Mezcla de Polvos 1999

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REVISIN

Dry mixing and coating of powders(,)

M. Alonso* and EJ. Alguacil*Abst rac t This paper presents a review on the mixing and coating of powders by dry processes. Th e

review surveys fundamental works on mixture characterization (mixing index definit ionsand sampling techniques), mixing mechanisms and models, segregation with especialemphasis on free-surface segregation, mixing of cohesive powders and interparticle forces,ordered mixing (dry coating) including mechanism, model and applications and mixingequipment selection.

Keywords Powder mixing, Powder coating. Segregation. Solids mixer.

Mezclado y recubrimien to d e polvos por va seca

R e s u m e n En este art culo se presenta una revisin bibliogrfica sobre el mezclado y recub rimien to demateriales pulverulentos mediante procesos por va seca. La revisin incluye trabajosfundamentales sobre caracterizacin de mezclas (definiciones de ndices de mezclado ytcnicas de mu estreo), mec anismo s y modelos de mezclado, segregacin con espec ial nfasisen la segregacin de superficie libre, mezclado de polvos cohesivos y fuerzas interpartculas,mezcla ordenada ( recubr imiento) incluyendo mecanismo, modelo y apl icaciones , yseleccin de equipos de mezclado.

Palabras clave: Me zclado de polvos. Re cub rim ien to de polvos. Segreg acin. Mezclado resde slidos.

1. INTRODUCTION

For thousands of years man has been mixingpowders for different purposes, mainly by themethod of stirring. The earliest mixing operationthat could be identified as such was probably thepreparation of natural earth pigmen ts in mortars .In this sense, the mixing of solid particles may beregarded as one of the oldest unit operations in theprocess industry. Solids mixing is an essentialoperat ion in the preparat ion of ceramic andpharmaceutical materials , plst ic processing,

fertilizer production, food manufacture, miningindustry, grain processingand perhaps mostimportantly in the powder metallurgy industry. T heimportance of mixing resides in the fact that it isnot only the base material, but a mix containing anumber of addit ives, which determines theproperties of the end produ cs .

In spite of being an ancient operation, solidsmixing is a relatively young science. The firstfundamental research on the subject was done in1933 by Oy am a , wh o studied the m otio n of

particles in rotating horizontal drums. Forty yearslater Cooke et al pub lishe d a classified list of 650

references on powder mixing, which gives anindication of the increasing interest placed on thematter. In this paper a general visin of previousworks on cohesionless powder mixing will first bepresented. It will be intentionally made as brief aspossible because some exhaustive and excellentreviews are already available and there seemslittle point in duplicating their contents. Theremaining part of the review is devoted to themixing of cohesive powders with especial emphasison the dry coating process, a special case of powdermixing in which fine cohesive particles of one

component cover the surface of coarse particles ofanother component .

2. CHARACTERIZATION OF SOLIDS MIXTURES

Most of the early investigations on powder mixingwere addressed to the assessment of the mixturequality, a topic which has given rise to majortheoretical and practical problems. As Enstadpointed out, it is obvious that a powder mixture cannever become fully homogeneous on a molecular

scale because it consists of discrete powder particlesof finite sizes. T he degree of hom oge neit y of a given() Trabajo recib ido el da de marzo de 1999 y aceptado en su forma final el 2 de julio de 1999.(*) Centro Nacional de Investigaciones Metalrgicas, CENIM (CSIC). Av. Gregorio del Amo, 8.28040 Madrid (Espaa).

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Dry mixing and coating o f powders

mixture must be a relative concept, since itdepe nds inevitably on the scale of scrutiny .

2.1. Mixing ndex

In 1970, Fan et al. reviewe d and discussed overthirty different ndices of degree of mixednessproposed by many investigators, all based somehowon the variance of sample compositions. A few morendices have been proposed since then. At thecompletely unmixed state, the variance of a binarymixture is given by[19] O Q = p (1-p), where p is theproportion of one of the components. Ideally, if bothconstituents have the same physical properties andtheir particles are geometrically identical, mixingwill progress until a state is reached in which the

probability of finding a particle of, say, the keycomponent is constant throughout the mixture.This state is commonly referred to as randommixture and its variance is given by[ CJR = f>(l-p)/n, where n is the number of particles in asample. At any other time of the mixing process thevariance of the sample compositions will lie betweenthese two extreme vales. The temporal variation ofthe variance is thus a measure of the change in themixture quality during the process. When thecomponents differ in particle size and density andwhen more than two components are present in themixture, other expressions for the limiting vales ofthe variance must be used; these have been given byseveral authors[2 0'23 1.

