilibrium is approached gradually from below, orvery often, after going through a maximum. In thislatter case, the uniformity of a mixture decreases inthe final period of the process, in spite of continuedmixing action. Boss and his co-workers [10, 11] inves-tigated the balanced degree of mixedness in systemsof different particle sizes. Two types of motionlessmixers were tested: (a) lamellar mixers composed ofslanted metal strips crossing each other similarly toSulzer SMX mixers, and (b) roof mixers consisting ofgrids of angle profiles arranged in horizontal rows atdifferent cross-sections. Similarly to the works of Fanand his co-workers, these experiments showed signif-icant segregation after certain passes through themotionless mixer. (In these experiments, increasingmixer lengths were simulated by repeated f lowsthrough a given length of mixer tube.)

ss0

2.3 Modeling and SimulationsTo describe a process or equipment theoretically, or

to predict the characteristic features and results oftheir applications under different conditions, math-ematical modeling and simulation proved to be widelyapplied and useful tools. To investigate motionlessmixers in solids mixing, various modeling principlesand simulation methods were used till now. Chen etal. [4] adapted the concepts of an axially dispersedplug-f low model, commonly used at that time todescribe the mixing of f luids in various unit opera-tions. In their work, a quasi-continuous deterministicmodel was applied to describe the axial dispersion ofparticles in a gravity mixer tube containing motion-less mixer elements. Residence time distributionswere measured by the stimulus-response technique,and apparent Peclet numbers and axial dispersioncoefficients were determined for three different kindsof solid particles, after different number of passesthrough the mixer tube.

Apparent Peclet numbers (Pe′) and axial dispersioncoefficients (K ′ax) have similar definitions here tothose used in f luids to characterize the intensity oflongitudinal mixing. Their values can be determinedfrom the residence time distribution of tracer parti-cles in the mixer tube determined by discrete sam-pling at the outlet at different times after they areintroduced at the inlet in the form of a plug [17]. Thesecond central moment m2 of the residence time dis-tribution is as follows:

m2�∑i

(ti�t— )2 · xi (3)

where ti is the residence time of tracer particles inthe mixer tube taken off by the i-th sample, and xi isthe mass fraction of tracer particles in the i-th sample.The mean residence time of all tracer particles alongthe mixer tube corresponds to the first moment of theresidence time distribution as:

t— �∑i

ti · xi (4)

The apparent Peclet number is determined fromthe mean residence time t— and the second centralmoment m2 of the residence time distribution, cor-rected by m2,0, which is the second central momentobtained in a plain tube, i.e. without motionless mixerelements:

Pe′� (5)

and the axial dispersion coefficient:

2t— 2

m2�m2,0

KONA No.20 (2002) 13

K ′ax� (6)

where Lmix is the length of the studied mixer section.The intensity of mixing, i.e. the achievable mixingeffect of motionless mixer elements per unit length isthe higher the lower Pe′ is or the higher K ′ax is.

Chen et al. [4] pointed out that smaller particleshad a higher apparent axial dispersion coefficientthan the bigger ones. By increasing the linear velocityof solids through the motionless mixers, an almostexponential improvement was obtained in the axialdispersion coefficient. A similar technique and modelwas used by Gyenis et al. [17] to investigate the influ-ence of different f low regimes, particle propertiesand length-to-diameter ratios of helical motionlessmixers on the resultant axial dispersion coefficient.

In mixing processes, especially in particulate sys-tems, stochastic behavior is a common feature whichcauses random variations both in f low characteristicsand in the local concentrations of components. Suchbehavior in gravity mixer tubes containing motionlessmixers was already recognized by the team of L. T.Fan [3, 7]. To interpret the experimental findings, adiscrete stochastic model was applied [3, 7, 9, 18]. Forthis, prior knowledge of the one-step transition proba-bilities of the particles was necessary, which weredetermined experimentally. This model seemed to besuitable to predict concentration distributions afterdifferent passes through the mixers. However, onexamining the results of experiments and thoseobtained by the stochastic model, two kinds of dis-crepancies can be recognized. One is that, in spite ofidentical particle properties, segregation and a spa-tially non-uniform mixing rate could be recognized[3]. Gyenis and Blickle proposed a possible theoreti-cal explanation of this behavior [19]. It was assumedthat spatially non-uniform transitions of particlesbetween the adjacent layers were caused by thechanging conditions during the non-steady-state f low.A correlation was proposed between the mixing rateand the energy dissipation caused by the interactionsof the particles and the mixer elements.

