Minimum fluidization velocity and defluidization behavior of binary-solid

liquid-fluidized beds

Mohammad Asif *, Ahmed A. Ibrahim

Department of Chemical Engineering, King Saud University, P.O. Box 800, Riyadh-11421, Saudi Arabia

Received 18 March 2001; received in revised form 10 October 2001; accepted 28 February 2002

Abstract

The minimum fluidization behavior of five different binary-solid systems with a wide range of composition is experimentally investigated

by carrying out slow defluidization of an initially fluidized bed. The size ratios of these binaries vary from 4 to 10 while their buoyed-density

ratios vary from 0.22 to 0.52 such that their larger components are lighter and smaller ones are denser. The difference in the physical

properties of the two constituent solid phases of the fluidized bed is found to strongly influence the evolution of the packing structure, and

consequently the minimum fluidization velocity during the slow defluidization process. For binaries with the same size ratio, segregation

increases with the decrease in their buoyed-density ratios. On the other hand, even for binaries with large difference in their densities,

increasing the size ratio enhances the mixing. Depending upon the composition of the bed, a completely mixed defluidized structure

sometimes develops for high size-ratio binaries. Finally, a simple correlation is proposed that can better describe the present minimum

fluidization velocity data than other existing correlations.

D 2002 Elsevier Science B.V. All rights reserved.

Keywords: Binary-solid; Defluidization; Liquid fluidization; Minimum fluidization velocity

1. Introduction

The minimum fluidization velocity is an important

hydrodynamic feature of fluidized beds. It marks the tran-

sition at which the behavior of an initially packed bed of

solids changes into a fluidized bed, and is therefore a crucial

parameter in the design of reactors or other contacting

devices based on the fluidized bed technology.

Besides its potential application in the development of

multi-functional reactors involving simultaneous reaction

and adsorption [1–4], the binary-solid fluidization can help

to alter the basic hydrodynamic characteristics of a fluidized

bed by the addition of another solid phase, which has dif-

ferent physical properties than the resident solid phase of the

fluidized bed. Yang and Renken [5] have recently made one

such application in enhancing the mass transfer coefficients

by adding smaller but denser inert glass beads in a fluidized

bed containing active resin particles. In the gas–solid fluid-

ization, the use of binary-solid fluidized beds for thermo-

chemical processing of biomass is well established as can be

seen from the work of Narvaez et al. [6], Olivares et al. [7]

and Berruti et al. [8]. In this application, an inert solid

species, often sand, is used to achieve the fluidization of the

biomass and control its residence time besides improving

the heat transfer.

Our main interest here is to examine the behavior of

binary-solid liquid-fluidized beds close to the conditions of

the minimum fluidization by carrying out a slow defluidiza-

tion of an initially fluidized bed. Six different solid samples

involving five different binary-solid systems are considered

here. These binaries significantly differ in the size as well as

the density such that their size-ratios vary from 4 to 10 with

two of them possessing size ratios higher than 6.5. For the

size ratio of constituent solid phases over 6.5 is known to

show contraction of the specific volume in their packing

behavior [9,10]. To our knowledge there has not been any

specific study of the minimum fluidization behavior,

whether gas–solid or liquid–solid, in this range of size

ratios. On the other hand, two binaries with almost the same

size ratio but considerable difference in their buoyed-density

ratios are also considered in order to delineate the effect of

the density difference on their behavior. Awide range of the

bed composition is studied for each binary-solid system.

The experimental minimum fluidization velocity data, thus

obtained, are compared with existing correlations with the

0032-5910/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved.

PII: S0032 -5910 (02 )00061 -X

* Corresponding author. Fax: +966-1-467-8770.

E-mail address: masif@ksu.edu.sa (M. Asif).

www.elsevier.com/locate/powtec

Powder Technology 126 (2002) 241–254

aim of improving their predictive capability particularly for

the binaries used in the present study.