The use of the variance as a measure of themixture quali ty has, however, a number ofdisadvantages: a) a mixture is a very complexassembly of particles and it is not reasonable toexpect that it can be described by a singlenum be r ; b) t he use of GQ to characte rize theunmixed state is misleading, since its valu isindependent of the initial arrangement of thecomponent powders within the mixer , c)although the variance decays inversely as thesample size for a random mixture and isindependent of the sample size for a totallysegregated mixture, the variance-sample sizerelationship is unknown for intermediate states sothat comparisons between mixing studies in whichdifferent sample sizes have been used are of limitedvalu ; and d) in using varian ce as th e uniq uecharacteristic of a mixture, it is implicitly assumedthat the sample composit ions are normally

distribu ted, w hich is far from reality[ . Toov ere m e the se difficulties, Buslilc prop osed a

simple numerical homogeneity index based on the

sample weight required to obtain a s tandarddeviation of %. Although Buslik's index is usefulfor the comparison of homogeneity of unlikesystems , its de term ina tio n in any practic al caseis, however, a laborious procedure, since it would

require repeated campaigns of sampling andanalysis to find the sample weight which givesprecisely a standard deviation of % .

Other mixing ndices, not based on the varianceof sample composit ions, have been reported.Shinnar et al}29 proposed the shortest distancebetween particles of the component present inlower concentration as a test to evalate therandomness of solid mixtures. Although the test isespecially sensitive n detecting clusters ofparticles, it is obvious that requires a considerable

amount of experimental work and thus lackspracticability.Most of the mixtures encountered in practice

are non-random due to incomplete mixing orse 'gregation. A non-random mixture can bedescribed as a mixture in which the compositionsof contiguous regions are correlated. AsDan ckw erts suggested, a mixtu re migh t becharacterized by its correlogram, i.e. therelationship between the coefficient of correlationof point samples and the distance between thesamples. From the correlogram parameters ofinterest, such as the scale and intensity ofsegregation, can be deduced. Scale of segregationrefers to the state of subdivisin of clumps orclusters of particles, whereas the intensity ofsegregation expresses the differences incomposition throughout the mixture. A number ofauthors hav e used correlation techniqu es toassess the degree of mixedness. The correlogram,however, becomes difficult to interpret and itscalculation is rather lengthy in cases in whichdiffusion is the pred om inan t mixing me chanism .

Akao et al. 5] presented a mixing index forbinary mixtures based on the mea n conta ct number,i.e. the m ean nu mbe r of particles of one com pone ntin contact with a given particle of the othercomponent. The idea of contact number was laterextended to multi-component mixtures 4 . Otherworks on mixing ndices include the use of non-parametric statistical tests (that is, tests which canbe performed without knowledge of the populationdistr ibution) '4 , th e an alysis of the Fourie rtransform spectrum of the com position data and

the applica tion of mu ltivariate statistics .In general, all the theories concerning mixturehomogeneity have been developed having in mind

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systems of free-flowing, cohesionless powders. If afine cohesive com po nen t is present in the m ixtureit may stick to the walls of the mixer, resulting in adifferent mean composition of the system. It hasbeen proposed that the mean concentration of thekey component should be checked in addition tothe mixing indices[52]. As a concluding remark forthis section a recent statement made by Gyenis etal [53] can be cited: uthe problem of finding anuniform and unambiguous definition of the degreeof mixing has still not been solved satisfactorily .

2.2. Sampling techniques

Fan et al[7] reviewed the common samplingtechniques that have been employed to assess the

homogeneity of solids mixtures. The most commonmethod of sampling is perhaps by thief prob, itsmain drawback being the disturbance caused byinserting the prob into the mixture[9 ] and thepossibility of removing non -represen tative samplesfrom segregating mixtures 4.

Another method consists in impregnating themixture with gelatin which, after setting, allowsthe wh ole mass to be sectioned into small elem entsfor analysis1551. Al th oug h in th is manner themixture can be closely examined withoutdistorting its structure, it is a time-consumingtechnique unuseful for practical purposes.

Radioactive tracer methods15 6'59 1 are simpler touse and can be applied to the continuousassessment of mixing processes. In 1957 Grayused an optic prob to measure the composition ofa binary mixture of different colored powders. Hismethod consisted in s topping the mixer atprescribed times and measuring the reflectivity ofthe mixture at several positions. This same methodwas used by Miles et alm to evalate theperformance of seven different mixers. Harwood etal [62] improved the optical technique adapting it tothe cont inuous measurement of the mixturecomposit ion. Satoh et al have also developed acontinuous optical method163,64] and applied t tothe evaluation of continuous powder mixers suchas ribbon blendersI65] and batc h mixers such ashiglvspeed mixer1661, rotary drum with simultaneousrocking motion[67Jand a mixer with a twisted,perforated rotating pate impeller1681. A reviewarticle of some of these works has beenpublished1691. Optic fiber probes have found other

applicat ions, such as in the measurement ofparticle size and particle velocity of powders in