The other discrepancy came from the fact that ear-lier stochastic models used only expected values tocharacterize the one-step transition probabilities, to-tally ignoring their possible random variation. Thiscan be quite high if large-scale f low instabilities occur,especially in larger mixer volumes. Gyenis and Kataiproposed [20] a new type of stochastic model toexplain and describe the high random variationsexperienced in repeated experiments in an alterna-

Lmix2

t— · Pe′

tively revolving tumbler mixer, with and withoutmotionless mixer grids. Some years later, this modelwas simplified for simulation purposes [21], and wasthen made more exact by Mihalyko and his co-worker[22], introducing the concept of a so-called doublestochastic model.

DEM simulations based on a Lagrangian approachalso helped to understand the features and workingmechanisms of motionless mixers in particulate sys-tems [23].

2.4 Application Studies for Bulk Solids MixingThe mixing of free-f lowing particle systems in grav-

ity f low through motionless mixers was investigatedby several workers [2-12]. Most of these studiesresulted in suitable homogeneity after a few passes,but in some cases, depending on the physical proper-ties of the components, considerable segregation alsoemerged. Herbig and Gottschalk [24] applied hori-zontal bars serving as motionless mixers built into agravity mixer. It was found that assuring the smallestpossible shear action is essential to suppress segrega-tion.

A special, alternatively revolving bulk solids mixerequipped with motionless mixer elements shown inFig. 2 was studied by Gyenis and Arva [13, 14, 25,26] and provides practically segregation-free mixing.This device consists of two cylindrical containers (1)and a mixer section between them containing hori-zontal mixer grids (2) composed of a number of

14 KONA No.20 (2002)

Fig. 2 Schematic diagram of the alternating revolving bulk solidsmixer(a) outline of the mixer, 1 - containers, 2 - grids composedof motionless mixer elements, 3 - components to be mixed,4 - mount with rotating shaft, (b) helical motionless mixersarranged in grids

(b)

3

4

1

2

1

(a)

ordered FixMix elements. The material to be mixed(3) is filled into the lower container, then the mixer isrotated intermittently. In other words, the mixer bodyis turned through 180° in one direction, then stoppedto allow the bulk solids that are meanwhile at the topenough time to f low down through the mixer ele-ments. After this, the mixer is turned again through180° but in the opposite direction. The whole proce-dure is then repeated till the required homogeneity isobtained. Because of the periodically reversing direc-tions of particle f low and the changing direction ofacceleration and deceleration of the particles, segre-gation can be almost totally avoided.

By this method, a considerable improvement of themixing rate was achieved, resulting in a short mixingtime and a high homogeneity at a reasonably lowpower consumption [27]. This was evidenced byexamining the mixing kinetics of particle systemscomposed of materials with extremely different physi-cal properties, listed in Table 1. The density ratios ofthe component particles were varied from 1.2 : 1 to2.9 : 1, while the particle size ratios were changedfrom 1 : 2.7 to 1 : 110 as seen from Table 2. Kineticcurves, i.e. the variation of the degree of mixednessas a function of mixer turns are plotted in Fig. 3. Itshows that this mixer provides rapid and segregation-free mixing. The degrees of mixedness were deter-mined from the concentration variations of 65 spotsamples taken after different numbers of mixer turnsor mixing times by metal templates according to aregular pattern. A detailed description of this sam-

pling method was given by Gyenis and Arva [13]. Themass of each sample was 20 g, and the compositionsof samples were determined from 3�2.5 g materialtaken off from each sample, by dissolving the sodiumchloride tracer particles and measuring the conduc-tivity of the solution, or in other cases, by weighingthe polypropylene tracer particles after mechanicalseparation of the samples.

Theoretical considerations gave an explanation ofthis segregation-free operation and of the high achiev-able equilibrium homogeneity [14].

Bauman [29] studied three different types of mo-tionless mixers (Kenics, Komacs and Sulzer SMX) tomix particulate materials differing in mean particlesize and size distribution, in bulk density and in massratio. It was concluded that the mass ratio of the com-ponents, as well as the shape and number of motion-less mixers played a significant role in the achievablehomogeneity. Kenics-type mixers proved to be thebest when mass ratios were equal. But, when thesediffered significantly, Komacs and Sulzer SMX mixersgave much better results.

