Segregation in binary and ternary liquid fluidized beds

Segregation in binary and ternary liquid fluidized beds

M.G. Rasul a,*, V. Rudolph b, M. Carsky c

aSchool of Advanced Technologies and Processes, Faculty of Engineering and Physical Systems, Central Queensland University,

Rockhampton, Queensland 4702, AustraliabDepartment of Chemical Engineering, University of Queensland, Brisbane, Queensland 4072, Australia

cDepartment of Chemical Engineering, University of Durban-Westville, Durban 4000, South Africa

Received 27 March 2000; received in revised form 17 September 2001; accepted 28 February 2002

Abstract

The mechanism underlying segregation in liquid fluidized beds is investigated in this paper. A binary fluidized bed system not at a stable

equilibrium condition, is modelled in the literature as forming a mixed part—corresponding to stable mixture—at the bottom of the bed and a

pure layer of excess components always floating on the mixed part. On the basis of this model; (i) comprehensive criteria for binary particles

of any type to mix/segregate, and (ii) mixing/segregation regime map in terms of size ratio and density ratio of the particles for a given

fluidizing medium, are established in this work. Therefore, knowing the properties of given particles, a second type of particles can be chosen

in order to avoid or to promote segregation according to the particular process requirements. The model is then advanced for multi-

component fluidized beds and validated against experimental results observed for ternary fluidized beds. D 2002 Elsevier Science B.V. All

rights reserved.

Keywords: Segregation; Mixing; Liquid fluidized bed; Binary and ternary particle mixtures

1. Introduction

Within all fluidized beds a dynamic equilibrium is

established between the driving force for segregation (as a

result of size, density or shape differences between the

particles) and mixing induced by bubbling, jetting, gulf

streaming, etc. In some process, e.g., fluid-bed reactors/

combustors, good mixing is desirable and segregation is

avoided; while in others, like mineral dressing for example,

segregation is the basis of the process. The degree of mixing

depends on the competition between the mixing and segre-

gation potential and it seems useful for better understanding

therefore to separate the driving forces for mixing and

segregation in given systems.

An interesting phenomenon, which is sometimes ob-

served in smoothly fluidized beds of size and density variant

binary mixtures, is named ‘layer inversion’. This provides a

convenient basis for observing and understanding segrega-

tion in binary fluidized beds. For these systems, at low

liquid velocities just above Umf, one of the components is

primarily found in a discrete layer at the bottom of the bed,

while the other is predominantly at the top. As the liquid

velocity is increased, the binary particles form a mixed part

at the bottom of the bed and a pure layer of one component

‘floating’ on the top. During increasing fluid velocity, the

particles from the pure layer move into the mixed part and

the pure layer diminishes. At the inversion velocity, the

whole system is entirely mixed, and without any segregation

driving force. This represents an equilibrium condition for

that mixture from which it will not segregate on its own

accord. If the liquid velocity is further increased, the liquid

volume and, consequently, also the particle fractions of the

two components in the mixed part changes, leaving an

excess of the second component. A new pure layer of this

excess component forms above the mixed part. If the fluid

velocity is increased further again, the bed may completely

segregate again with the second component at the top.

By adding an excess of one component or the other, the

bed may, at a constant liquid velocity, be cycled through

‘inversion’ since the particles in excess to the stable mixture

form the pure floating layer.

A given mixture which is not at the stable equilibrium

state will exhibit a driving potential to segregate into a

mixed layer (at the equilibrium concentration) and a pure

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

PII: S0032 -5910 (02 )00049 -9

* Corresponding author. Tel.: +61-7-4930-9676; fax: +61-7-4930-9382.

E-mail address: [email protected] (M.G. Rasul).

www.elsevier.com/locate/powtec

Powder Technology 126 (2002) 116–128

‘floating’ layer of one component or the other, depending on

which one is in excess to equilibrium. This layer inversion

phenomenon has been extensively reported in the literature

from quite different perspectives [1–11].

Fluidization of multi-component particle mixtures con-

sisting of both density and size different particles may result

in the stratification of different mixed or pure layers along

the axial direction of the fluidized bed [12–15], as shown in

Fig. 1 for ternary mixture of zircon, glass beads and coal

[15]. The location of these stratified layers and volumetric

concentrations corresponding to each layer (mixed or pure)

are, as will be shown, fully predictable from the knowledge

of the operating conditions (fluid velocity and bed compo-

sition) and the basic properties of the fluid and particles.