2. Experimental

The test section of the fluidized bed consisted of a

transparent perspex column of 60-mm internal diameter

and 1.5-m length. A perforated plate with high density of

2-mm holes, located on a square pitch, and 4% fractional

open area was used as the distributor. Both its top and

bottom faces were covered with a fine mesh, and were

preceded by a 0.5-m-long calming-section packed with 3-

mm glass beads.

Water was used as the fluidizing medium with its temper-

ature carefully controlled at 20 jC. The water flow rate was

controlled using one of three calibrated flowmeters of

suitable range. An immersion cooler was used to remove

the heat generated by the water pump, and maintain the

water temperature constant in the water tank.

The bed heights were read visually with the help of a

ruler along the length of the column. The pressure drop

along the bed was measured using a manometer. The

observation included measuring the flow rate, the bed height

and the pressure drop across the bed.

2.1. Properties and fluidization behavior of solid particles

Six different types of solid samples were used in the

present study. Their physical properties are tabulated in

Table 1. The glass and sand samples consisted of the

fraction between the two adjacent sieves except SN257,

which had a relatively wider size distribution with 33% of

212–250-Am range and 67% of 250–300-Am range. The

mean particle diameter for the fraction between the two

adjacent sieves was taken to be the arithmetic mean of the

sieve openings while the volume-mean diameter of the

SN257 sample was computed to be 257 Am. Both the

volume-equivalent mean diameter and the shape factor of

the larger solid species are reported in Table 1. Although the

two larger solid species were almost of the same shape and

size, their densities were significantly different, thereby

leading to a 100% difference in their minimum fluidization

velocities and 50% difference in their terminal velocities.

The fluidization behavior of particle samples was indi-

vidually examined using water at 20 jC. The bounded

particle terminal velocities, Ut, reported in Table 1 were

obtained by fitting the mono-component expansion data

with the Richardson–Zaki [11] equation. On the other hand,

the minimum fluidization velocities were evaluated from the

pressure-drop versus liquid superficial velocity profiles.

It is of common knowledge that as the ratio of the particle

diameter to the tube diameter is lowered, wall-effects increas-

ingly influence the fluidization behavior. In order to quantify

wall-effects in the present case, the unbounded terminal

velocities of both the larger solid species were computed

using the correlation of Di Felice [12]. These were found to

be 97.5 mm/s for the PET and 154.7 mm/s for the PlG, and in

neither case the difference between the bounded and

unbounded terminal velocities exceeded 3.4%.

Binary systems considered here are shown in Table 2. It

is clear that there is a significant variation in the size of

binaries; their size ratios vary from 4 to 10 with those of

two binaries greater than 6.5. Densities of their constituent

solid phases are also substantially different. These differ-

ences in their physical properties are clearly reflected in the

ratios of their minimum fluidization velocities and terminal

velocities as seen in the table. Note that Umf ratios are much

bigger than their corresponding Ut ratios. While it is

desirable to have higher Umf ratios as seen later, it is not

so for Ut ratios in view of the fact that the upper range of

operation of a liquid-fluidized binary-solid-fluidized bed

will generally be limited by the lower terminal velocity of

the two components.

It is also worthwhile to point out here that all these

binaries show the phenomenon of the layer inversion. The

Table 1

Physical properties of individual particle species and their fluidization properties using water at 20 jC

Solids species Material Shape Size range

(Am)

Mean diameter

(Am)

Particle density

(kg/m3)

Umf

(mm/s)

Ut

(mm/s)

SN257 sand nearly spherical 212–300 257 2664 0.83 31.5

SN275 sand nearly spherical 250–300 275 2664 1.0 34.4

GB463 glass spherical 425–500 463 2465 2.5 58.0

GB655 glass spherical 600–710 655 2465 4.7 82.4

PET polyethylene

terephthalate resin

cylindrical

(w = 0.85)

2790F 60 1396 11.8 94.3

Plastic PlG cylindrical

(w = 0.87)