Motionless mixers are now increasingly appliedin various process technologies to mix particulatesolids. An interesting example for this is, e.g. the indus-trial standard of Tennessee [30], which mandates theuse of Komax, Ross, Koch (Sulzer) or similar com-monly accepted motionless mixers to manufacturehydraulic cement.

3. Bulk Solids Flow through Motionless Mixers

3.1 Gravity Flow StudiesThe continuous f low of bulk solids in vertical tubes

through Kenics-type motionless mixers was studied

KONA No.20 (2002) 15

Component Mean particle size, Density, mm kg/m3

Quartz sand 0.17 2650

Sodium chloride 0.46 2160

Wheat f lour 0.05 1510

Polypropylene granules 5.50 0910

Table 1 Particle sizes and densities of the constituents in mixesshown in Fig. 3.

Component Size ratio, Density ratio, � �

Quartz sand - Sodium chloride 1 : 2.7.. 1.2 : 1

Quartz sand - Polypropylene 1 : 32.4 2.9 : 1

Wheat f lour - Polypropylene 1 : 110. 1.7 : 1

Table 2 Size and density ratios of the constituent particles inmixes shown in Fig. 3.

wheat flour - polypropylene granules

quartz sand - polypropylene granules

quartz sand - sodium chloride

0 2 4 6 8 10 12

Number of mixer turns

Deg

ree

of m

ixed

ness

, M

14 16 18 20 22 240,0

0,2

0,4

0,6

0,8

1,0

Fig. 3 Kinetic curves obtained by the mixer shown in Figure 2with extreme particle systems (particle sizes, densities,and their ratios are given in Tables 1 and 2)

by Gyenis and his co-workers [12, 31, 32] under dif-ferent conditions. These mixer tubes consisted ofthree sections: (1) a plain feeding tube at the top, (2)motionless mixers in the middle, and (3) anotherplain tube below the motionless mixers. The massf low rate of solids was controlled by two means: (a)by adjusting the feeding rate at the inlet, or (b) bycontrolling the particle discharge at the bottom. Localparticle velocities were measured by fiber-opticalprobes that captured light ref lection signals. Averageand local solids hold-ups were determined by weigh-ing the material remaining in the tube after closingboth ends, and by gamma-ray absorption during oper-ation at different cross-sections, respectively. Theaxial mixing intensity was characterized by apparentPeclet numbers and dispersion coefficients calculatedfrom residence time distributions of tracer particles.The details of experiments and the applied experi-mental devices were described in several papers ofGyenis and his co-workers [12, 31, 32].

Experiments [12, 31, 32] and DEM simulations [23]equally revealed that, depending on the feeding anddischarging conditions, three characteristic f lowregimes could be distinguished in such gravity mixertubes, shown schematically by visualized simulationresults in Fig. 4.

A first type of f low regime takes place, shown inFig. 4a, if a solids f low withdrawn from the bottom,e.g. by a belt or screw conveyor, is less than the maxi-mal possible throughput of the gravity mixer tube,determined by its diameter and the configuration ofmotionless mixers. Naturally, the inf low of particles atthe tube inlet must be unlimited in this case, e.g.directly from a hopper. This 1st f low regime is charac-terized by dense f low, i.e. high solids hold-up in allthe three tube sections.

By increasing the discharged f low rate in this 1st

f low regime, the solids hold-up in the mixer tubedecreases slightly, mainly due to the growing “gasbubbles” just below the lower surface of the motion-less mixer elements. After reaching the maximalthroughput, which is achieved by unlimited outf low,the solids hold-up suddenly drops to a well-deter-mined value, resulting in a second f low regime shownin Fig. 4b. It is characterized by a dense sliding parti-cle bed in the upper tube, accelerating particle f lowalong the mixer elements and almost free-falling parti-cles in the lower plain tube section below the mixersection. The transition between the 1st and 2nd f lowregimes can be well recognized from the snap-shotsin Fig. 4d, obtained by DEM simulation, showing theactual situations at successive moments in time.