A n illustrative exam ple of the use of the on-lin eoptical measuring method is shown in figures 1 and2. Figure 1 shows a typical higlv spe ed mix erequipped with six optical probes at differentheights and radial positions. Each prob contains

two optical fibers, one for sending light into themixture, the other for collecting the light reflectedby the mixture and conducting it to a photosensor.In this manner, with the data supplied by thesensors and the previously determined calibrationcurve of the powder system in consideration, themixture composition at different points can becontinuously measured. Experiments were donewith binary mixtures of different-colored powders.One of the components (white) is first placed inthe vessel, which is then vibrated at a prescribed

frequency Ny while the impeller is set in motion atthe desired speed N R . Th e second com pone nt(colored) is the n added at time t = 0 on to the bedin the form of a pulse input. The concentrationcurves and their corresponding mixing curves areshown in figure 2. The degree of mixing appearing

Vessel

170]motion

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Weight

Figure 1. High speed stirred mixer with optical probes.Figura 1. Mezclador de agitacin de alta velocidad con sondas pticas.

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in the y-axis of th e mixing curves is defined as propertie s; if th e ope rating con ditio ns are prM = 1 -a I a o, wh ere G is the standa rd de viat ion of selected (case 1) th e system at tains an idethe conc entrati ons measured at the six sampling perfect mixing state (rando m mixing); at dipoints and GQ is the standard deviatio n of the con ditio ns (case 2, lower rota tion speedcompletely unmixed state, i .e. at time t = 0. Cases vibr atio n frequency) the circu lation of pow der

1 and 2 in figure 2 correspo nd to a binary mix ture wi thi n the mix er is very irregular, mix ing whose com pon ents hav e identical physical and a complete mixed state canno t be at ta

Figure 2 . Concentration curves (left) and mixing curves (right) for different types of mixing processes.Figura 2. Curvas de concentracin izquierdo) y curvos de mezclado derecha) para tipos diferentes de procesos de mezclado.

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M. ALONSO AND FJ. ALGUACIL

even after a long mixing time. Case 3 is that of abinary mixture of fine cohesive powders; the timerequired to attain the random mixing state is largerthan in the case of coarse partiles (case 1) because

fine powders tend to form agglomerates whichhave to be broken up in order to achieve a goodmixture quality at the microscopic level. Cases 4-6correspond to binary mixtures differing in particlesize or density; in these cases, segregation preventsthe achievement of complete mixing. Segregationwill be discussed below in greater length. Case 7 isthat of mixing of coarse particles with the samepartiles which have been previously coated withdye fine particles; the coating process will also betreated below separately. The last case shown infigure 2 reveis the presence of electrostatic effectsin mixing; it is observed a very irregular patternwith brief mixing stages followed by segregation.This example serves to demnstrate the usefulnessof the optical method as a practical means tocontinuously assess the state of mixing and, moreimportantly, to evalate the performance of a givenmixer and establish the optimum operat ingconditions.

However, even if satisfactory mixing is achievedin the mixer, it cannot be assumed that the qualityof mixing wil l remain unchanged duringsubsequent han dlin g and storage . Th is isespecially true in the case of mixtures ofcohesionless powders except those consisting ofidentical monosized materials. In industry, theinterest is in the quality of the mixture leaving themixer and therefore, as suggested by Ha rnb y ,samples should be taken from the outlet stream. Inalmost all of the laboratory studies on mixing,samples have been, however, removed from insidethe mixer.

3. MIXING MECHANISMSTwo fundamental processes take place in a

mix er : first, a tra nsp ort of groups of par ticle sfrom one regin to another and, second, a randommotion of individual particles relative to oneanother. These processes have been referred to asconvective and diffusive mixing, respectively. Inthe convective mechanism groups of particlesmove relative to each other with differentvelocities, leaving a thin layer (about 10 particle

diameters in thickness) between them, termed thefailure zone . The presence of these shearingplanes have led a number of authors to proposeshearing as another mixing mechanism, but it

accounts for essentially the same phenomenonoccurring in the convective process and there is noneed to make a distinction between them.

