analysis of the effect of particle size distributions on the fluid dynamic behavior and segregation...

ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERINGAsia-Pac. J. Chem. Eng. 2007; 2: 3–11Published online 30 May 2007 in Wiley InterScience(www.interscience.wiley.com) DOI:10.1002/apj.045

Research ArticleAnalysis of the effect of particle size distributions on thefluid dynamic behavior and segregation patterns offluidized, vibrated and vibrofluidized beds

Roger Valeri Daleffe, Maria Carmo Ferreira and Jose Teixeira Freire*

Programa de Pos-Graduacao em Engenharia Quımica, PPGEQ, Universidade Federal de Sao Carlos - UFSCar, Rodovia Washington Luiz, km 235, SaoCarlos - SP, Brazil

Received 21 December 2006; Revised 23 January 2007; Accepted 19 February 2007

ABSTRACT: In this work, the effects of particle size distribution on the dynamics and segregation patterns in fluidized,vibrated and vibrofluidized beds were investigated. Four particle size distributions composed of glass spheres weretested: binary, flat, Gaussian and a reference one, all of them with a mean Sauter diameter equal to 2.18 × 10−3

m. The experimental setup consisted basically of a circular glass chamber with a height of 0.50 m and diameter of0.114 m and was operated in different modes: as a fluidized bed (� = 0), or either as vibrated or vibrofluidized beds(� = 2). The pressure drops in the fluidized and vibrofluidized beds were not significantly affected by the particle sizedistributions. Well-defined segregation patterns were observed in fluidized and vibrated beds, with the small particlesconcentrated at the top and the large particles at the bottom in the fluidized bed, and with a reversed pattern inthe vibrated bed. Segregation patterns in the vibrofluidized bed depended on the values of the vibration parameters.Segregation in vibrofluidized and vibrated beds was minimized by operating at high amplitudes of vibration. 2007Curtin University of Technology and John Wiley & Sons, Ltd.

KEYWORDS: vibrofluidized bed; vibrated bed; fluidized bed; fluidization; particle size distribution; size segregation

INTRODUCTION

The handling of particles with a wide distribution ofsizes is common in the processing of particulate mate-rials, such as in drying. Even if they are originallyuniform, the size and mass of particles may sufferchanges during the processing, resulting in particleswith nonuniform characteristics. In the drying of pastesin beds operated with inert particles, the formation ofliquid and/or solid bridges may cause particle agglomer-ation, giving rise to clusters and increasing particle sizedistribution (Chen et al ., 1991). In gas–solid fluidizedbeds, the presence of particles with different densitiesand/or sizes may cause vertical segregation (Beeck-mans et al ., 1985). Occasionally, a segregation patternmight be desirable (as in processes involving particleseparation), but in most fluidized beds it is unwantedsince it may jeopardize particles circulation, thus caus-ing unstable fluidization patterns and reducing the heatand mass transfer rates. The use of particulate materi-als with adhesive, cohesive or pasty characteristics may

*Correspondence to: Jose Teixeira Freire, Programa de Pos-Gra-duacao em Engenharia Quımica, PPGEQ, Universidade Federal deSao Carlos – UFSCar, Rodovia Washington Luiz, km 235, P.O. Box676, Sao Carlos – SP, Brazil. E-mail: [email protected]

also contribute to segregation because such character-istics make fluidization difficult. According to Wu andBaeyens (1998), a particulate bed may be considered‘well-fluidized’ in the sense that all the particles arefully supported by the fluidizing gas, but may still besegregated in the sense that the local bed compositiondoes not correspond to the overall average. In a bedconstituted by particles with identical densities and dif-ferent sizes, segregation is likely to occur when there isa significant difference in the drag force per unit weightbetween different particles. Particles subjected to largervalues of drag force per unit weight (the smaller parti-cles) tend to migrate to top of the bed, while the onessubjected to small values of drag per unit weight tendto sink to the bottom (Chiba et al ., 1980).

Gibilaro and Rowe (1974) and Naimer et al . (1982)discussed in detail the mechanisms of mixing andsegregation in fluidized beds and proposed models todescribe particle segregation in binary mixtures of solidsfluidized by a gas. Authors such as Cheung et al . (1974)Chiba et al . (1979) Noda et al . (1986) and Formisani(1991) investigated the minimum superficial velocityrequired for fluidizing mixtures of solids of differentsizes. In spite of the many researches reported in theliterature, it seems there is still no general criterion to

2007 Curtin University of Technology and John Wiley & Sons, Ltd.

4 R. V. DALEFFE, M. C. FERREIRA AND J. T. FREIRE Asia-Pacific Journal of Chemical Engineering

identify the minimum fluidization velocity of mixturesof particles (Gauthier et al ., 1999).