Another f low regime evolves when the solids f lowrate is controlled at the inlet of the tube, with free out-f low at the bottom. In this case, the f low rate of bulksolids fed into the tube must be lower than the maxi-mal attainable throughput of the motionless mixers.This 3rd f low regime, shown in Fig. 4c, is character-ized by almost free-falling particles in the upper andbottom plain tube sections with very low and progres-sively decreasing solids concentration. In the mixersection, however, a rapid sliding particle f low takesplace along the surface of the mixer elements with amuch higher solids hold-up compared to the upperand lower tube sections. When the solids f low rate inthis f low regime is increased from zero to the maxi-mal attainable capacity, the average solids volumefraction in the tube also increases from zero to a maxi-mal value. Reaching this latter stage, the upper tube

16 KONA No.20 (2002)

Fig. 4 Characteristic f low regimes in gravity mixer tubes withmotionless mixers in the middle tube section(a) 1st f low regime, (b) 2nd f low regime, (c) 3rd f low regime,(d) transition between the 1st and 2nd f low regimes

(a) (b)

0.0s

limited discharge

unlimited inf low unlimited inf low limited inf low

free outf low free outf low

0.4s 0.8s 1.2s 1.4s 1.8s

(c)

(d)

section above the motionless mixers suddenlybecomes choked with this sliding particle bed. Thiscauses a rapid transformation from the 3rd to the 2nd

f low regime.Visual observations and experimental data revealed

that in these f low regimes, a different and well-defined correlation exists between the solids hold-upin the mixer tube and the mass f low rate of particlestaken off at the bottom or fed into the tube.

As seen from Figs. 4a-d, the particle concentrationand thus solids volume fraction changes from place toplace along the length of the tube. However, since theusual mixer tubes are composed of several sections(e.g. feeding, mixing and post-mixing sections) and,very frequently, free tube sections (inter-element dis-tances) can be present between the individual mixerelements, it is reasonable to characterize operationconditions by the mean solids volume fraction aver-aged within the whole tube.

Plotting this mean solids volume fraction vs. themass f low rate, important characteristics of theabove-described f low regimes can be recognized, alsoindicating the conditions of transitions between them,as is shown in a general status diagram in Fig. 5.

The upper, slightly slanted curves of this diagramcorrespond to the changes in the 1st f low regime.Namely: by increasing the discharged mass f low rateat the tube bottom, the solids volume fraction aver-aged within the whole mixer tube also decreasesslightly, mainly due to the increasing void fractionwithin the section containing motionless mixers.Decreasing the l/d ratio of the mixer elements alsodecreases the mean solids volume fraction, making

these curves steeper.Achieving the maximum throughput of the given

mixer tube, the average solids volume fraction sud-denly drops to a distinct point shown in Fig. 5, whichcharacterizes the 2nd f low regime in the given system.It should be emphasized in this respect that localsolids volume fractions in this f low regime changesfrom place to place, generally decreasing in down-wards direction from the inlet of the mixer section,and especially in the plain tube below the mixer ele-ments. However, the average solids volume fraction isa well-determined distinct value, belonging to themaximal possible mass f low rate of particles underthis condition. This mass f low rate and average solidsvolume fraction depend on the diameter of tube, onthe physical properties of material, e.g. particle size,density, shape, surface properties, particle-particleand particle-wall frictions, as well as on the geometri-cal and other properties of the motionless mixer ele-ments, on the length ratios of feeding, mixing andpost-mixing sections, on the distance between themixer elements, etc. From Fig. 5, it is clearly seenthat by decreasing the l/d ratio of the helical mixerelements, the maximal throughput of the tube belong-ing to the 2nd f low regime also decreases. The gapbetween the solids volume fraction at the end point ofthe 1st f low regime curves and at the 2nd f low regimemainly depends on the length of the plain tube belowthe mixing section and on the distances between themixer elements: the gap diminishes if these plain tubesections are shorter.

In the 3rd f low regime, shown by the lower curvesin Fig. 5, the mean solids volume fraction increasesas the mass f low rate of solids fed into the tube inletis increased. The higher the retaining effect of themixer elements against the particulate f low, i.e. thelower their l/d ratio, the higher the mean solids vol-ume fraction in the tube will be: i.e. the slope of thecorresponding curves becomes steeper. After achiev-ing the maximum throughput of the mixer tube fromthis side, the feeding section becomes choked andthe mean solids volume fraction in the tube suddenlyincreases: i.e. the 3rd f low regime transforms to the2nd f low regime. This transformation is reversible, butsome hysteresis loop was experienced here. The gapsbetween the ends of the 3rd f low regime curves andthe data point of the 2nd f low regime mainly dependon the length of the feeding section.