If a smaller component is present in the failure

zone it may be able to move downwards inter-particle percolatiorP^) provided the particle weightis mu ch greater than the inter-particle cohesiveforc. This phenomenon will occur even if the sizesof the particles do not differ appreciably, becausethe velocity gradient existing in the failure zonefavors the formation of a loosely-packed localstructure within which the particles have a greatermobility. Inter-particle percolation, a mechanismof both mixing and segregation, has beenextensively studied by Bridgwater et al. . Theyhave proposed[76] this mechanism as an explanationof the overmixing, that is, the deterioration nmixture quality with time if the mixing time is toolong, a ph en om en on tha t Rose described interms of a demixing potential . Inter-part iclepercolation is controlled primarily by particlediameter ratio and shear strain in the failurezone ; oth er factors, such as particle density,particle elasticity, strain rate and friction, appear tobe less im po rtan t . W hils t small particles ten dto drain downwards through the failure zone, largeparticles move towards the regin in which there ismore mobility of the smaller ones, i.e. in thedirection of increasing strain rate, where thefrequency of voids occurrence is greatest. Thisprocess by which large particles move smalldistances through the voids has been termedparticle migrationm. Inter-particle percolatio n andparticle migration are some of themicromechanical processes which togetherconstitute the mixing or segregation action.

Whenever the component powders differ insize, shape or density, mixing and demixing

processes caused by the mechanisms describedabove take place simultaneously and if the processis prolonged an equilibrium between mixing andsegregation is reached, after which the quality ofthe mixture remains unch ange d .

3.1. Mixing models

The first fundamental studies on powder mixingwere carried out using horizontal rotating drums,which are probably the simplest mixing vessels. In

this type of mixer, mixing proceeds almostexclusively by diffusion and, accordingly, it hasbee n mod eled by mean s of Fick's diffusion equ atio nby severa l work ers ' . T h e diffusion m od el is,

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however, restricted to ideal mixtures of identicalcohesionless powd ers ' and add ition al terms inFick's equation are needed in the case of segregating

[96, 97]systems

Ot he r autors hav e used a stochastic approach tomodel the mixing process. Inoue et al. modeledmixing in a V-type tumbling mixer as a discretesteady-state Markov process. The Markov chainmodel has also been used to describe mixing inmotionless mixers, bo th for binary ideal and multi-com pon ent non-id eal systems. In contin uousform, the Markov chain model leads to the so-called Kolmogorov diffusion equation 10 inwhich, besides a diffusive term similar (but notidentical) to that of Fick's equation, there is anadditional drift (convective) term. The stochasticmodels can predict the concentration distributionand its variation with time from prior knowledge ofthe one-step transition probabilities (which areobtained experimentally)and can be applied to anyclass of mixer regardless the mechanism(s) bywhic h mixing proceeds . T he stochastic approachcan also be employed to model more complexmixing processes, such as those carried out inmixers having moving mechanica l e lements(impellers, screws, ribbons).

4. SEGREGATION

In any process involving the motion of particlesrelative to one another, differences in propertiessuch as particle size, density, shape and particleresilience will cause the separation of the bulkmass into regions, each of them containing only likeparticles. Among the properties just enumerated,particle size seems to be the most important factordetermining the segregating behavior of granularmaterials. On the one hand, smaller particles maypercolate downwards through the intersticesbetween larger particles. But on the other hand, ifthe particles are too small the particle-particlecohesive forc may overeme the body forc (e.g.gravity) acting upon the particle, thus decreasing itsmobility and hindering segregation. Furthermore, ifone component consists of coarse cohesionlessparticles and the othe r is a fine cohesive powder, th efine particles may adhere to the surface of the largerparticles, yielding a fairly homogeneous mixturewh ich does no t tend to segregate . Also, smalladditions of liquids such as water (possibly with

surface-active agents) can remarkably reduce theflowability of th e pow ders and thu s pre ve ntsegregation. It may be accepted as a general rule that

segregation problems arise only in systems ofcohesionless free-flowing materials.

When powder beds are vibrated, the largerparticles rise to the surface and the fines percolatedownwards. In this case, it seems that segregation

persists even if the larger particles are much densertha n the smaller ones and this experim ental factsuggests that segregation in vibrated beds can beexplained on the basis of geometrical considerationsalone11051.

However, if the separation of particles takesplace by the so-called free surface segregationmechanism ], the origin of segregation is not of ageometrical nature alone and the effect of the sizeratio (related to the tendency of smaller particles topercolate) m ay be compen sated for by an appropriate

density ratio (which is a measure of the tendency ofthe particles to sink in a mdium of lower density).Free surface segregation is the process by whichpowders segregate wh en poured into a heap andth same mechanism is the cause of segregation intumbling mixers operating under certain conditions.