There are significant differences between the published

models for binary inversion as shown below by a compa-

rative analysis of published models for the prediction of

volume fractions of solids and liquid corresponding to

segregation potential-free mixture conditions. One model

[7] is identified as providing a good mechanistic explanation

and acceptable predictive agreement with the experimental

results available in the literature. On the basis of this model,

comprehensive criteria for mixing/segregation of binary

mixtures are established. The model is further advanced

for multi-component liquid fluidized systems and verified

on three-component fluidized systems.

2. Binary fluidized bed models

A basic requirement of a layer inversion model is that it

should provide:

(i) combinations of binary mixtures for which inver-

sion will occur,

(ii) layer inversion velocity,

(iii) volume fractions in the mixed part of the bed, and

(iv) the material which will be segregated at the top.

No single literature article has covered all these require-

ments, although there is general consensus that one group of

particles must be relatively larger and less dense, the other

smaller and more dense, if layer inversion is to occur. For

the convenience of analysis, let us consider that Particle 1

are smaller in size and have greater density (‘‘heavy’’ and

‘‘small’’), and Particle 2 are larger in size having smaller

density (‘‘light’’ and ‘‘large’’). The models which have been

compared are briefly described below.

Pruden and Epstein [4] provided the simplest approach;

by asserting, layer inversion occurs at a fluidizing velocity

where both monocomponent beds have the same bulk

density. This theory implies a single inversion velocity for

a given set of particles where two monocomponent zones

exchange positions. It fails to account for the influence of

the mixture composition, which is observed in practice to

influence the inversion velocity. Epstein et al. [16] and

Epstein and LaClair [17] introduced a serial model for

predicting mixture voidage at completely mixed condition.

In this model, the mixture expansion is simply the sum of

expansions of the separate pure components. This serial

model fails to predict mixture voidage under segregating

conditions, and is therefore also not acceptable.

A mechanistic model was proposed by Van Duijn and

Rietema [5,6] to explain layer inversion and to predict the

volume fraction of the particles. They provided an analysis

based on the momentum balance which is related to the

interaction forces between the fluid and solid, and solid and

solid, per unit volume. These interaction forces for which no

general equations are available are functions of particle

mobility which depends on particle size, viscosity and

porosity. However, the system can be solved to predict

volume fractions for segregation potential free mixtures.

While the analysis is very elegant, it fails completely to

predict the experimental observations, as will be shown

later.

Moritomi et al. [1] presented a full set of experimental

observations of layer inversion for both size and density

variant particles. They also provided a model to predict

relationships between the bulk compositions by assumingFig. 1. Possible layer arrangements for ternary mixture of zircon (Z), glass

beads (GB) and coal (C).

M.G. Rasul et al. / Powder Technology 126 (2002) 116–128 117

viscous flow and Stokes’ law [2,3]. They base their analysis

on force balances for each component particle and mono-

component voidage functions derived from a unit cell

model. To quantify the interaction force when particles of

different size and density are fluidized together, they

assumed that the presence of second component particles

does not change the flow field (i.e. the drag force), but does

change the buoyancy force. This assumption is contentious:

for example, it would break down for the case of two groups

of particles of the same size and density fluidized together.

However, the simplification allows a solution of the three

unknown parameters e, a1 and a2 at a given superficial

liquid velocity Uf, given the properties of particles and

liquid, and the monocomponent voidage functions.

Jean and Fan [8] appear to suggest the inversion to be the

result of a mixing effect. They proposed that the layer

inversion takes place at the fluid superficial velocity at

which the segregation velocity of smaller particles (defined

by Kennedy and Breton [13]) is maximum, although the

reason for this condition is not made clear. It is also not clear

why their model has to be based on the smaller particle

alone. They used the serial model proposed by Epstein et al.

[16] to evaluate mixture voidage, e. This serial model fails

to predict mixture voidage when the mixture is not at stable

equilibrium conditions (e.g., not completely mixed).