A vibrated bed consists of a granular bed of solidssubjected to a continuous mechanical vibration, with noair percolation. Segregation in vibrated granular bedscontaining a mixture of particulate material with dif-ferent sizes has been extensively investigated. Rosatoet al . (1987) mentioned the occurrence of the ‘BrazilNut Effect’. This is a well-known phenomenon thatappears when a mixture of particles with different sizescontained in a vessel is subjected to a vertical vibration:the larger particles tend to migrate to the top of the bed,while the smaller ones tend to sink to the bottom (Bridg-water, 1976; Williams, 1976). The physical mechanismscausing this effect are not yet fully understood andhave intrigued researchers over the last 70 years (Rosatoet al ., 1987). Among the possible mechanisms causingthis segregation pattern are suggested the ‘percolation’model and the ‘granular convection’ model. The firstmodel considers that when a mixture of multisized par-ticles is shaken, the smaller particles fill in the transientgaps that open beneath the larger particles, in a kind of‘geometrical rearrangement’ which dislocates the largeparticles to the top of the container. Although the grav-itational force acts on every particle, only the smallerones can fill in the gaps (Williams, 1976; Rosato et al .,1987; Jullien et al ., 1992). In the convection model, itis assumed that particles in a shaking recipient undergoa convective flow, rising at the middle and falling atthe sides. Segregation occurs because the large parti-cles, once swept up to the top of the recipient, cannotbe entrained into the downflow through the very nar-row outer region of downward motion, staying at the topof the bed (Knight et al ., 1993; Shinbrot and Muzzio,1998). Other possible mechanisms are still under inves-tigation, among them are reported the condensation,granular diffusion, controlled reorganization, entropy (ata nongravity environment) and inertial (Hong et al .,2001). Segregation in vibrated beds is affected not onlyby the size of particles but also by other particle prop-erties and by characteristics of the granular bed and ofthe equipment as well. They include the particle den-sity and shape, the angle of repose, granular temperaturegradients, vibration parameters, presence of electrostaticcharges, etc. (Akiyama and Nishiyama, 1994; Huertaand Suarez, 2004).

Vibrofluidized beds combine air percolation andmechanical vibration simultaneously, being consideredan appealing alternative for drying of adhesive, cohesiveor pasty materials. The vibration supplies an additionalenergy to promote vertical dislocation of particles andalso contributes to reduce particle agglomeration bybreaking up liquid and/or solid bridges. To quantify theeffects of vibration on the dynamic behavior of parti-cles, the dimensionless vibration number (�) is usually

adopted, defined as:

� = A(2π f )2

g(1)

where A and f are respectively the amplitude and thefrequency of vibration and g is the acceleration due togravity.

Daleffe et al . (2005) carried out a number of experi-mental investigations on the fluid dynamics in vibroflu-idized beds and reported very different dynamic patternswith identical values of �, since distinct values of A andf might be combined to yield identical values of �. Forthis reason, they have wondered about the validity ofusing only the dimensionless vibration number to quan-tify the vibration effects on fluidized beds. They sug-gested that, besides the dimensionless vibration number,the amplitude or the frequency of vibration should beinformed as well, in order to fully characterize a givenoperational condition.

In the literature, there is plenty of work reporting thefluid dynamic behavior in gas–solid vibrofluidized bedswith particles of uniform size (Bratu and Jinescu, 1971;Gupta and Mujumdar, 1980; Daleffe and Freire, 2004).However, few have focused on the effects of particlesize distribution on the fluid dynamic behavior and onthe occurrence of segregation. Concerning segregationin vibrated beds, an inspection of the literature showscontradictory results. There are results even consideredquestionable by a few authors, probably because thedimensionless vibration number (�) is often used asthe only quantification of the vibration conditions,leading to misinterpretations of analysis, by the reasonspreviously discussed by Daleffe et al . (2005).

From this brief review it is verified that there isconsiderable amount of work discussing the effects ofparticle size distribution on fluid dynamics and segre-gation patterns in fluidized beds, but in vibrofluidizedbeds, research is still incipient. In vibrated beds, on theother hand, there are still gaps on the available theo-ries adopted to describe size segregation. The purposeof the present work is to experimentally investigate theeffects of particle size distribution on fluid dynamicalbehavior of fluidized, vibrated and vibrofluidized beds,and to evaluate the segregation patterns in these bedsfor different conditions.