2880F 90 1760 26.5 149.5

Table 2

Binary systems studied

Binary System Ratio of

Component 1 Component 2 Size Buoyed

density

Umf Ut

1 PET SN257 10.8 0.22 14.2 3.1

2 PET SN275 10.1 0.22 11.8 2.8

3 PET GB463 6.0 0.27 4.7 1.7

4 PET GB655 4.3 0.27 2.5 1.2

5 PlG GB655 4.4 0.52 5.1 1.9

M. Asif, A.A. Ibrahim / Powder Technology 126 (2002) 241–254242

experimental overall bulk density profiles of individual

species, as obtained from overall expansion, are shown in

Fig. 1a and b, which can be used to gauge the segregation

tendency of a particular binary system. For example, it is

obvious from Fig. 1b that the segregation tendency of

Binary 4 will be much higher than that of Binary 5. In the

event of segregation, the denser layer, needless to say, will

tend to occupy the lower region of the binary-solid bed.

Note that in the present study the denser layer at lower

liquid velocities is the one of the smaller components, which

has a lower minimum fluidization velocity than its larger

counterpart. This configuration is clearly different from the

equal-density coarse-fine combination where the coarse

solid species with higher Umf will constitute the lower layer.

It was found during experiments that the initial packing

of the bed of particles substantially affected its pressure-

drop profile. This is shown in Fig. 2 that different pressure-

drop profiles were obtained when the flow rate of the liquid

was progressively increased in an initially packed bed

depending upon the porosity of the packing structure, being

higher for the denser packing. On the other hand, hardly any

difference was seen in the pressure-drop profiles when the

bed was slowly defluidized by decreasing the flow rate in an

initially fluidized bed. Moreover, such an equilibrium

defluidized bed structure yielded reproducible pressure-drop

profiles when the bed was fluidized again. Therefore, most

experimental runs involved recording the pressure-drop

profile by slowly defluidizing an initially fluidized bed.

Fig. 1. (a) Experimental bulk density profiles of mono-component bed of solid particles of SN275, GB463 and PET. (b) Experimental bulk density profiles of

mono-component bed of solid particles of GB655, PET and PlG.

M. Asif, A.A. Ibrahim / Powder Technology 126 (2002) 241–254 243

Once the defluidized structure started to develop in the bed,

the procedure of the slow defluidization involved decreasing

the liquid velocity in small increments and allowing enough

time for the pressure drop to stabilize between successive

readings. This was important in view of long transients of

particle movement observed during this phase of partial

defluidization. Needless to say, as commonly suggested in

the literature the minimum fluidization velocity was

obtained where pressure-drop profiles of the packed and

the fluidized bed intersect each other. For example, it was

taken to be about 5.6 mm/s in Fig. 2.

3. Existing correlations for the prediction of the

minimum fluidization velocity

There are several correlations proposed in the literature

for the prediction of the minimum fluidization velocity of

fluidized beds containing two or more different solid spe-

cies. Recently, Wu and Baeyens [13] have listed some of

these. However, only three main approaches, which in a

broader sense underlie most existing correlations, are dis-

cussed in this section.

The most common approach to predict the hydrodynamic

features of fluidized beds containing two or more solid

species is to modify the correlation used for the mono-

component beds to account for the presence of two compo-

nents in the fluidized bed. For the prediction of the mini-

mum fluidization velocity, mean values of particle

properties, i.e. diameter and density, can be used directly

in the Ergun equation [14]. Owing to the difficulty involved

in characterizing the particle shape factor and the porosity of

the bed, it is, however, quite common to introduce some

modifications in the Ergun equation, whereby terms involv-

ing these quantities are replaced by constants [15]. The

generality of such modifications, however, remains doubtful

as pointed out by Lippens and Mulder [16]. Even greater

uncertainty is likely in the event of their extension to binary

systems. Another important question in this context is the

appropriate averaging procedure for the particle properties.