Based on a simple analysis, a parameter wasdeveloped which has shown to be useful forcorrelating mixing data in free-surface segregatingsystems. The segregation parameter S is given by

d 1 V c p - D

where p and d are the coarse-to-fine density and sizeratios, respectively, l)c is the solid volum e fraction ofcoarse particles and f e) a certain function of the bedporosity 8. Figure 3 shows the relationship betweenthe mixing index and the segregation parameter forexperim ents carried out in a rotary drum with binarymixtures of components differing in size and/ordensity. The mixing index M is defined so that itranges between 0 and 2; vales of M between 0 and1 describe the situations in which the coarse particlesfloat and accumulate at the outer regin of the bulk,whereas vales of M between 1 and 2 correspond tothe case where the coarse component sinks andconcentrates at the core. A valu of M equal toeither 0 or 2 means complete component segregation. For M = 1 the tendency of floating equals thatof sinking an d th e large particles (or th e fines for th atmatter) are distributed evenly within the bulk of themixture. A s demo nstrated in figure 3 , the segregation

parameter S defined above is useful to predict thesegregating behavior of binary mixtures: the coarseparticles beh ave as floaters if S < 1 and as sinkers if S

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2x0)O.EO)E>8iV * o

A 7 XAy, 0

VV

V , i V

T r - l r~~7|

, H

y \-jJA

.~A

' Jcoarse 1floats J

i , i

Ai

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

segregation parameter, S ( - )igur 3. Mixing ndex as a function of the segregation pa

rameter. Different symbols correspond to different binarymixtures.

Figuro 3. ndice de mezclado en funcin de l pormetro desegregacin. Smbolos diferentes corresponden a mezclasbinarias diferentes

> 1; ideally, the sinking and floating tendencies willbe balanced if S = 1 (perfect m ixing ). The validity ofthe model has also been confirmed by later

[108,109]expenments

At very low concentration of coarse particles,mixing/demixing is controlled by the ability of thecoarse material to open voids in the layers below dueto its specific weight. Fines percolation does not playany role at this level of concentration, in agreementwith the findings of Arteaga and Tzn11101 andNikitidis et al lu] conc erning the segregation ofdifferent-sized particles in silos. At the other extreme,at very high concentration of coarse particles,segregation is controlled by fines percolation, whichmeans that the coarse particles will invariably behave

as floaters regardless of their density.Alternative models of free-surface segregationhav e also been proposed by other autho rs[U2, n buttheir predictions have not been checked withexperimental results. Segregation in continuousmixers has been studied by Weinektter et al.using an optical prob to continuously assess themixture composition.

Another demixing mechanism is the so-calledtrajectory segregation, which may occur when theparticles are dispersed in a fluid mdium. In thiscase, segregation occurs because the drag forc onthe particle depends on its size, density and shape.This is the main segregation mechanism, thoughnot the only one, in gas fluidized beds u ' l .

In some instances, particle segregation is adesirable phenomenon. Thus, Izumikawa et al. lused shape segregation to recover copper fromintegrated circuit panels. Thes e panels are made ofcopper, epoxi resin and glass fiber. During grinding

of the pane ls, the particles of the th ree com pon entsattain different shape: spherical copper particles,flakeTike epo xi parti cles and fibrous glass pa rticle s.After grinding, the mixture is conveyed by aninclined belt conveyor, whereby the sphericalcopper particles roll downwards and segregate fromthe other components. In this simple manner, upto 80 % of the initial copper can be recovered.Separation of differently shaped particles can also beachieved in rotating vibrating conical d is k s[ 1 2 3' .

5. MIXIN G OF COHESIVE POWDERSCohesive forces such as van der Waals forc,moisture bonding, electrostatic forc, solid bridgingand mechnical inter locking, promote theagglomeration of powder particles. If the particlebody forc (gravity, centrifugal forc) is greater thanthe inter-particle cohesive forc, the agglomerateswill be dispersed into their primary constituentparticles and the powder will flow freely. Powdersexceeding 100 jum in diameter usually showcohesionless behavior, although some powders,presumably closely sized ones, show it down to30 jum1101. The micro-processes and mixing-demixing mechanisms discussed above would applyto aggregates of cohesive materials rather thanindividual particles. There is an additional factorthat must, however, be taken in consideration,namely, the innate and finite cohesin of theagglomerate that comprises many individualparticles. The flow behavior of cohesive materialshas been studied and reviewed extensively byMolerus[125127] and, in spite that a complete theory is

still not available, two basic points appear to havebeen definitively established, at ieast quaiitatively:a) the action range of the cohesive forces dependsfundamentally on particle size, in such a way that forlarge particles the range of inter-particle attraction(i.e. that within which the cohesive forces exceedthe body forces) s com parable with the scale ofsurface roughness and would prevent effectivebonding[128]; b) a decrease in contact rea will resultin lower cohesin, so that particle shape1 2 andparticle surface texture[130] play significant roles in

the cohesive behavior of the powder.Due to the absence of long-range segregation, amixture of cohesive powders is usually of good

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quality when analyzed at a large scale of scrutiny,but at a small scale of scrutiny a high intensity ofsegregation can occur . Th e role of the mixer inthis case is to provide enough energy to repeatedlybreak the agglomerates down to the scale of the

cons tituent particles . Com paratively, fewstudies have been done on the mixing of cohesivepowders. In contrast, the mixing of coarsecohesionless powders with fine cohesive particleshas received relatively more attention, especiallybecause of the peculiarities and applicability of theresulting so-called ordered mixtures.