It should be noted that Fig. 5 is a general diagramonly and therefore does not give precise quantitativedata on given particle systems or mixer tube configu-rations. It is a summary of our experiences and mea-

KONA No.20 (2002) 17

Fig. 5 General status diagram of f low regimes in gravity mixertubes containing motionless mixers

1st f low regime

l/d�1

l/d�1

00,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

500 1000 1500

Mass f low rate, kg/h

Mea

n so

lids

volu

me

frac

tion,

(1-

ε)

2000 2500

l/d�1.5

l/d�1.5

l/d�2

l/d�2

2nd f low regime

3rd f low regime

surements carried out with different particle systemsand mixer tubes under different conditions [12, 31,32]. However, this is a quite realistic diagram regard-ing the scales of its axes and tendencies of its curves,since they are close to the results obtained for thegravity f low of quartz sand of 0.17 mm mean particlesize in a gravity mixer tube of 1.6 m length and 0.05 minner diameter, with about 0.6 m total length of helicalmixer elements. Very similar curves were obtained byrecent DEM simulations for polymer particles with 3mm diameter and 1190 kg/m3 density [23], with thedifference that the corresponding mass f low rateswith similar mean solids fractions are somewhatlower compared to those of quartz sand.

Measurements [12] and DEM simulations [23]revealed a periodic variation of the local solids volumefractions along the motionless mixers in the middletube section. As typical examples, Figs. 6a,b,c showthe results obtained by the DEM simulation of partic-ulate f low in a mixer tube of 0.05 m ID and 0.80 mlength, composed of a feeding, a mixing and a post-mixing section of 0.20, 0.30 and 0.30 m length, respec-tively. The number of spherical model particles in thetube used for the DEM simulation was changed from10,000 to 65,000, with 3.0 mm diameter and 1190kg/m3 density. Other parameters such as stiffness,restitution coefficients, particle-particle and particle-wall frictions, and inlet velocity were described indetail by Szepvolgyi [23]. The mass f low rate con-trolled at the inlet or at the outlet of the tube to gener-ate different f low regimes was varied between 300and 1500 kg/h. From this diagram, it is seen that peri-odicity of local solids volume fractions took place inall the three f low regimes, due to the multiple interac-tion with the motionless mixers, which caused peri-odic deceleration and acceleration of the f low alongthe mixer lengths. These diagrams also show signifi-cant differences between the three f low regimesregarding the change of local solids volume fractionalong the various sections of the mixer tube.

Experimental studies revealed that these f lowregimes had a great inf luence on the mixing perfor-mance, too. Fig. 7 shows some examples for resi-dence time distributions of tracer particles measuredduring gravity f lows through Kenics-type motionlessmixers [12]. The model material for these experi-ments was quartz sand, the same as used for thesolids volume fraction measurements, and a shortplug of sodium chloride or polypropylene granuleswas used as the tracer. It was found that residencetime distributions were somewhat broader in the 1st

f low regime relative to the 2nd or 3rd f low regimes,

especially for smaller length-to-diameter (l/d) ratios.However, due to the higher throughput and lowermean residence time, the apparent Peclet numbersand axial dispersion coefficients were more beneficialin the 2nd and 3rd f low regimes, mainly for higher l/dratios. The best homogeneity values were obtained inthe 2nd f low regime and, at higher mass f low rates inthe 3rd f low regime, close to its transition point [12].