Gibilaro et al. [7] have derived a relationship linking the

volumetric concentrations (a1, a2) of the two solid species

that can coexist at any part of a fluidized bed. This is given by,

17:3

Re

� �n

þ0:336n� �1=nqfU

2f

davgða1 þ a2Þð1� a1 � a2Þ�4:8

¼ a1ðq1 � qf Þg þ a2ðq2 � qf Þg ð1Þ

where n is Richardson–Zaki [18] exponent, given as

n = 2.55–2.1{tanh (20e� 8)0.33}3, and davg represents the

average diameter of the binary components given by,

davg ¼d1d2ða1 þ a2Þd1a2 þ d2a1

ð2Þ

Eq. (1) is justified on the basis that the right-hand side

represents the pressure gradient, DP/L, required to support

the weight of the particles in a uniform zone of a binary

fluidized bed, whereas the left-hand side represents the

pressure gradient brought about by energy dissipation due

to flow. The bulk density and local voidage of the mixed

bed are given by,

qbm ¼ eqf þ a1q1 þ a2q2; e ¼ 1� a1 � a2 ð3Þ

Using this model for a given binary system and fluid

velocity Uf, the volume fraction pair a1 and a2 which

satisfies Eq. (1) may be obtained. These then provide a

Fig. 2. Bulk density evaluation for lead glass–coal binary system.

Fig. 3. Comparison of different models for segregation potential-free volume fractions for glass beads–hollow char system (Moritomi et al. [1–3]).

M.G. Rasul et al. / Powder Technology 126 (2002) 116–128118

corresponding mixture density locus (Fig. 2) using Eq. (3).

They then postulate from elementary stability considerations

that the composition of bottom zone corresponds to the

point for which the bulk density is maximum. These provide

the predicted line for segregation potential-free (i.e. equili-

brium) mixtures for the corresponding fluid velocities.

However, they did not provide experimental evidence.

Kwauk’s [9] model is qualitative rather than quantitative,

and depends on the relative bulk densities of the particles and

their expansion characteristics. This model is reasonably

predictive for systems where complete segregation occurs,

i.e. where there is no layer inversion. It does not provide a

method for predicting mixture properties for a given fluid

velocity, or inversion velocity for a given mixture.

di Felice et al. [10,11] have analysed the forces on a single

foreign particle in a fluidized suspension of other particles.

The theoretical development presented by di Felice et al.

seems acceptable for determining whether the foreign particle

will float or sink, but it is difficult to see how the analysis can

be extended to mixtures, i.e. where the ‘foreign’ particles also

make up a significant proportion of the bulk.

2.1. Comparative study of different models

A case study is used here to evaluate the different models.

The system is a binary mixture of glass beads (d = 163 Am,

q = 2450 kg/m3,Umf = 0.3 mm/s,Ut = 15.2 mm/s) and hollow

char (d = 775 Am, q = 1500 kg/m3, Umf = 4 mm/s, Ut = 50.4

mm/s) used in experiments by Moritomi et al. [1–3] and for

which a full data set is provided in the literature. Fig. 3 shows

the volume fractions at complete mixing of the binary fluid-

ized bed predicted by the different models as well as the

measured values reported byMoritomi et al. There are clearly

significant differences between the models themselves, and

for most of the models, from the experimental values.

Moritomi et al.’s model differs significantly from their

experimental measurements. This may be due to the fact that

the model has been developed considering buoyancy using

suspension density of the bed and applied at laminar flow.

This predicts much lower velocities for the beginning of the

mixing. Van Duijn and Rietema’s [5,6] model provides an

incorrect trend. The model proposed by Jean and Fan [8] is

somewhat better and not fairly tested in this comparison

because some simplifications of their model with respect to

voidage have been made. The model proposed by Gibilaro et

al. [7] shows good agreement with the experimental results

and is consequently used as the basis for model development

in this paper. This paper also provides further experimental

results and a more comprehensive analyses to establish (i)

criteria for binary particles of any type (both size and density

variant, size variant only, density variant only) to mix/

segregate or invert, and (ii) a mixing/segregation regime

map for a given fluidizing medium. Then, the model is

advanced to multi-component fluidized beds, illustrated by

three-component fluidized systems.

3. Experimental

3.1. Binary fluidized bed

A sketch of the experimental apparatus is shown in Fig.