Different types of property averaging are found in the

literature. For example, Thonglimp et al. [17] and Noda et

al. [18] used the following,

1

qs

¼ X1

qs1

þ X2

qs2

ð1Þ

1

d̄ qs

¼ X1

d1qs1

þ X2

d2qs2

ð2Þ

where quantities with an over-bar indicate mean values, and

X1 and X2 are fractions of components 1 and 2, respectively.

As far as the question of the averaging of particle

densities is concerned, the volume-averaged mean density

appears more appropriate if deduced from the pressure-drop

consideration in a binary-solid-fluidized bed. On the other

hand, averaging of particle diameter is perhaps more flex-

ible. But, it is the surface-to-volume averaging which has

been commonly used [19–21].

In view of the above the discussion, the following

general form of the Ergun equation with mean particle

properties is used for the minimum fluidization velocity,

1:751

e3mf

� �qfUmf d̄

l

� �2

þ1501� emf

e3mf

� �qfUmf d̄

l

� �

¼ d̄3qf ðqs � qf Þgl2

� �ð3Þ

where the term on the right-hand side is the dimensionless

Galileo number (Ga). The following definitions of the mean

Fig. 2. Effect of the initial packing structure on the pressure-drop profiles in a binary-solid bed containing SN257 and PET for X1 = 0.75.

M. Asif, A.A. Ibrahim / Powder Technology 126 (2002) 241–254244

Fig. 3. (a) Effect of the liquid velocity and the bed composition on the height of the lower pure component layer of sand for Binary 2 (Fixed SN275weight = 528 g).

(b) Effect of the liquid velocity and the bed composition on the height of the lower pure component layer of glass for Binary 3 (Fixed GB463 weight = 500 g). (c)

Effect of the liquid velocity and the bed composition on the height of the lower pure component layer of glass for Binary 4 (Fixed GB655 weight = 500 g).

M. Asif, A.A. Ibrahim / Powder Technology 126 (2002) 241–254 245

diameter and the mean density are used in the above

equation,

d̄ ¼ 1

X1

w1d1þ ð1� X1Þ

w2d2

ð4Þ

qs ¼ X1qs1 þ ð1� X1Þqs2 ð5Þ

Besides the property-averaging approach mentioned

above, approaches based on the averaging of the minimum

fluidization velocities of the two components are also

proposed in the literature. Among early researchers, Otero

and Corella [22] proposed the arithmetic averaging of

minimum fluidization velocities of the constituent solid

phases. On the other hand, assuming the binary-solid-fluid-

ized bed as consisting of two completely segregated mono-

component layers, some others recommended using the

harmonic averaging of minimum fluidization velocities

[23]. The model, thus obtained, is similar to the serial model

used for the prediction of the overall bed void fraction.

Though inherently perceived to be applicable for segregated

beds, this approach has been shown to hold good even if the

components are substantially mixed [24]. Introducing a

more general expression for such averaging approaches,

we can write

Umfp ¼ X1U

pmf1 þ ð1� X1ÞUp

mf2

� �ð6Þ

where p =� 1 yields the harmonic averaging, whereas p = 1

leads to the arithmetic averaging. It will be interesting to see

whether other values of p can improve predictions and will

be considered here later.

Although based on minimum fluidization velocities of

constituent solid phases, Cheung et al. [25] proposed a

slightly different approach. Their empirical correlation is

given by,

Umf

Umf2

¼ Umf1

Umf2

� �X 21

ð7Þ

where Umf1 and Umf2 are the minimum fluidization veloc-

ities of components 1 and 2, respectively. And, X1 is the

fluid-free volumetric fraction of the larger component. The

experimental data of Formisani [20] were found to show

good agreement with the above equation.

It is worthwhile to point out here that approaches based

on Eqs. (6) and (7) benefit from the incorporation of the

mono-component Umf data as against the property-averag-

ing approach based on the Ergun equation. Moreover, the

latter needs information about the particle shape factors and

the porosity at the minimum fluidization conditions. While

the issue of the difference of the shape factors can be

addressed by using the equivalent particle diameter for

individual components in Eq. (4), the porosity of the

packing of two particle mixtures of different sizes is known

to show substantial contraction, and therefore need to be

properly accounted for in the prediction of Umf of binary

particle mixtures.