EXPERIMENTAL

Experimental setup and materials

The experimental apparatus is shown in Fig. 1.The vibrofluidized bed is composed of a circular

glass chamber with a height of 0.50 m, diameter of0.114 m and wall thickness of 0.003 m. Air is pro-vided by a blower and the airflow rate is obtained using

2007 Curtin University of Technology and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. 2007; 2: 3–11DOI: 10.1002/apj

Asia-Pacific Journal of Chemical Engineering PARTICLE SIZE DISTRIBUTION AND BEHAVIOR OF FLUIDIZED BEDS 5

Figure 1. Schematic diagram of the experimental setup.

a previously calibrated orifice plate. Both the orificeplate and the pressure tap located at the bottom ofthe bed are connected to pressure transducers linkedto a data collecting system. The data acquisition systemwas developed in the graphic language G, using thesoftware Labview 7 Express, with an acquisition boardA/D PCI-6024E from National Instruments on an AMDAthlon XP 1800+ computer. Air temperature was keptconstant using an electrical resistance heater connectedto a controller. A water cooler is used as an auxiliaryequipment to control temperature. An eccentric mech-anism is used to adjust the amplitude of vibration, anda mechanical controller located at the axle of the elec-tric motor allows for the adjustment of the frequency ofvibration. The acceleration, velocity and amplitude ofvibration are obtained by a Bruel & Kjær 4371 piezo-electric accelerometer linked to a Bruel & Kjær 2525signal conditioner. The frequency of vibration is mea-sured with an optical tachometer, Minipa MDT-2244A.For image and video acquisition, a Sony DSC-V1 digitalcamera supported by a tripod is used, with an effectiveresolution of 5 mega pixels and Carl Zeiss Vario-Sonnarlenses. At each condition, the bed operation was filmedfor 10 s at a recording rate of 30 frames per second. Thevideos were used in the analysis of particle segregationpatterns and also to estimate the mean voidages on thebed. From the analysis of the complete sequence of therecorded frames, an average bed height was obtained atevery condition, and the value was then used to estimatethe mean voidage. For sampling of particles from thebed, an Electrolux A10 vacuum cleaner is used, prop-erly modified to have its suction power reduced (Jose

et al ., 1994). This was done by replacing the originalinternal filter by one with a smaller flow area, in orderto increase the pressure losses and reduce the suctionvelocities. The original collecting tip was also replacedby one with a reduced transverse section area, in orderto minimize disturbances in the granular bed during thesamplings.

‘Ballotini’ glass spheres with a density of 2500(±5) kg m−3, determined by picnometry, and meandiameters of 1.29 × 10−3, 2.18 × 10−3 and 3.67 × 10−3

(±0.05 × 10−3) m were used in the experiments. Thetotal mass of the inerts used in every essay was of 1.6(±0.1) ×10−3 kg, corresponding to a static bed heightof 0.10 (±0.05) ×10−2 m.

Experimental procedure

The bed was operated in three modes: vibrofluidized(with simultaneous vibration and aeration), vibrated(with vibration only) and fluidized (with aeration only).All the experiments were replicated in order to checkthe reliability of data. To minimize the presence ofelectrostatic charges, an earthed copper wire was rolledup around the chamber wall, with the rings locatedat an equally spaced distance of 1.0 × 10−2 (±0.05 ×10−2) m from each other. The tests were carried out ata constant temperature of 40 (±0.5) ◦C.

Four particle size distributions were tested, as shownin Table 1. The reference sample was composed ofmonosized particles, with ds = 2.18 × 10−3 m. Fromthe definition of Sauter mean particle diameter given



Table 1. Composition of particle size distributions,with ds = 2.18 × 10−3 m.

Distribution % Xi dp(10−3 m) Sieves (10−3 m)

Reference 100.00 2.18 2.00–2.36Binary 37.10 1.29 1.18–1.40

62.90 3.67 3.35–4.00Flat 24.89 1.29 1.18–1.40

32.80 2.18 2.00–2.3642.31 3.67 3.35–4.00

Gaussian 18.00 1.29 1.18–1.4057.00 2.18 2.00–2.3625.00 3.67 3.35–4.00

by

ds = 1∑

i

Xi

dpi

(2)

where Xi is the particle mass fraction and dpi is themean sieved diameter, the remaining samplings wereobtained by combining particles of three different dpi atdifferent proportions to yield the same ds adopted in thereference sampling.