5.1 . Inter-particle forces

Th e m echanisms of inter-particle adhesin may be

classified into two groups : a) those wh ichrequire no material bridges (van der Waals,electrostatic and magnetic attraction forces,mechanical interlocking and chemical forces) andb) those which oprate through material bridges(solid bridges, capillary bonding forces andinmobile liquid bridges ). The forces of the firstgroup are the only ones to consider when thepowder is in equilibrium with a dry atmosphere andthose of the second group become important ashumidity increases .

The van der Waals forces are related toelectromagnetic fluctuation phenomena in solids.These forces originate when the randommovement of electrons on a particle's surfacemomentarily con cntrate to form dipoles which, inturn, are attracted to other dipoles nearby . Thevan der Waals forces are only noticeable when theparticles can come sufficiently cise together, atseparation distances of the order of the size of amolecule, 0.2 to 1 nm . Wh ilst the gravitationalforc is proportional to the cube of the particlediameter, the van der Waals forc is proportiona l tothe diameter and, therefore, the magnitude of theattractive van der Waals forc becomes negligiblecompared with that of the body forc when theparticle size exceeds a certain valu (of the order ofa few microns) . Th e van der Waals forcbetween two smooth spheres of radii r \ and ri isF=AR/6H2, where H is the distance between thespheres, R = riri/iri+ri) , and A is the Ham akerconstant of the material. A list of Hamakerconstants of many materials can be found inreference . Th e most impo rtant parameter

determining the van der Waals attraction forc isthe interparticle separation distance H; in turn, His affected by the surface roughness and the

presence of spacers (small molecules or finesadsorbed) on the particle surface . Due to elasticand/or plstic deformation at the po int of contact,the contact rea between the interacting solidsincreases and this results in an increase in the van

der Waals forc , in such a way tha t the totalforc is given by ll36] F = (A/6H2)(R+r2/H), where ris the radius of the extended contact rea. Theadhesin forc between flattened particles maybecome 20 times tha t of unflattened particles ,although this effect is negligible for materials w ithhardness above 108 dyn/cm . In the aboveequations for the estimation of the adhesin forcit is common to use a valu of 0.4 nm for theinterparticle separation distance H .

Electrostatic forces arise, for ins tance, w hen two

solids are in rubbing contact (tribo-electriccharging). In this situation, they will charge eachother electrostatically and electrons are transferreduntil, at equilibrium, a contact potential differenceis established . In general, the magnitude ofelectrostatic forces on particles are quite smalland some orders of magnitude smaller than theomnipresent van der Waals forc . Electrostaticand van der Waals forces both promote thedeformation of particle surface, augmenting thecontact rea and, thus, the adhesin forc . Th eother mechanisms belonging to the first groupcited above are far less important.

Among the adhesin mechanisms which occurthrough the formation of material bridges, moisturebonding is perhaps the most important. At lowrelative humidities, moisture is in the form ofadsorbed water vapor. At a critical valu of therelative humidity (between 65 and 80 %),condensation of water vapor occurs at the contactpoints generating liquid bridges . Below a relativehumidity of 65 %, capillary forces play no part ininter-particle adhesin , but in the range ofeffective moisture bonding they can become aboutone order of magnitude larger than the van derWaals forc . The effect of humidity is, however,to increase the magnitude of the van der Waalsforc because of the decrease in interparticledistance. On the other hand, electrostatic forcesdecay rapidly with humidity because humiditycauses the surrounding air to become conductiveand promotes the discharge of the particles .

6. DRY COATING OF POWDERS

As mentioned previously, when a fine cohesivepowder is mixed with a coarser granular material,

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the structure of the resulting mixture consists in alayer of fines adhered on the surface of the largerpartiles. Hersey coine d the term ordered mixturefor this kind of mixture, to distinguish it from therandom mixture that results when cohesionless

powders are mixed.There exist several factors peculiar to ordered

mixtures, not found in random systems: a) it hasbeen found tha t in ordered mixtures thevariance is not affected by the sample size as wouldbe the case in a random mixture; b) the degree ofhomogeneity attainable in ordered mixtures is farlarger than in random mixtures118, 143, 145' 146); c)provided that the number of fines does not exceedthat of adherence sites on the carrier (larger)partiles' surface, ordered mixture are more stable

than random mixtures to constituent segregationunder vibration, handling and conveying154,143,145'151]. Although resistant to constituent segregation,ordered mixtures can exhibit a type of segregationthat has been termed ordered unit segregation ,consisting in the appearance of fractions rich andpoor in the fine com pon ent due to the polydispersenature of the coarse powder.