4. Results and discussion

It was observed that the difference in particle properties

significantly affected the defluidization mechanics and,

consequently, the minimum fluidization behavior of bi-

nary-solid fluidized beds. This issue is therefore first dis-

cussed in the following. The predictive capability of existing

Fig. 4. Effect of the bed composition on the minimum fluidization velocity of the binary-solid fluidized bed for Binary 1 and Binary 2.

M. Asif, A.A. Ibrahim / Powder Technology 126 (2002) 241–254246

correlations is examined next in the light of the present data

and an attempt is made to improve their predictive capability.

4.1. Defluidization mechanics of binary-solid fluidized beds

During the process of slow defluidization, the evolution

of the defluidized packing structure of each binary system

differed significantly from the other due to the difference in

their physical properties. Close to the minimum fluidization

conditions, unlike the commonly studied gas fluidization of

the coarse–fine combination of equal-density solids where

fines naturally tend to migrate towards the upper part of the

fluidized bed, the fines or smaller component, being denser

in the present case, showed a tendency of migration towards

the lower region of the bed. As a result, the lower layer

sometimes consisted only of the denser component, and

sometimes it was composed of both components. The

mixing and segregation behavior of the two components

were found to mainly depend upon their size and density

differences besides being affected by the overall composi-

tion of the bed.

In spite of the difference in their size distribution, the

behavior of Binaries 1 and 2, both with size-ratios greater

than 6.5, was similar. Depending upon the overall compo-

Fig. 5. (a) Effect of the bed composition on the minimum fluidization velocity of the binary-solid fluidized bed for binaries in the present study. (b) Effect of the

bed composition on K for binaries in the present study.

M. Asif, A.A. Ibrahim / Powder Technology 126 (2002) 241–254 247

sition of the bed, three different types of defluidization

dynamics were observed for these binaries and are discussed

in the following.

For beds with composition, X1, as high as 0.6 and so long

as the liquid velocity was close to the Umf of the PET, a pure

component layer of the sand was seen developing in the

lower zone of the bed with occasional straying of the PET

from the upper mixed layer consisting of PET and sand into

the lower layer of pure sand. As the liquid velocity was

gradually decreased, the lower interface of the upper mixed

layer started to stabilize and became more distinct. At this

stage, the sand from the lower mono-component layer

appeared moving into the upper mixed layer where both

components apparently developed uniform concentration.

The motion of the sand through the interstices of the PET

imparted movement to the PET as well. This situation

prevailed till the liquid velocity was decreased to a value

slightly higher than the Umf of the sand when the much

slower motion of the sand could still impart vibratory motion

to the PET and the whole bed appeared to be fluidized. The

notable difference in beds with different compositions is seen

in the height of the lower pure component layer, which for

the same liquid velocity decreases as the fraction X1 is

increased. This can be seen in Fig. 3a. The reason is obvious.

The bed with higher PET fraction can accommodate greater

amount of sand, and since the amount of the sand is fixed in

all these runs (weight of sand = 528 g), this leads to smaller

height of the lower layer of the sand.

As the fraction X1 was increased to 0.75, its initial

defluidization behavior was similar to what has been dis-

M. Asif, A.A. Ibrahim / Powder Technology 126 (2002) 241–254248

cussed above. This, however, changed as the liquid velocity

was decreased. As seen in Fig. 3a, no lower layer of pure sand

was observed with the progress of the defluidization process.

Marked with long transients, a defluidized zone containing

mainly the PET with the entrapped sand slowly started to

develop at the bottom of the bed. The sand appeared moving

up through the interstices imparting its momentum to the

PET. Thus, two visually distinct zones existed in the binary-

solid-fluidized bed: the lower defluidized zone marked with a

complete absence of any particle motion, and the upper

fluidized zone in which the motion of the sand caused overall

particle motion however small. With the further decrease in

the liquid velocity, the upper fluidized zone gradually

decreased in size while the lower defluidized zone increased

and ultimately engulfed the whole bed. At this stage, the sand

was seen dispersed throughout the bed with apparently higher

concentration at the top of the bed.