Some preliminary tests allowed the establishment ofthe intervals of the vibration parameters. To obtain agiven value of the dimensionless vibration number (�),different combinations of amplitude (A) and frequencyof vibration (f ) were chosen. The values of � weresettled on 0 (in the tests with fluidized beds) and2 (±5%), with amplitudes of 0, 0.003 and 0.009(±0.005 × 10−1) m and frequencies of vibration equalto 0, 7.43 and 12.87 (±0.5%) Hz.

Fluid dynamical experiments were carried out byadjusting the parameters for a given experiment, andthen keeping the bed fluidized until the stabilizationof operational conditions. The characteristic curvesof either the fluidized or vibrofluidized beds werethen obtained. Pressure drops were measured as afunction of the superficial air velocity (Us), accordingto the classical methodology described by Bratu andJinescu (1971). For every particle distribution andset of vibration parameters, the pressure drops weremeasured as the superficial air velocity was reduced.Simultaneously, the standard deviations of pressuredrops were recorded by the data acquisition system. Thedata were collected at a frequency of 167 Hz for 3 s.

The complete fluidization velocity (Ufc), defined asthe minimum air velocity at which all the particles aresuspended (Tannous et al ., 1998; Gauthier et al ., 1999),was determined for each condition. To ensure that allthe particles were suspended during operation, the airfluidization velocity was kept at a value 10% above Ufcin all the experiments.

To quantify the segregation, particles were sam-pled from the bed by inserting the modified probe tip

vertically at three different vertical positions, locatedat the distances 0, 0.05 and 0.10 (±0.05 × 10−2) mfrom the plate distributor. The experiments were per-formed as follows: a mixture of particles was prepared,and after adjusting the vibration parameters, the parti-cles were fed into the bed. The bed was then operatedfor 6 min at a specified fluidization velocity and wasfilmed and photographed during the operation. The par-ticle bed heights were determined from visual inspec-tion of the videos, and the mean voidage at everycondition was then obtained. The air supply and thevibration were cut off and solid samplings were per-formed in the static beds, at the previously specifiedheights. The modified sampling system allowed uniformand continuous sampling of a representative amount ofparticles (0.16 ± 0.1 × 10−3 kg), with minimum distur-bances in the granular bed of particles. At every height,the samplings were carried out by scanning the wholetransversal section area. The samples were then siftedto determine their size distributions.

RESULTS AND DISCUSSION

Figure 2 shows the characteristic curves and standardpressure drop deviations for the fluidized beds with uni-form sized particles (a) and with different particle sizedistributions (b). The data show the typical behaviorexpected in fluidization as the size of the inert parti-cles is increased, i.e. the minimum fluidization velocityincreases and the pressure drop at the fixed bed regiondecreases. Such a behavior occurs because the largerand heavier particles require greater airflow rates to befluidized, since the drag and gravitational forces actingon the bed of particles must be balanced. In the fixedbed region, the larger particles provide more permeablebeds, favoring the airflow through the bed and reduc-ing the pressure drop. Figure 2(b) shows that particlesize distribution has little effect on the bed pressuredrop. Only the curve of binary distribution is locatedslightly under the others, particularly at the transitionregion between the fixed and fluidized regimes. Thestandard deviations of pressure drops, however, clearlyshow a delay in the onset of fluidization for this sizedistribution.

It can be seen in Fig. 3(a) and (b) that a lowamplitude (0.003 m) and a high frequency (12.87 Hz)of vibration did not cause a significant change in thedynamic behavior of inert particles, as compared tothose presented in Fig. 2(a) and (b). In Fig. 3(b), onecan observe that the complete fluidization velocity issmaller for the flat and Gaussian distributions.

When the vibrofluidized bed was operated at a highamplitude (0.009 m) and a low frequency of vibration(7.43 Hz), the dynamics of particles were more affectedby vibration parameters as compared to the previouscase, as can be noted in Fig. 4(a) and (b). The increase



Figure 2. Pressure drop in the bed and its standarddeviations as a function of superficial air velocity at thefluidized bed: (a) uniform sizes; (b) particle size distributions.