4. The fluidized bed is 93-mm ID Perspex column with a

porous plate distributor. The properties of the two sets of

particles used in the binary experiment are summarised in

Table 1. The median size in Table 1 is the average of size

range of particles. As it was difficult to get monocomponent

particles with narrow size distribution, their effective diam-

eter (deff) were determined by fitting monocomponent bed

expansion using Eq. (1) and considering volumetric con-

centration of one component equal to zero as shown in Fig.

5 for lead glass and coal. The deff was used for model

prediction as this is more representative diameter, which

Fig. 4. Schematic diagram of the experimental set-up of the liquid fluidized

bed.

Table 1

Properties of particles used in binary experiments

Material Size range (Am) Median size,

dmed (Am)

Effective diameter,

deff (Am)

Density (kg/m3) Umf (m/s) Ut (m/s)

(1) Lead glass (LG) 125–150 137.5 127 2920 2� 10� 4 1.45� 10� 2

(2) Coal (C) 710–1000 855 755 1360 5� 10� 3 4.6� 10� 2

(1) Rutile 75–90 82.5 82.5 4200 3� 10� 4 1.15� 10� 2

(2) Sand 150–212 181 175 2450 2.5� 10� 3 1.95� 10� 2


will be shown in Section 4, compared to the median size

(dmed) for the size range of particles used in the experiments.

The liquid used was water at ambient conditions. To

determine experimentally the volume fractions of the vari-

ous components, e, a1 and a2, four methods were used:

Method 1: Sampling from the stable mixed zone

Method 2: Measurement of height of the completely

mixed bed

Method 3: Measurement of expansion of the monocom-

ponent layer above mixed part

Method 4: Pressure drop measurements.

The details of these procedures can be found in Ref. [15].

3.2. Ternary fluidized beds

The same type of apparatus as shown in Fig. 4 was used

for the ternary systems. The column used was made of

perspex with inside diameter of 50 mm and total height of

1.8 m, fitted with a porous plate distributor at the bottom.

Water was used as fluidizing liquid and its flow rate was

measured by rotameter. The pressure drop across the mixed

bed was measured by manometer. The experiments were

carried out for two ternary mixtures, namely zircon–glass

beads–coal mixture and rutile–sand–resin mixture. The

physical properties of these particles are given in Table 2.

These properties were determined in similar fashion as

mentioned in Section 3.1 for lead glass and coal. The

volume fractions of the particles and liquid were calculated,

based on the experimental measurement of bed heights and

pressure drops across the corresponding mixed layers

(Method 4).

4. Results and discussion

4.1. Binary mixtures

Fig. 6 compares the experimental values of volume

fractions as a function of superficial fluid velocity for both

the particles and fluid with the prediction of Gibilaro et al.’s

[7] model and using median diameter (dmed) as particle

diameter. In the fluidized mixture, the experimentally meas-

ured volume fraction of particle 2 (large and light) shows

excellent agreement with the predicted values corresponding

to fluid velocities, whereas the volume fractions of particle 1

(small and heavy) slightly overestimates and mixed bed

voidage slightly underestimates the measurement when

prediction is done using median diameter . These discrep-

ancies result from the discrepancy associated with the

predicted bed expansion for individual components as

shown in Fig. 5. When effective diameter is directly used

in the model, the data fit is much better as shown in Fig. 7.

Therefore, the effective diameter represents accurate particle

size for the particle size range used in the experiments and

has been used for the model prediction.

A consequence of the model developed by Gibilaro et

al. [7] is that for a given fluid velocity, the stable binary

mixture represents unique volume fractions of each of the

particle phases and the liquid phase for a given fluid

velocity. Unless the overall bed composition corresponds

exactly to this ratio there will be an excess of one of the

components, which will form a separate monocomponent

zone above the mixed zone. This is shown in Fig. 8 for a

particular mixture of 817-g lead glass and 250-g coal. At a

velocity of 9.45 mm/s, corresponding to the inversion

velocity for this particular mixture, the whole bed is mixed

Fig. 5. Monocomponent bed expansion as a function of superficial fluid

velocity.