When the fraction X1 was increased to 0.86 for either

Binary 1 or 2, no lower layer of the pure sand is found as

depicted by Fig. 3a. Rather, a complete mixing of the two

components was observed with the sand dispersed through-

out the bed. In this case, no PET motion was visible once

Fig. 6. (a) Comparison of predictions of Eq. (6) for different values of parameter p with the experimental data for Binary 2. (b) Comparison of predictions of

Eq. (6) for different values of parameter p with the experimental data for Binary 3. (c) Comparison of predictions of Eq. (6) for different values of parameter p

with the experimental data for Binary 4. (d) Comparison of predictions of Eq. (6) for different values of parameter p with the experimental data for Binary 5.

M. Asif, A.A. Ibrahim / Powder Technology 126 (2002) 241–254 249

M. Asif, A.A. Ibrahim / Powder Technology 126 (2002) 241–254250

the liquid superficial velocity was decreased below the Umf

of the PET. The sand entrapped in the interstices of the PET

nonetheless showed localized, albeit little, movement.

The defluidization behavior of Binary 3 with the size

ratio of 6.0 is shown in Fig. 3b. The layer of the glass

owing to its higher bulk density constituted the lower layer.

Unlike the earlier case, however, no substantial reduction in

the size of the lower glass layer is noticed for small

fractions of the PET in the bed. Especially, up to X1 = 0.4,

the size reduction can be considered not too significant.

Comparing this with the earlier case of PET-sand binary

systems, it is obvious here that as the size ratio is decreased,

the capacity of the bed of the larger component to absorb its

smaller counterpart is substantially reduced. The intermix-

ing of the two components was observed mainly at the

interface with a gradually decreasing concentration of the

glass away from the interface.

Fig. 3c shows the height of the lower layer of the pure

glass in the case of Binary 4, which has the smallest of all

size-ratios considered here. Hardly any reduction in the

size of the lower layer of the glass is observed in this case.

Although the mono-component overall bulk density pro-

files of the two binaries, i.e. 3 and 4, are not much

different as seen in Fig. 1, yet Binary 4 showed much

stronger segregation behavior at all bed compositions. The

upper layer of the larger component fails to absorb its

smaller counterpart apparently due to the fact that their

size difference is not large enough to allow the passage of

the smaller component through the interstices of the larger

ones.

On the other hand, Binary 5 showed a different type of

behavior than all others discussed before. Note that Binary 5

has almost the same size ratio as Binary 4 but the buoyed-

density ratio of the former is almost twice that of the latter

Fig. 7. (a) Comparison of correlation predictions with the experimental data for Binary 1. (b) Comparison of correlation predictions with the experimental data

for Binary 2. (c) Comparison of correlation predictions with the experimental data for Binary 3. (d) Comparison of correlation predictions with the experimental

data for Binary 4. (e) Comparison of correlation predictions with the experimental data for Binary 5.

M. Asif, A.A. Ibrahim / Powder Technology 126 (2002) 241–254 251

and the others. No lower layer of a distinct solid phase is

observed in this case. As the process of the slow defluidiza-

tion was carried out from high liquid velocities, the upper

layer of GB655 slowly started receding into the lower layer

consisting mainly of the PlG. This led to an increase in the

glass concentration in the lower mixed layer. With a further

decrease in the liquid velocity, a defluidized layer was

observed to develop from the bottom of the fluidized bed

containing mostly the larger component trapping the smaller

component alongside. Above the defluidized layer, the

smaller component imparted its motion to the larger par-

ticles and kept them fluidized. As the liquid velocity was

decreased further, the lower defluidized zone slowly

increased in the size and finally covered the whole fluidized

bed. From the visual observation, it appeared that the

concentration of the smaller component was lower in the

bottom and progressively increased along the bed height.