Figure 3. Pressure drop in the bed and its standarddeviations as a function of superficial air velocity: � = 2; A =0.003 m; f = 12.87 Hz: (a) uniform sizes; (b) particle sizedistributions.

in the amplitude of vibration, accompanied by a drop inthe frequency, resulted in more expanded beds, favor-ing air percolation and reducing the pressure drops. Thetransition between the fixed and fluidized regimes wassoftened as well, and complete fluidization velocitiesare not so clearly defined as in the curves shown inFig. 3. Since air percolation becomes easier, the onsetof fluidization is delayed and, compared to the previ-ous case, the complete fluidization velocities are raised.An inspection of Figs 3 and 4 also shows that withan identical value of the dimensionless vibration num-ber (� = 2) very distinct fluid dynamic patterns wereobserved, corroborating that this parameter alone doesnot characterize the vibration conditions, as previouslynoted by Daleffe et al . (2005)

Figure 5(a) presents the particle mass fraction forthe binary distribution as a function of dp for afluidized bed, and Fig. 5(b) shows a photo of thebed obtained during the operation. Segregation appearsclearly in Fig. 5(a). In the three measurement positions,the compositions of the mixture differ from the originaland a vertical concentration gradient appears over thewhole bed height. Analysis of Fig. 5(a) and (b) indicatethat most of the small particles were dragged by the airand migrated to the top of the bed, while a significantfraction of the large particles stayed preferentiallyat the bottom, a behavior that agrees with reportsfrom the literature (Gibilaro and Rowe, 1974; Wu and

Figure 4. Pressure drop in the bed and its standarddeviations as a function of superficial air velocity: � =2; A = 0.009 m; f = 7.43 Hz: (a) uniform sizes; (b) particlesize distributions.



Baeyens, 1998). At the middle height of the bed, thereis approximately 50% of particles from each size ofa uniform composition, but very different from theoriginal one. The presence of small and large particlesat H = 0.05 m is visualized in Fig. 5(b), as well as thepresence of layers of large particles at the bottom andsmall particles at the top.

The mass fraction as a function of particle diameterfor binary distribution in a vibrofluidized bed at lowamplitude of vibration is depicted in Fig. 6(a), and aphoto of the bed under operation is shown in Fig. 6(b).At this condition, particle mixing improved as compared

to the fluidized bed, with a weak concentration gradientover the bed height. However, a segregation patternis still observed, with the small particles tending tomigrate to the top of the bed and the large particlestending to sink to the bottom. At the middle height,the composition of the mixture is close to that ofthe original distribution, but considering the wholebed height, the tendency of segregation is clear. Amean voidage of approximately 0.52 was observedat this condition, which is slightly smaller than thevalue obtained in the fluidized bed (0.54), indicatinga tendency to form denser beds. The mean voidages

Figure 5. Fluidized bed: � = 0; Us = 1.57 m s−1; ε = 0.54: (a) Xi as a function of dp;(b) photo of the bed under operation.

Figure 6. Vibrofluidized bed: � = 2; A = 0.003 m; f = 12.87 Hz; Us = 1.33 m s−1;ε = 0.52: (a) Xi as a function of dp; (b) photo of the bed under operation.



were obtained using the complete video sequences,but they can be hardly considered as accurate values,in spite of being useful for a comparison amongthe different conditions. Since it is not possible toshow the whole video sequences here, Figs 5(b) and6(b) are examples (photos) of these conditions. Fora vibrofluidized bed operated with high amplitude ofvibration and low frequency, Fig. 7(a) shows that theoriginal composition is maintained for the whole bed

height, with no segregation tendency. A comparisonbetween Figs 6(b) and 7(b) shows a more expandedbed at a higher amplitude of vibration (estimated ε =0.61), which probably helps to promote the mixing ofparticles. It is worth noting that both behaviors wereobtained for a value of � = 2.

The results shown in Fig. 8 were obtained in avibrated bed (without aeration), with vibration condi-tions identical to those of Fig. 6. Figure 8(a) indicates

Figure 7. Vibrofluidized bed: � = 2; A = 0.009 m; f = 7.43 Hz; Us = 1.50 m s−1;ε = 0.61: (a) Xi as a function of dp; (b) photo of the bed under operation.