Table 2

Properties of particles used in the experiments with ternary mixtures

Ternary mixtures Particles Size range (Am) Median size,

dmed (Am)

Effective diameter,

deff (Am)

Density (kg/m3)

Set 1 (1) zircon � 75 + 90 82.5 78.5 4600

(2) glass beads � 150 + 250 200 185 2450

(3) coal � 600 + 710 655 625 1360

Set 2 (1) rutile � 75 + 90 82.5 82.5 4200

(2) sand � 150 + 212 181 167 2450

(3) resin � 600 + 710 655 580 1300


and there is no pure layer. At lower velocities coal forms

the excess floating layer, and at higher velocities, glass

forms the excess floating layer. Fig. 9 shows measured bed

heights for the above mixture. These bed heights include

the mixed bed height and total bed (mixed bed + excess

layer) height. It is seen that the mixed bed height and total

bed height converge to a single point at inversion velocity

and thereafter diverge rapidly. All these bed heights

depend on the given proportion of the binary particles,

i.e. the inversion velocity depends not only on the physical

properties of the particles and fluid but also on the

proportion of the components loaded in the bed. This

has been experimentally verified in this study, and pre-

viously also by Moritomi et al. [1]. Similar results were

Fig. 6. Volume fractions of solids and fluid as a function of superficial fluid velocity for lead glass–coal binary system under stable equilibrium condition and

predicted using median size (dmed) as particle diameter.

Fig. 7. Volume fractions of solids and fluid as a function of superficial fluid velocity for lead glass–coal binary system under stable equilibrium condition and

predicted using effective diameter (deff) as particle diameter.


achieved for the rutile–sand mixture system. A fundamen-

tal characteristic of this model is that it predicts that the

top layer of excess component may be made up of either

of the particles for a given liquid velocity. This can be

explained and interpreted from the plots of mixture bulk

density and bulk density of monocomponent beds when

each particle type is fluidized separately as shown in Fig.

10 for rutile–sand system. Fig. 10 can be analysed as

follows:

. At liquid velocities lower than Uf2 (Fig. 2), the

maximum bulk density corresponds to a monocomponent

bed of particle 1 (i.e. a2 = 0). In this case the most stable

particle arrangement corresponds to complete segregation,

i.e. two superposed monocomponent zones with component

1 at the bottom (Fig. 10(a)).

. At fluid velocities in the range between Uf2 and Uf6

(Fig. 2), the maximum bulk density corresponds to a

mixture of both components. The densest mixture compo-

sition changes with the liquid velocity, but can be calculated

or measured. In this flow range, the binary particles form a

completely mixed bed or a mixed part at the bottom of the

bed and a pure layer of excess component floating on the

mixed part, depending on the flow conditions, as shown in

Fig. 10(b)–(d).

. At fluid velocities higher than Uf6 (Fig. 2), the bed

segregates completely again (if Uf6 is lower than Ut1), this

time with component 2 at the bottom (Fig. 10(e)). At fluid

velocity equal to or greater than Ut1, all particle 1 are

washed out of the bed.

Therefore, knowing the physical properties of the par-

ticles, the designer can consequently maximize or minimize

the segregation potential according to their particular proc-

ess requirement.

So far we have dealt with binary mixtures where

particle 1 were smaller in size but had higher density than

particle 2. In the case of binary mixtures, where particles

differ only in size (at the same density), or in density (at

the same size), there is always complete segregation in the

absence of mixing forces. Fig. 11 shows calculated mix-

ture density loci for 2- and 3-mm glass beads (q = 2450

kg/m3), as a function of the larger particle volume frac-

tions. The maximum bulk density always corresponds to a

Fig. 8. Excess component as a function of superficial velocity.

Fig. 9. Bed heights as a function of superficial velocity.

Fig. 10. Mixture bulk density and bulk density of monocomponent bed as a

function of superficial fluid velocity for rutile– sand binary mixture.

Fig. 11. Bulk density evaluation for 2- and 3-mm glass bead binary system.


monocomponent bed of 3-mm glass beads (i.e. at a2 mm

GB = 0) correctly predicting complete segregation, i.e. two

superposed monocomponent zones. The larger particle

zone has the higher bulk density and therefore settles to

the bottom. Greater size differences imply stronger segre-

gation potential.

A similar observation was made for a binary system

where both particles had the same size of 200 Am,

namely glass beads (q = 2450 kg/m3) and ilmenite

(q = 4600 kg/m3). The maximum bulk density always

corresponds to a monocomponent bed of ilmenite (Fig.

