parametric study of fine particle fluidization under mechanical vibration

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Powder Technology 161

Parametric study of fine particle fluidization under mechanical vibration

Chunbao Xu 1, Jesse Zhu *

Particle Technology Research Centre, Department of Chemical and Biochemical Engineering The University of Western Ontario,

London, Ontario, Canada, N6A 5B9

Received 28 July 2004; received in revised form 20 September 2005; accepted 13 October 2005

Available online 28 November 2005

Abstract

Investigations into the effects of vibration on fluidization of fine particles (4.8–216 Am average in size) show that the fluidization quality of

fine particles can be enhanced under mechanical vibration, leading to larger bed pressure drops at low superficial gas velocities and lower values

of umf. The effectiveness of vibration on improving fluidization is strongly dependent on the properties (Geldart particle type, size-distribution and

shape) of the primary particles used and the vibration parameters (frequency, amplitude and angle) applied. The possible roles of mechanical

vibration in fine particle fluidization have been studied with respect to bed voidage, pressure drop, agglomeration, and tensile strength of particle

bed. Vibration is found to significantly reduce both the average size and the segregation of agglomerates in the bed, thus improving the fluidization

quality of cohesive particles. Also, vibration can dramatically reduce the tensile strength of the particle bed. Obviously, vibration is an effective

means to overcome the interparticle forces of fine powders in fluidization and enhance their fluidization quality.

D 2005 Elsevier B.V. All rights reserved.

Keywords: Fluidization; Fluidization quality; Fine particles; Mechanical vibration; Tensile strength; Particle agglomeration; Particle shape

1. Introduction

Fluidization is a widely used process for powder handling in

industry because of the favourable gas–solid and solid–solid

contacting efficiencies. However, fine particles smaller than

about 35 Am in size are very cohesive and are generally

believed to be not suitable for fluidization due to the strong

interparticle forces [1,2]. Such fine particles are classified as

Geldart group C (cohesive) particles [3]. Group C particles tend

to cling to each other as a consequence of the interparticle

forces and therefore form channels and agglomerates in

fluidization, which often lead to poor fluidization or even

complete de-fluidization.

Mechanical vibration has proved to be an effective means

for improving the fluidization of cohesive particles [4–8].

Vibration prevents the solids from channelling and seriously

agglomerating by supplying the bed with the energy required to

overcome the interparticle forces. With the application of the

vibration, the fluidization quality, the gas–solid contact

0032-5910/$ - see front matter D 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.powtec.2005.10.002

* Corresponding author. Tel.: +1 519 661 3807.

E-mail address: [email protected] (J. Zhu).1 Present address: Department of Chemical Engineering, Lakehead Univer-

sity, Thunder Bay, Ontario, Canada, P7B 5E1.

efficiency and the efficiency of heat and mass transfer can be

significantly improved. Using a self-developed vibro-fluidized

bed, Mori et al. [4] found that particles smaller than 24 Am that

are not fluidizable under non-vibrated conditions could be

completely fluidized under vibration (50 Hz/0.5 mm) at a gas

velocity less than 4.5 cm/s, giving appreciable bed expansion.

According to Dutta and Dullea [9], when applying vibration to

cohesive powders, improved fluidization quality was observed

by increased bed pressure drop and bed expansion and

decreased elutriation. As a result, vibro-fluidized beds are

now used in industries for handling particulate materials such

as fluidization, mixing, granulation, drying, coating, etc.

[10,11].

Despite many previous studies on the effect of mechanical

vibration, a comprehensive and parametric investigation on the

fluidization behaviour of fine particles under vibration is still

not available in the literature. Therefore, in the present work,

the effects of vibration on the fluidization of a wide range of

fine particles including Al2O3, TiO2, CaCO3 and glass beads,

4.8–216 Am in average size, are studied with respect to bed

pressure drop, bed expansion ratio, agglomeration of the fine

particles, and tensile strength of bed materials. Influencing

factors controlling the performance of vibration, including

properties of primary particles and vibration parameters, and

(2006) 135 – 144

www.e

C. Xu, J. Zhu / Powder Technology 161 (2006) 135–144136

the possible roles of vibration in fine particle fluidization are

extensively discussed.

2. Experimental

The experimental setup is illustrated in Fig. 1, consisting of

a fluidized bed column made of Plexiglas (100 mm i.d. and

1000 mm tall), a vibration generation system, a data acquisition

system with LabVIEW, and a gas flow control system.