18 KONA No.20 (2002)

Fig. 6 Variation of the local cross-sectional solids volume frac-tions along the tube length in the three characteristic f lowregimes(a) 1st f low regime, (b) 2nd f low regime, (c) 3rd f low regime

3rd f low regime

motionless mixerspost mixing

sectionfeedingsection

0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,80Length from the inlet, l

0,7

0,6

0,5

0,4

0,3

0,2

0,1

0,0Cro

ss-s

ectio

nal s

olid

s ho

ld-u

p, (

1-ε)

2nd f low regime

post mixing section

feedingsection

motionlessmixers

0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,80Length from the inlet, l

0,7

0,6

0,5

0,4

0,3

0,2

0,1

0,0Cro

ss-s

ectio

nal s

olid

s ho

ld-u

p, (

1-ε)

1st f low regime

motionless mixerspost mixing

sectionfeedingsection

0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,80Length from the inlet, l

(a)

(b)

(c)

0,7

0,6

0,5

0,4

0,3

0,2

0,1

0,0Cro

ss-s

ectio

nal s

olid

s ho

ld-u

p, (

1-ε)

3.2 Gas-solids two-phase flows Experiments were carried out by Gyenis et al. [12]

in a concurrent downward gas-solids two-phase f lowin a test device where the f low rates of both phasescould be controlled more or less independently. Byincreasing the gas f low rate, the mass f low rate andthus the solids hold-up could be enhanced consider-ably, which is generally beneficial to the performance

of in-line mixers and other operations by effective gas-solids contacting.

Motionless mixers can also be applied in counter-current gas-solids two-phase f low for more effectivephase contacting. It is known that f luidized bedprocesses often use various types of inserts in theparticle bed to improve the f luidization behavior [33].Motionless mixers can replace the usual inserts,favorably inf luencing the minimum f luidization gasvelocity, solids hold-up, and heat and mass transferbetween the phases by enhancing the relative veloci-ties and avoiding f luidization abnormalities.

4. Other Applications in Bulk Solids Handling

4.1 Improvement of Bulk Solids Flow andReduction of Bulk Volumes

In handling bulk solids, motionless mixers are wellsuited to eliminate problems in the bulk solids f low,and to decrease the bulk density in storage and trans-port.

In silos, inserts are frequently used to enhance f lowuniformity in space and/or time [34], avoiding pulsa-tion and bridging, which may totally stop the f low.Concentric, inverted or double cones, slanted platesor rods are frequently used for this purpose. In thisway, funnel f low can be transformed to mass f low,avoiding segregation during discharge. For this pur-pose, various forms of motionless mixers can also beused, but before their application, careful design workis necessary with preliminary investigation of mater-ial properties and its f low behavior through themotionless mixers to avoid potential troubles.

According to our experiences, motionless mixers ingravity tubes make the f low of fine powders more sta-ble, even if they are cohesive to some extent, such asf lour or ground coffee. It should be noticed, however,that this is true only for continuous or non-inter-rupted f lows. If continuous discharge is stopped, trou-bles can arise in re-starting the f low. This difficultycan be avoided by applying quasi-motionless mixers,connected to each other elastically, joining them bysprings, thus making the individual mixer elementsmobile to a certain extent [35]. Stresses inside thebulk solids column cause some passive movements ofthe mixer elements, which is enough to start or to sta-bilize the f low, therefore avoiding choking.

In loading a container, silo, truck or railroad boxcarfrom a spout or hopper, the bulk volume of solids mayexpand. Therefore, during storage or transportation,a considerable part of the available space is occupiedby air. However, if particulate materials are passed

KONA No.20 (2002) 19

Fig. 7 Residence time distribution curves obtained with Kenics-type motionless mixers in different f low regimes(a) 1st f low regime, (b) 2nd f low regime, (c) 3rd f low regime

3rd f low regime

0,0 1,0 2,0 3,0 4,0 5,0 6,0Residence time, τ

3,0

2,5

2,0

1,5

1,0

0,5

0,0

Freq

uenc

y, f(

τ)

without motionless mixer, G�2000 kg/hl/d�2, G�1760 kg/hl/d�1.5, G�470 kg/hl/d�1.5, G�1700 kg/hl/d�1, G�700 kg/h

2nd f low regime

0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0Residence time, τ

3,0

2,5

2,0

1,5

1,0

0,5

0,0

Freq

uenc

y, f(

τ)

without motionless mixer, G�2000 kg/hl/d�2, G�2300 kg/hl/d�1.5, G�1500 kg/hl/d�1, G�950 kg/h

1st f low regime

3,0 4,0 5,0 6,0 7,0 8,0 9,0 10,0Residence time, τ

(a)

(b)

(c)

3,0

2,5

2,0

1,5

1,0

0,5

0,0

Freq

uenc

y, f(

τ)

no mixer, G�830 kg/hl/d�2, G�830 kg/hl/d�1, G�710 kg/h

through motionless mixers, the expansion of bulk vol-ume can be reduced by 20-40 percent compared toloading via plain tube, as was proven by experimentswith wheat grains [36]. When bulk solids, which wereexpanded already, are passed through motionlessmixers, absolute reduction can also be achieved. Bythis method, as much as 4-10 percent more bulksolids can be stored or transported in a given volumeof a container or ship. To this end, motionless mixerelements should be well designed to avoid attrition orbreakage of the grains or particles.