6.1. Mechanism of ordered mixing

The coating process of powders follows in generalthe three following stages[157,158] (Fig. 4): (i) at thebeginning of the operation, the fine aggregatesadhere to the coarse partiles in their immediatevicinity; (ii) when a coarse particle carrying finesadhered onto its surface collides with a non-coatedparticle, it transfers part of its fines to the latter;(iii) by friction and colusin between partiles, theagglomerates of fines are gradually dispersed ontothe surface of the carriers, which results in anincrease in the coated surface rea. The dispersinof fines is actually occurring from the earlier stagesof the process. The dispersin rate and the degreeto which the agglomerates are broken up dependstrongly on the mechanical energy input and,therefore, on the type of mixer used. There exists aespecial type of mixer, the Angmill MechanofusionSystem, which imparts such a high level ofmechanical energy to the particles that the particlesurface texture is greatly modified, it melts locallyand a partial or total penetration of the finecomponent into the body of the larger particlestakes place (last stage in Fig. 4).

The exchange of fine particles (eitherindividually or as agglomerates) between carriersresulting in the uniform distribution of the minor

0,0o o

Q

0) initial condition

1) formation offirst carriers

2) carriers transferring finesto non-coated particles

3) breaking-up ofagglomerates anddispersin of fineson the surface ofcarriers

4) mechanofusion

igur 4 . Mechdnism of the coating-mechanofusion process.

Figura 4. Meconismo de l proceso de recubrimiento-mecano-fusin.

constituent within the bulk of the mixture is astochastic process which can be modeled by aFokker-Planck type equation which, based oncertain exchange-probability functions, describesthe temporal evolution of the distribution of fineswithin the carriers as a convective-diffusionprocess1159'1631.

In an actual process, the mximum number offines in a coating monolayer lies between twolimits. The upper limit corresponds to the case ofhexagonal-close packing, which gives a coatedsurface fraction of about 0.91 (or, equivalently,average distance between centers of contiguousfines equal to one fine diameter). The lower limitcorresponds to a completely random packedmonolayer, that is, a layer formed in the absence ofexternal forces and in this case the coated surfacefraction is approximately equal to 0.51 (averagedistance between centers of neighboring finesequal to 4/3 times their diameter)1164'1651.

The presence of fines on the surface of thecoarse particles affect the flow and packingcharacteristics of the latter. These properties arecon trolle d by two factors : a) the surface textur eof the non-coated portion of the carriers, whichchanges as a consequence of the inter-particle

friction occurring during mixing and, b) theamount and degree of dispersin of the coatingagent over the bulk material.

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6.2. Applications of ordered mixing

Ordered mixing was originally applied almostexclusively to the pharmaceutical industry, wherea finely-divided active drug ingredient is adsorbed

onto the surface of a coarse excipient to prepare asolid drug delivery system11661. The presence ofthe drug in f inely-divided non-agglomeratedform results in high dissolution rates[167'168]. On theother hand, the coarse carrier particles give themixture the required flowability and tablettingcharacteristics1166'1681.

The dry coating of powders offer attractivepossibilities for the prepa ration of comp osites w hich,however, have remained relatively unexplored untilquite recently. A peculiarity of ordered m ixtures, n otfound in random ones, is that the fine componentoccupies specific and fixed positions throughout thesystem. This has two immediate effects: first, itprevens segregation of the constituents duringhandling and compounding. Second, compaction ofordered mixtures results in a regular distribution ofthe fine com pone nt within th e matrix formed by thecoarse particles. Furthermore, the minorcomponent, even at very low concentration, canform a continu ous three-dim ensional networkimbedded in the matrix material The regularity ofthe network can be controlled by selecting an

appropriate size distribution for the core particles.The properties of the composite will depend alsoupon the degree of dispersin of the coating agenton the surface of the core particles, which in turndepends on mixing time and on the level ofmechanical energy imparted by the mixer to thepowder. Therefore, the preparation of new materialsvia powder coating permits, in principie, easycontrol of the structural characteristics of theproduct . An example is the preparat ion ofelectroconductive plastics by compaction of metal-coated plstic powders[169170]. Figure 5 shows silver-coated polymethyl methacrylate (PMMA) particlesprepared with the Angmill Mechanofusion System;hot-pressing of the coated particles yields a structure(Fig. 6) in which the silver particles form a 3-Dnetwork imbedded in the plstic matrix. Theconductivity of this structure follows the laws oftypical percolating systems: only above a certaincritical concentration of metal, continuous metalpaths spanning the composite are formed and thematerial becomes conductor. It is worthwile to pointout that this compounding method via dry coating

permits preparation of electroconductive plasticswith metal loadings much lower than in the case of

324

Figure 5. Silver-coated PMMA.