Compressed air stripped of trace humidity through a fixed

bed of silica gel is used as the fluidizing gas, with the flow rate

controlled by a series of rotameters (Omega Engineering Inc.)

and a digital mass flow controller (Fathom Technologies). All

the flowmeters are carefully calibrated with a Wet Test Meter

(GCA/Precision Scientific). A polyethylene porous plate (15–

45 Am pore size, 30% pore volume and 6.4 mm thick) serves as

the gas distributor. It has been measured that for all types of

particles studied, the grid pressure drop is larger than 30% of

the bed pressure drop at a superficial gas velocity at 2 cm/s,

ensuring a uniformly distributed fluidizing gas in the bed.

Pressure drops across the whole bed are obtained with a

differential pressure transducer. Mechanical vibration is gener-

ated by a pair of vibrators mounted opposite one another on the

two sides of a steel-made base and driven by an ABB inverter

with a vibration frequency ( f) varying from 0 to 50 Hz. By

changing the unbalanced weights of the vibrator, various

amplitudes (A) between 0 and 3 mm (depending on the

frequency used) can be obtained. The amplitude of the

vibration base is measured using a quartz shear ICP\

accelerometer (Dalimar Instruments Inc.) with the sensitivity

of 10.09 mV/m/s2 at 100 Hz. The vibration angle or direction

can also be varied within 0–90- through adjusting the

mounting angles of the vibro-motors on the vibration base,

where the angle of 0- corresponds to horizontal vibration and

90- the vertical vibration.

Earlier work such as Chen et al. [12], has demonstrated that

the effectiveness of mechanical vibration for improving the

Inverter

Vibrator

Compressed Air

Silica GelColumn

Data AcqusitionSystem

Gas Outletto Bag Filter

PressureTransducer

Rotameter

Mass-flowController

PiezoelectricAccelerometer

Fluidized BedColumn

Fig. 1. Schematic diagram of the experimental apparatus.

fluidization state of fine particles reduces greatly as the static

bed height (L0) increases, due to the dissipation of the vibration

energy along the bed height. Consequently, many previous

studies on the vibration-assisted fine particle fluidization have

employed a small value of the static bed height [8,13]. In the

present study, the static bed height is fixed to about 10 cm for

all experiments, with L0 /D�1.0, so as to avoid the problem

related to dissipation. In addition, for every experimental run,

the particle bed is loosened with a flow of air at 2.0 cm/s for

10–20 min prior to the fluidization experiments. During the

bed-loosening process as well as the subsequent fluidization

process, the entrained fines are returned to the bed, to prevent

the lowering of the static bed height due to possible particle

carryover. The entrained fines during the experiments are

collected by a bag filter, made of densely woven cloth, placed

externally right above the free board in a cylindrical column,

and returned manually to the bed by gently tapping the column

upon the completion of the bed-loosening process or in about

every 5 min during the fluidization. Then, with decreasing gas

velocity (ug), pressure drops across the whole bed (DP) and the

bed height (L) are measured simultaneously. When vibration is

applied to the bed, the differential pressure signals measured

across the particle bed fluctuate due to the influence of the

vibration. This fluctuation strongly depends on the vibration

parameters (frequency, amplitude and direction). To reduce the

negative effects of the signal fluctuation and ensure enough

quantities of data for acquiring accurate average bed pressure

drop, the pressure signals are sampled by a data acquisition

system with LabVIEW at a frequency of 1000, much higher

than the vibration frequency applied to the particle bed, and

over long enough sampling period (60–120 s).

To assess the fluidization quality, the normalized bed

pressure drop is adopted. It is defined as the ratio of the

measured pressure drops across the whole bed (DP) to the

normal pressure caused by particle weight (msg /S), where ms

denotes the weight of solids in the bed and S the cross-sectional

area of the fluidization column. When the entire bed is

fluidized, the normalized pressure drop, DP / (msg /S), should

attain unity and remain stable thereafter even if the gas velocity

further increases, provided that the bed is completely fluidized.

Also worth mentioning is that in this study, the average bed

voidage ((b) rather than the bed expansion ratio (convention-

ally used by other researchers) is used in this study to

characterize the bed expansion in fluidization for the following

two reasons: (1) (b is calculated from the bed height data, thus

directly related to the bed expansion ratio, and (2) more

importantly, it is more advantageous to use (b instead of the

bed expansion ratio for the vibration-assisted fluidization,

because often no bed expansion but consolidation is observed

for a particle bed under vibration particularly when the

superficial gas velocity is below the minimum fluidization

velocity [8,13].