12). Experimentally, particles of ilmenite always formed a

pure bottom layer.

4.2. Criteria for binary particles to mix and invert

From the previous analysis, the following criteria for

smoothly (particulately) fluidized systems, with no external

mixing forces, can be deduced. Binary particles 1 and 2 mix

and show layer inversion when,

� d1 < d2and q1 > q2;� qb1 intersects qb2 in operating flow range;� Umf2 <Ut1 <Ut2; and� at least one particle must be fluidized.

The above points clearly indicate that for binary mix-

tures, there is a range of density ratios (q1/q2) and size ratios

(d1/d2) for which mixing will occur. The relative concen-

trations to get a completely mixed bed or a partially mixed

bed can be predicted from the method established by

Gibilaro et al. [7] following the procedure shown earlier.

For an ambient water fluidized bed, the numerically calcu-

lated boundary line for the mixing/segregation regime is

shown in Fig. 13. For a fixed value of q1/q2, for example at

q1/q2 = 2.15, the particle size ratio (d1/d2) can be varied.

Low values of d1/d2 provide figures similar to that shown

in Fig. 2 (mixing), and higher values (for example, at a

value of d1/d2 = 0.4) provide figures similar to that shown in

Fig. 11 (segregation). An empirical expression for the

boundary is,

q1=q2 ¼ 16:9e�5:443ðd1=d2Þ ð4ÞParticles of any combination, in the absence of mixing

forces, having density ratios and size ratios within the area

bounded by this curve will mix, whereas outside the curve

binary particles will always segregate. The precise mixture

concentrations will obviously depend on the fluidizing

conditions and the physical properties of the solids and

fluid. The Fig. 13 also shows some experimentally demon-

strated points.

4.3. Multi-component mixtures

4.3.1. Model

The model of Gibilaro et al. [7] was used in the previous

section for description of segregation/mixing behaviour of

binary mixtures in liquid fluidized beds. Here, the model is

extended for multi-component fluidized beds. For N-com-

ponent fluidized bed, fluid volume fraction (e), mixed bed

bulk density (qbm) and average particle diameter (davg) can

be generalised as,

e ¼ 1�XNi¼1

ai ð5Þ

qbm ¼Xni¼1

aiqi þ eqf ð6Þ

davg ¼

XNi¼1

ai

XNi¼1

aidi

� � ð7Þ

In the model development, it is assumed that the fluid-

ization behaviour depends only on hydrodynamic forces andFig. 12. Bulk density evaluation for 200-Am glass bead and ilmenite binary

system.

Fig. 13.Mixing/segregation regime map for binary water fluidized beds.


that the interaction forces between the particles are negli-

gible. Hence, the pressure gradient required to support the

weight of the particles in a mixed zone of multi-component

fluidized bed equates the pressure gradient brought about by

energy dissipation due to flow. Therefore, the Eq. (1), an

established model for fluidization, can be generalized and

formulated for a N-component system as,

XNi¼1

aiðqi � qf Þg ¼ 17:3

Re

� �n

þ0:336n� �1=nqfU

2f

davg

�XNi¼1

ai

!1�

XNi¼1

ai

!�4:8

ð8Þ

where, davg has been defined in Eq. (7).

Again, the discussion is limited to the systems without

mixing forces such as bubbles, vibrations, etc. Knowing

the fluid and particle properties, if Uf and a3 are chosen for

a ternary mixture, then a1 can be evaluated numerically

from Eq. (8) as a function of a2. Based on these, a

corresponding mixture density surface can be obtained

from Eq. (6). The fundamental base of this model solution

is to maximize the bulk density of the mixture, which in

effect minimizes the potential energy of the system. Fig. 14

shows the surface of the bulk density plot, obtained

numerically for fluid velocity of 8 mm/s, for zircon–glass

beads–coal ternary mixture used in the experiments. The

figure clearly shows that the maximum bulk density of bed

corresponds to a point where the volume fraction of one

component becomes zero, i.e. there are no stable mixtures

containing all three particle species. This appears to be

generally true, whatever the properties of the three par-

ticles. Consequently, the analysis for ternary mixtures is

much simplified, since it can be done as a series of binary

mixture calculations. Thus, the location and volume frac-

tions of the stratified mixed beds can be predicted from the

bulk density evaluation of three binary fluidized beds made

of (i) zircon (1) –glass beads (2); (ii) zircon (1) –coal (3);

and (iii) glass beads (2) –coal (3) as shown in Fig. 15. The

figure also shows the bulk densities of the monocomponent

beds for each component.