While for smaller X1 the presence of the glass beads was

clearly visible close to the distributor, no glass was, how-

ever, seen in the distributor region and even close to it when

X1 was as high as 0.86.

4.2. Minimum fluidization velocity of binary mixtures

Fig. 4 presents the experimental data for Binaries 1 and

2, which differ only in their size distribution. Apparently, no

effect of the size distribution is seen on the minimum

fluidization velocity of the binary mixtures. It is noteworthy

here that as long as the fraction of the larger component in

the bed is less than 0.6, the minimum fluidization velocity of

the binary mixture remains unchanged. It is only when

X1 = 0.75, is there any clear difference observed. Moreover,

when the fraction of the larger component is further

increased to 0.86, the minimum fluidization velocity of

the mixture is almost the same as that of the mono-

component bed of the PET.

This dependence of the minimum fluidization velocity on

the bed composition is in fact closely related to the defluid-

ization behavior as discussed before. So long as enough

sand is available to fill all the interstices of the upper PET

layer and still available to constitute a lower pure compo-

nent layer, the behavior at the minimum fluidization is

virtually controlled by the smaller component. This situation

changes when X1 is increased. At X1 = 0.86 the amount of

the smaller component is not enough to fully occupy all the

available interstitial space of the PET layer, and are there-

fore not able to exert their influence on the bed behavior.

From the standpoint of modifying the behavior of a bed

containing the PET by the addition of another solid, it is

quite obvious from this figure that a sixfold decrease in the

minimum fluidization velocity of the larger component is

achieved by the addition of the smaller but denser compo-

nent in the present case.

Fig. 5a presents the experimental data for all the five

binaries. The overall trend is seen to be similar to what has

been seen before in Fig. 4. The Umf of the binary mixture is

significantly lower than that of the larger component. It is

nonetheless noteworthy that as the size ratio is decreased,

the steepness of the Umf profile also decreases. Now, the

minimum fluidization velocities of binary mixtures are

lower than those of the larger component even when the

fraction of the larger component in the bed is as high as 0.86

for low size-ratio binaries. At the same time even for beds

with low fractions of the larger components, the minimum

fluidization velocity is affected due to their presence. Since

using absolute values of Umf for the sake of comparison

appears little unwieldy, the following dimensionless param-

eter is defined

K ¼ Umf � Umf1

Umf2 � Umf1

� �: ð8Þ

The comparison is shown in Fig. 5b. Salient features of Fig.

5a are more pronounced here. While the effect of the size

ratio on the steepness of the K-profile is clearly evident,

increasing the buoyed-density ratio, on the other hand, tends

to mitigate the effect of the size ratio for lower X1, but

enhances the same for higher X1. Recall that the size ratios

of Binaries 4 and 5 are almost the same with the buoyed-

density ratio of the latter being almost twice that of the

former. Now, the presence of even a small amount of the

larger component can be felt on the minimum fluidization

velocity of the smaller component for Binary 5. Its behavior

at higher X1 on the other hand is quite close to Binary 3,

which has a higher size ratio.

4.3. Prediction of the minimum fluidization velocity of bi-

nary solids

As pointed out before that though there are several

correlations available in the literature to predict the mini-

mum fluidization velocity of a binary-solid mixture, three

approaches can nonetheless represent a majority of them.

The simplest of these appears to be the direct averaging of

the minimum fluidization velocities represented by Eq. (6)

with its generality enhanced by the introduction of the

parameter p. For the arithmetic averaging p is 1, whereas

p =� 1 is the harmonic averaging. Predictions of these

existing averaging rules are compared with p =� 0.5 as

shown in Fig. 6 for different binaries. It can be seen here

that the prediction of the latter is clearly superior in most

cases except for Binary 4 where its predictions are slightly

poor when compared with the harmonic averaging. A more

judicious choice of parameter p will perhaps incorporate

the size ratio and buoyed-density ratio in assigning its

value.