4.2 Coating, Size Enlargement, Size ReductionMotionless mixers are applicable not only to blend

particulate solids, but also to contact different parti-cles effectively with each other. In a suitably designedgravity mixer tube supplied continuously with twoparticulate solids differing in size, a coating of the big-ger particles with the smaller ones can be realized ifsuitable binding material is also supplied. Gyenis etal. [37, 38] reported on a coating process of jellybon-bons with crystalline sugar, applying motionlessmixers. Similar equipment was used for coatingammonium nitrate fertilizer granules with limestonepowder to avoid sticking during storage. Granulationor controlled agglomeration of particulate solids isalso conceivable by this method, but a crucial point isto ensure proper conditions to avoid sticking of solidsor deposition of the binding material onto the surfaceof the mixers. Disintegration or size reduction, as wellas controlled attrition [39], can also take place duringinteraction between the particles and motionless mix-ers, especially at higher velocities ensured by gas-solids two-phase f lows.

4.3 Applications in Pneumatic ConveyingAs was mentioned above, concurrent gas-solids

f low in vertical tubes containing motionless mixersincreases the f low rate and solids hold-up, alsoenhancing the mixing process compared to simplegravity f lows of particles [12]. Because of the retain-ing effect of motionless mixers, the velocity differ-ence between the phases and also the residence timeof the particles can be increased considerably, com-pared to a plain tube. Such conditions are favorablefor heat and mass transfer processes or chemicalreactions in gas-solids contactors, thus decreasing thenecessary dimensions. This makes the realization ofvarious operations during pneumatic conveying [39]conceivable. But for this, carefully planned pilot-scaleexperiments and caution in design are needed toavoid troubles, e.g. choking or damage of the parti-

cles.Motionless mixers may be useful tools in pneumatic

conveying lines, e.g. in horizontal tube sections. DEMsimulation studies revealed that particles that tendedto settle downwards could be re-dispersed into thegas stream again by suitably designed motionlessmixer elements [23, 40]. This may reduce the salta-tion velocity, thus diminishing the required gas f lowrate. By using motionless mixers, a given section ofpneumatic conveying system can also serve as aneffective gas-solids contactor, too, or to realize othertypes of solids treatments simultaneously with con-veying. Caution and preliminary experiments men-tioned above are also recommended here.

4.4 Heat Treatment of Particulate SolidsHeat transfer processes in particulate solids can be

improved by motionless mixers built in a cooler orheater, due to the multiple transmissions of particlesfrom the bulk material to the heating or cooling sur-face and back. In some cases, heat-transmitting tubesor lamellas themselves, arranged, e.g. in a hopper,can modify the f low pattern of the solids, similarly tomotionless mixers.

Very often, heat treatment is carried out in rotaryheater or kiln, as is frequently used in the cementindustry or, in smaller dimensions, in food process-ing. Motionless mixers fixed inside a rotating unit,shown in Fig. 8, enhance the heat transfer betweenparticles and a streaming gas, or between the par-ticles and the heated surface, as was patented byBucsky et al. [41]. It also ensures uniform tempera-ture distribution throughout the cross-section of theparticle bed, which is of crucial importance in thetreatment of heat-sensitive materials. Such a device isalso applicable for drying particulate solids.

20 KONA No.20 (2002)

motionlessmixersgas

out

hot gas inroastedproductout

grains in

Fig. 8 Rotary heater with motionless mixers to roast agriculturematerials

4.5 DryingGodoi et al. [42] used a vertical tube equipped with

helical motionless mixers with perforations on theirsurface for the continuous drying of agriculturalgrains. The particulate materials to be dried were fedcontinuously at the top, and slid or rolled down a-long the surface of the mixer elements. Heated gasstreamed up along the f low channel between themixer elements and through their perforations. Dueto the interactions between the grains, the motionlessmixers and the gas, an effective mass and heat trans-fer was achieved. The rotary equipment in Fig. 8 alsocan be used for such a purpose.