A general rule to explain this figure is that the location of

the different layers (mixed or pure) depends on the magni-

tude of the bulk density. The highest bulk density layer is

found at the bottom of the bed and the lowest bulk density

layer is found at the very top. Fig. 15 shows a bulk density–

velocity plot for the zircon–glass beads–coal system. At,

for example, 9 mm/s superficial velocity, the highest density

corresponds to a mixture of zircon–glass beads (a1 = 0.062,a2 = 0.1 by calculation), and this will form as the lowest

layer. If the zircon and glass beads are in exactly this ratio,

then the coal forms a separate layer ‘floating’ on top of this

(Fig. 1(c)).

By reducing liquid velocity to Uf = 8 mm/s, the equili-

brium mixture of zircon and glass beads, which has the

highest density, changes (a1 = 0.086 and a2 = 0.08) so that

there is now an excess of glass beads. The ‘‘mixture’’ with

the next highest bulk density is pure glass beads, which

forms a second layer, and the coal forms a third layer

floating on the top (Fig. 1(b)).

By further reducing fluid velocity to Uf = 6 mm/s, three

separate pure layers are formed, where the zircon layer

forms a bottom layer, glass beads form a middle layer and

coal forms a top layer (Fig. 1(a)).

On the other hand, by increasing liquid velocity up to

Uf = 10 mm/s, the bed again forms a mixed layer of zircon

and glass beads at the bottom. Now, zircon is in excess, so a

mixed layer of zircon and coal forms in the middle, and a

pure layer of excess coal at the top (Fig. 1(d)).

Fig. 14. Bulk density evaluation for zircon–glass beads–coal ternary

mixture.

Fig. 15. Mixtures bulk density and bulk density of monocomponent

bed as a function of superficial velocity for zircon–glass beads–coal

ternary mixture.


At Uf = 12 mm/s, the bottom and middle layers are again

zircon–glass beads and zircon–coal, respectively, (though

with different concentrations of the components) but the top

layer is formed by pure layer of excess zircon (Fig. 1(e)).

AtUf = 16.9 mm/s, all the zircons are washed out from the

bed, leaving binarymixture of glass beads and coal in the bed.

At this velocity, the bed forms a mixed coal–glass beads part

at the bottom and a pure layer of coal at the top (Fig. 1(f)). By

further increasing the superficial velocity, the whole bed is

completely mixed (Fig. 1(g)). The inversion velocity is 18.3

mm/s. At higherUf, the system forms a pure top layer of glass

beads and a mixed bottom layer (Fig. 1(h)).

Ternary (multi-component) fluidized beds separate into a

set of binary or monocomponent fluidized beds, and the

volume fractions of solids and fluid corresponding to each

layer can be predicted using the same mechanistic principle

as for binary fluidized beds based on the system physical

properties and bed composition.

Fig. 16. Photograph of ternary fluidized systems.


4.3.2. Experimental

Fig. 16 shows photographs of experimentally observed

ternary bed behaviour of a mixture of 100-g zircon, 85-g

glass beads and 30-g coal.

. The photograph shown in Fig. 16(a) was taken at

Uf = 4.92 mm/s. This shows three pure layers superposed

with zircon at the bottom, glass beads in the middle and coal

at the top. This arrangement reflects what may be expected

at that velocity based on the model predictions.

. The fluid velocity was then increased to Uf = 8.16 mm/

s, where (i) a mixed layer of zircon and glass beads was

found at the bottom; (ii) another small layer of glass beads

was observed in the middle; and (iii) a pure layer of coal at

the top as shown in Fig. 16(b).

Fig. 16 (continued).


. At Uf = 8.83 mm/s, the bed was observed to have (i)

completely mixed layers of zircon and glass beads at the

bottom with a pure layer of coal at the top as shown in Fig.

16(c).

. At Uf = 10 mm/s, the bed again formed three different

layers of (i) a mixed layer of zircon and glass beads at the

bottom; (ii) another mixed layer of zircon and coal at the

middle; and (iii) a pure layer of excess coal at the top (Fig.