Figure 8. Vibrated bed: � = 2; A = 0.003 m; f = 12.87 Hz; Us = 0 m s−1; ε = 0.40: (a) Xias a function of dp; (b) photo of the bed under operation.



a tendency of small particles to migrate to the bottom ofthe bed, with particle concentrations close to the origi-nal ones at the top. Analysis of Fig. 8(a) might suggestthat at the middle and top bed heights, the particlesare perfectly mixed, but such a behavior was not reallyobserved, as can be noted in Fig. 8(b), in which a segre-gating pattern with small particles over an intermediarylayer of large ones is detected in the expanded bed. Thebed vibration promotes collisions between small andlarge particles, and the smaller ones were thrown upby vibration. The large particles that tend to migrate tothe top formed a physical barrier which prevented per-colation of all the small particles to the bottom. Theseparticles did not penetrate the mixture, forming a thinlayer of small particles over the large ones. In the parti-cle sampling, the air supply and the vibration were cutoff, and the small particles deposited as a layer overthe top of the bed were suctioned with the large ones,leading to nonrepresentative measurements of particleconcentrations at this position.

Figure 9 shows the results obtained in a vibrated bed,at identical vibration conditions of Fig. 7. Raising theamplitude of vibration improved the particle mixing ascompared to the results showed in Fig. 8, at a loweramplitude. A segregation pattern is still detected, withthe larger particles tending to migrate to the top of thebed. A comparison of results from Figs 8 and 9 againshows very distinct fluid dynamic patterns obtained withsame value of �. In general, a large amplitude (andlow frequency) produces an expanded bed, while a lowamplitude (and high frequency) produces a compact bed(Daleffe et al ., 2005). Bed voidage changed from 0.40to 0.50. The different bed densities can be observed inthe photos from Figs 8(b) and 9(b). The differences in

the local structures, voidages and circulation patternsdefine the distinct behaviors observed experimentally.

The analysis of segregation patterns obtained in thedifferent beds indicates that in fluidized beds the dragforces acting on the particles predominate, with the aircarrying the small particles to the top of the bed. Invibrated beds, on the other hand, the forces related tovibration dominate the segregation, with the large par-ticles being moved to the top. In vibrofluidized beds,these forces may be compromised in order to improvethe mixing and minimize segregation. By adequatelychoosing the vibration parameters and aeration rates,different degrees of mixing can be achieved. In a prac-tical application, additional factors may have to beconsidered. In the drying of pastes, for instance, thepresence of solid or liquid bridges may affect the beddynamics and even change the particle size distribu-tions, modifying the segregation patterns. Differencesin the density or shape of particles may also producedistinct segregation patterns. The point, however, is thatthe versatile characteristics of vibrofluidized beds allowtheir operation at very different dynamic behaviors byonly changing the operating parameters, which is anappealing feature to be explored in industrial applica-tions involving segregation.

The results obtained for the flat and Gaussian dis-tributions were qualitatively similar to those for binarydistribution, and for sake of conciseness they will notbe presented here.

CONCLUSIONS

In beds of particles with uniform size, the completefluidization velocity increases as the particle diameter

Figure 9. Vibrated bed: � = 2; A = 0.009 m; f = 7.43 Hz; Us = 0 m s−1; ε = 0.50: (a) Xias a function of dp; (b) photo of the bed under operation.



is raised and the pressure drop is reduced. Such areduction occurs until the onset of fluidization. Oncethe particles are fluidized, the pressure drop in thebed is not affected by increasing in particle diameter.For the conditions tested, the fluid dynamic behavior,investigated through the measurements of pressure dropand pressure deviations as a function of air velocity, wasnot significantly affected by changing the particle sizedistributions.

In fluidized beds with different particle size distri-butions, clear segregation patterns were observed, withhigh concentration of small particles at the top and oflarge particles at the bottom of the beds. In vibratedbeds, the segregation patterns showed the oppositebehavior, with the large particles concentrated at thetop and the small ones at the bottom. The segregationpatterns in vibrofluidized beds changed depending onthe operational conditions. At a low amplitude of vibra-tion, the pattern was similar to that of the fluidized bed,but a better degree of mixing was reached, since thegradient concentration over the bed height was soft-ened in the presence of vibration. Operation at highamplitudes of vibration seems to be the best configura-tion to minimize segregation, since the particles werecompletely mixed along the bed height for all the par-ticle distributions tested. The results also show that theuse of a same value of �, with different combinationsof amplitude and frequency of vibration, produces verydifferent behavior concerning fluid dynamics. This con-firms that the dimensionless vibration number shouldnot be adopted as a universal parameter to characterizethe dynamics of vibrofluidized beds.

Acknowledgements

The authors thank the Brazilian funding agencies CNPq,PRONEX and FAPESP for their financial support.

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