4.6 Dust SeparationMotionless mixers are applicable for the separation

of particles from gases. The dust or volatile solidscontent of hot industrial gases often causes troublesin pipeline operation due to deposition onto the tubewall, especially at critical sections. Based on labora-tory- and pilot-scale experiments, Ujhidy et al. [43]described a new gas purification method and equip-ment applying helical motionless mixers shown inFig. 9. Solid particles are captured by a liquid filmtrickling down along the surface of mixer elements,totally avoiding plugging and thus extra maintenanceof the gas pipeline system. Applying proper condi-tions, i.e. optimal superficial gas velocity and suitablemotionless mixer geometry, the dry separation ofsolids is also feasible, especially above one hundredor several hundred microns particle size. This effectis due to the centrifuging and collision of particleswith the motionless mixers.

Concluding Remarks

As was seen from this review, motionless mixersare useful tools for process improvements: not onlyfor f luid treatments, but also in bulk solids technolo-gies. In this latter field, the most detailed knowledgeis available in bulk solids mixing, discussed in a greatnumber of papers. Investigations started more thanthirty years ago, elucidating the kinetics and mecha-nisms of this operation, mainly in gravity mixingtubes, but also in a special alternatively rotating bulksolids mixer. Modeling and simulations helped tounderstand experimental findings and to predict thebehavior and results of such equipment.

Particulate f lows in motionless mixer tubes showexiting phenomena which greatly inf luence theprocesses taking place in these devices. Other appli-cations such as to improve the bulk solids f low intubes, chutes and silos, or to reduce the bulk volumeexpansion led to significant results. In gas-solids two-phase f lows, namely in pneumatic conveying andsimultaneous treatment of bulk solids, their use offersnew possibilities for realization and process improve-ment. Coating, size enlargement, size reduction andattrition, heat treatment, drying, wet dust removaland dry particle separation are also promising fieldsof applications.

Acknowledgement

The author wishes to acknowledge the support ofthe Hungarian Scientific Research Fund (OTKAT29313).

Nomenclature

d diameter or width of motionless mixer element m

K ′ax axial dispersion coefficient, Eqn.6 m2/sKm kinetic constant of mixing �Ks kinetic constant of segregation �Lmix total length of the studied mixer section mL length, measured from the inlet ml length of one motionless mixer element ml/d length-to-diameter ratio of a motionless

mixer element �M degree of mixedness, defined by Eqn.2

[15, 16] �s estimated standard deviations of sample

concentrations taken from a mixture �s0 estimated standard deviations of sample

concentrations taken in a totally segregated

KONA No.20 (2002) 21

Slurry collecting basin

Dusty gas inlet

Purified gas outlet

Slurry outlet

Droplet separationunit with motionlessmixers

Dust separationtubes with wettedmotionless mixers

Washing liquid inlet

Fig. 9 Dust removal unit applying motionless mixers

state �xi mass fraction of the tracer particles within

the i-th sample taken at the outlet of the mixer tube �

Pe′ apparent Peclet number, Eqn.5 �m2 second central moment of the residence

time distribution of the tracer particles, Eqn.3 s2

ti the residence time of tracer particles within the i-th sample s

t— the mean residence time of all tracer particles in the mixer tube, Eqn.4 s

Φ segregation potential [14] �

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KONA No.20 (2002) 23

Author’s short biography

Janos Gyenis

Professor Janos Gyenis graduated in Chemical Engineering at the University ofVeszprem, Hungary. He received Dr. Habil and Ph.D. degrees at the Technical Uni-versity of Budapest, and a D.Sc. title at the Hungarian Academy of Sciences. Atpresent, he is a full professor at the University of Kaposvar, Department of Engi-neering, and director of the Research Institute of Chemical and Process Engineer-ing. Since 1971, he has been involved in a number of collaborative research workswith leading laboratories and university departments in Europe, the United Statesand Asia. He is now working with the mixing and f low of particulate solids and theapplication of motionless mixers for various purposes. Up to now, he has publishedabout 120 papers and he is co-inventor of 22 patents.