16(d)).

. At Uf = 11.4 mm/s, the bed formed (i) a mixed layer of

zircon and glass beads at the bottom; (ii) another mixed layer

of zircon and coal at the middle; and (iii) a pure layer of

excess zircon, as expected, at the top as shown in Fig. 16(e).

. At Uf = 16.9 mm/s, all the zircons were washed out

from the bed, leaving glass beads and coal. At about this

velocity, the bed formed a mixed part at the bottom and a

pure layer of coal at the top (Fig. 16(f)).

. The glass beads and coal were completely mixed at

Uf = 18.25 mm/s as shown in Fig. 16(g).

. With further increase in fluid velocity, the glass beads

formed a pure layer at the top with a mixed layer at the

bottom. A photograph at Uf = 21.1 mm/s is shown in Fig.

16(h).

The experimentally measured volume fractions corre-

sponding to mixed layers made up of Z–GB, Z–C and

GB–C are compared with their prediction in Fig. 17. The

experimental results show reasonable agreement with the

model prediction. These experimental observations agree

both qualitatively and quantitatively with the predicted

states, confirming that the prediction method is sound and

this model can be applied satisfactorily to ternary fluidized

systems.

Another set of experiments was done for the rutile–

sand–resin ternary mixture. Fig. 18 shows the bulk density

evaluation of three binary fluidized beds comprised of (i)

rutile (1) and sand (2); (ii) rutile (1) and resin (3); and (iii)

sand (2) and resin (3). Similar analysis as for the zircon–

glass beads–coal system was done and predicted states of

the bed were confirmed experimentally from both qualita-

tive and quantitative perspectives.

Fig. 18. Mixtures bulk density and bulk density of monocomponent bed as

a function of superficial velocity for rutile– sand– resin ternary mixture.

Fig. 17. Comparison of experimental volume fractions with the model

prediction for zircon–glass beads–coal mixture. (a) Zircon–glass

beads; (b) zircon–coal; (c) glass beads–coal.


5. Conclusions

A model by Gibilaro et al. [7] appears to satisfactorily

explain the behaviour of liquid binary fluidized beds. A

mixture of particles not at a stable equilibrium condition will

segregate to form a mixed part—corresponding to a stable

mixture—and a pure layer of excess component at the top.

The volume fractions of the particles and fluid correspond-

ing to the stable mixture can be predicted from the system

physical properties. For segregating systems, the equili-

brium volume fractions, and therefore the maximum segre-

gation possible under given conditions, can be calculated.

Experimental results show good agreement with the pre-

diction. A criterion is presented to predict whether a given

binary mixture will mix/segregate or show layer inversion.

For any given fluidizing medium, a mixing/segregation

regime map can be drawn in terms of size ratio and density

ratio of the particles.

The binary bed model has been successfully extended for

multi-component fluidized beds. Reasonable agreement

between the model prediction and experiment has been

demonstrated for three-component (ternary) fluidized sys-

tems. Ternary bed fluidized systems separate into different

mixed layers and a pure layer of excess component. Loca-

tion of the stratified mixed layers, also the volume fractions

of solids and liquid corresponding to each mixed layer, and

the pure layer can be predicted from the binary bed bulk

density evaluation. The conditions for particles to mix or

segregate can be satisfactorily predicted from the system

physical properties and bed composition for both binary and

multi-component fluidized systems. Operations could be

designed or manipulated according to the requirements to

facilitate either mixing or segregation.

Nomenclature

A Cross-sectional area of the fluidized bed, m2

davg Average particle diameter, m

deff Effective particle diameter, m

di Particle size for species i, m

g Gravitational constant ( = 9.81), m/s2

Re Reynolds number ( = dUfqf/lf), –

Uf Superficial fluid velocity, m/s

Uti Terminal velocity of species i, m/s

Greek Letters

ai Volume fractions of solids species i, –

e Voidage (liquid volume fraction), –

qi Particle density of species i, kg/m3

qf Liquid density, kg/m3

qbi Bulk density of fluidized bed composed of solid

species i, kg/m3

qbm Bulk density of mixed bed, kg/m3

lf Viscosity of liquid, Pa s

References

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Segregation in binary and ternary liquid fluidized beds