The predictive capability of the property averaging in

conjunction with the Ergun equation and that of Eq. (7) [25]

is also examined here in the light of the present data. Also,

presented along with in Fig. 7 are predictions of Eq. (6) with

p =� 0.5. It is obvious here that the predictions of the latter

are, in general, superior to others.

M. Asif, A.A. Ibrahim / Powder Technology 126 (2002) 241–254252

5. Conclusions

Five different binaries were considered in the present

study. While Binaries 1 and 2 differed in their size distri-

bution, no apparent difference is observed in their defluid-

ization behavior. As the size ratio is decreased, the

segregation tendencies increase for binaries with a substan-

tial difference in their densities. This is seen from the

behavior of Binaries 1 to 4. While complete mixing devel-

ops for Binaries 1 and 2, Binary 3 shows partial mixing. The

lowest size ratio binary, i.e. Binary 4, on the other hand,

exhibits complete segregation of the two components in its

equilibrium defluidized structure. This picture, however,

completely changes when the buoyed-density ratio is

increased. For almost the same size ratio binaries, i.e. 4

and 5, much enhanced mixing is observed for Binary 5,

which has twice the buoyed-density ratio of Binary 4.

A key feature of the defluidization dynamics described

above is the complete absorption of the smaller component

by the matrix of the larger component for the largest size

ratio binaries considered here. This phenomenon, though

known to exist above the size ratio of 6.5 in the packing

structures of binary particle mixtures, is clearly seen for the

size ratios of 10.1 and 10.8 in the present case. The same

effect is seen to be much weaker for the size ratio of 6.0 and

almost non-existent for the size ratio as high as 4.

It is abundantly clear that the addition of the smaller

component of higher density can considerably lower the Umf

of a bed of larger particles. The bed composition, however,

needs to be carefully controlled, if the size ratio of the two

components exceeds 6.5. For such binaries, so long as the

fraction of the larger component is kept below 0.6, the

minimum fluidization velocity of the mixed bed is virtually

controlled by the Umf of the smaller component. On the

other hand, the Umf of the mixed bed is unaffected by the

presence of smaller component if its fraction is low enough

as to be completely absorbed by the matrix of the larger

component. As the size ratio of binaries of the same buoyed-

density is decreased, even a small fraction of the smaller

component is seen affecting the Umf of the mixed bed, but

the magnitude of the reduction may not be sizeable.

From the comparison of the minimum fluidization data, it

is evident that the proposed generalized averaging procedure

can better describe the present experimental data by using

the value of parameter p =� 0.5. A more judicious choice of

the value of this parameter is expected to incorporate the

property difference of the binaries.

Symbols used

di Diameter of ith particle species [mm]

GB463 Glass beads with properties described in Table 1

GB655 Glass beads with properties described in Table 1

g Gravitational acceleration [m s� 2]

p Exponent p in Eq. (6)

PET Polyethylene terephthalate resin with properties

described in Table 1

PlG Plastic with properties described in Table 1

SN257 Sand sample with properties described in Table 1

SN275 Sand sample with properties described in Table 1

Umf Minimum fluidization velocity [mm s� 1]

Uo Liquid (superficial) velocity [mm s� 1]

Ut Particle terminal velocity [mm s� 1]

X1 Fluid-free volume fraction of particle species 1 [–]

Greek symbols

e Overall bed void fraction [–]

c Buoyed density ratio=[(qs1� qf)/(qs2� qf)] [–]

K Parameter defined in Eq. (8) [–]

l Fluid viscosity [kg m � 1 s� 1]

qf Fluid density [kg m� 3]

qs Solid density [kg m� 3]

w Shape factor or sphericity [–]

Subscript

1 Larger but lighter component

2 Smaller but denser component

mf Minimum fluidization condition

Acknowledgements

Authors gratefully acknowledge the Research Center at

the College of Engineering, King Saud University, Riyadh,

Saudi Arabia for its support of the project.

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