Figuro 5. PMMA recubierto con partculas de plata.

conventional compounding via powder mixing. Themethod has been put into practice in an industrialscale, for manufacturing high-efficiency contactmaterials to be used in the electrical industry11711.

Dry powder coating has be en also applied to the

dispersin of ceramic powders into superplastical loys . A no the r interest ing applica t ion ofpowder coat ing is the preparat ion of porousstructures wi th possible use in, for instan ce, thecatalyst industry. An example is shown in figure 7.First, NaCl crystals are coated with plstic fineparticles (PM M A) . The coated powder is then hot-pressed (yielding a structure similar to that shownin Fig. 6), and placed in stirred water; after the salt

Figure 6 . 3-D silver network imbedded in PMMA matriz.Figura 6. Red tridimensional de plata en la matriz de PMM A.

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M. ALONSO AND F.J. ALGUACIL

has dissolved, a highly porous structure (porosityabo ve 90 % ) rem ains (Fig. 7).

7. MIXINGEQUIPMENTSELECTION

The selection of the most appropriate mixer for agiven duty must take into account severalaspects : loading, the mixing operation itselfdischarge, cleaning, contamination, wear, spacerequirement, noisiness and capital, fixed andvariable operational costs. Regarding the mixingopera t ion itself the factors to be consideredinclude the degree of hom ogene ity attainablein the mixer, the time required to achieve thisdegree and the energy consumption (mixing time xpower input).

A general reliable design method is still lacking,mainly because the scale-up problem is yetunsolv ed . In order to preserve g eom etricsimilari ty between the part icles and theequipm ent, eve n if the practical problem of mak ingsmaller particles to study their mixing behavior ina laboratory scale mixer can be overeme, willfrequently result in changes in the physicalproperties of the materials. Thus, while a powdermay originally have been cohesionless, reducing itsparticle size in proportion to the reduction in mixer

size may result in it becoming cohesive. If,alternatively, the particle size is mantained but themixer size is reduced, geometric similarity does notexist and the model mixer cannot be assumed to berepre senta tive of a larger mix er . Bridgwaterconcludes that laboratory tests for mixers are ofrestricted valu and suggests that work shouldconcntrate on industrial scale studies.

Figure 7 . Porous structure resulting after salt extraction fromPMMA-coated NaCl crystals.

Figuro 7. Estructuro porosa resultante tros la extraccin de lo salde una estructuro de cristales de NaCl recubiertos con PMMA.

Rev. Metal. Madrid 35 1999)

Concerning the mixing of cohesionlesspowd ers, W illiams classifies the mixers into twogeneral broad types: segregating and non-segregatingmixers. Segregating mixers are those which relymainly on diffusive mixing (e.g. tumbling mixers),whereas non-segregating (or less segregating) arethose which rely on convection rather than onsurface effeets (e.g. mixers with mechanicalstirrers). Segregation can, however, oceur aftermixing, i.e. during discharge, transportation orstorage. Will iam s recom me nds to carry outmixing as near as possible to the part of the processwhere the mixture is to be used, with as littleintermediate handling as is practicable.

In the case of cohesive powders, as for instancein powder coating, the mechanical energy inputcharacteristics of the mixer constitute the primaryfactor affecting the rate and degree of mixingattainable. Thus, tumbling mixers are not capableof breaking the agglomerates down into theirconstituent primary particles and, henee, are notsuitable for mixing cohesive powders.

A number of s tudies comparing theperformance of different types of mixers 5'1 6'2 5 , 6 1'7 i . 1 2 81 7 6 - 1 7 9 ] a n d e c o n o m i c a s p ec t s l 8 0 ) areavailable, but most of them have been done usingcohesionless free-flowing materials and their

conclusions might not be valid for other types ofpowders.

8. CONCLUDING REMARK

The fact that there are no general rules forselecting the appropriate mixer for a given dutyclearly indicates that, in spite of being among theoldest unit operations, our present state ofknowledge of powder mixing is still very far fromsatisfactory and h at a lot of work rem ains to be

done.Acknowledgments

This work was partly supported by GrantsDGES/PB96^0920 and CAM^07/M/0053/1998.

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153

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165;

166;

167168

169;

170;

171

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175;

176;

178;

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