The particles used in this study are Al2O3 (4.8 Am), TiO2

(5.2 Am), CaCO3 (5.5 Am) and glass beads (6.1, 10, 39, 65 and

216 Am average in size), pertaining to Geldart groups C, A and

B particles. Table 1 gives the key physical properties of these

powders and Fig. 2 shows the size distribution. To minimize

Table 1

Particles used in the experiments

Powders dp(1) (Am) Density (kg/m3) HR

(3) ( – ) AOR(4) (-) Geldart group(5) Morphology(6)

qp qbt(4) qba

(4)

Al2O3 4.8 3850 1610 790 2.04 52.6 C Irregular

TiO2 5.2 3880 760 450 1.69 45.9 C Irregular

CaCO3 5.5 2700 1160 520 2.23 50.0 C Irregular

GB-S(2) 6.1 2500 1160 600 1.93 53.6 C Spherical

GB-S(2) 10 2500 1550 1000 1.55 49.1 C Spherical

GB-S(2) 39 2500 1510 1360 1.11 33.5 A Spherical

GB-I(2) 39 2500 1660 990 1.68 44.7 A or C Irregular

GB-S(2) 65 2500 1510 1370 1.10 30.4 A Spherical

GB-S(2) 216 2500 1620 1590 1.02 20.4 B Spherical

1The volume-weighted mean diameter by laser diffraction (Malvern Mastersizer 2000).2Soda lime silica glass beads (GB): -S (spherical shape), -I (irregular shape).3Hausner ratio=qbt /qba.4Analyzed by a Hosokawa Powder Tester.5Geldart [3].6Determined by SEM.

C. Xu, J. Zhu / Powder Technology 161 (2006) 135–144 137

the influence of moisture, all types of particles were subject to

drying overnight at 80 -C under vacuum before being loaded

into the bed for the fluidization tests. To investigate the

influence of the particle shape, two glass bead samples of same

mean diameter at 39 Am but different shapes (spherical and

irregular) are also examined in this study. The irregular shaped

glass bead sample (39 Am) is prepared by jet milling of the

glass beads (65 Am) followed by sieving to the desired size.

Fig. 3 shows the SEM photos of these two samples of glass

beads of different shapes.

3. Results and discussion

3.1. Fluidization behaviour of fine particles under mechanical

vibration

For the Group C particles of Al2O3 (4.8 Am), TiO2 (5.2 Am),

CaCO3 (5.5 Am) and glass beads (6.1 and 10 Am) under no

vibration, the whole bed usually tends to lift as a plug with a

relatively high pressure drop when the air flow is initially

turned on and increased slowly. Channelling and agglomerat-

ing take place when the gas velocity further increases, with

0.01 0.1 1 10 100 10000

20

40

60

80

100

Cu

mu

lati

ve v

olu

me

per

cen

tag

e (%

)

Particle size (µm)

Al2O3 (4.8µm) TiO2 (5.2µm) CaCO3 (5.5µm) GB-S (6.1µm) GB-S (10µm) GB-S (39µm) GB-I (39µm) GB-S (65µm) GB-S (216µm)

Fig. 2. Size distribution of the powders used.

essentially no fluidization. When mechanical vibration is

applied, however, the fluidization state of all these particles

can be significantly improved. When the gas velocity increases

to a certain value, depending on the powder type and the

vibration conditions, the plug and channel phenomena disap-

pear, the bed pressure drop increases and smooth bed

expansion starts. For fine particles of TiO2 (5.2 Am), Al2O3

(4.8 Am) and CaCO3 (5.5 Am), the entire fluidization of the bed

is still not obtainable even under vibration. In this case, the

Fig. 3. SEM photos of glass beads (39 Am) of different shapes: (a) spherical and

(b) irregular.


observation is that only a partial fluidization can be achieved at

the top-bed, while stagnant agglomerates begin to form at the

bottom of the bed. On the other hand, an entire fluidization is

attained for the glass beads (6.1 and 10 Am) under vibration,

and a minimum fluidization velocity can be determined from

the plots of bed pressure drop against superficial gas velocity,

as will be discussed later.

Fig. 4 shows plots of the normalized pressure drop and the

average bed voidage against the superficial gas velocity

during fluidization of the typical group C particles of TiO2

(5.2 Am), Al2O3 (4.8 Am) and glass beads (6.1 Am) with and

without mechanical vibration (50 Hz/0.3 mm). For these three

group C powders under no vibration, a nearly linear

relationship between the pressure drop and the superficial

gas velocity is clearly observed in the log–log coordinates,

which is typical for a fixed bed. However, by applying the

vibration (50 Hz/0.3 mm), higher pressure-drops are obtained

for all these powders, suggesting an improved gas–solid

contacting efficiency. In particular, for glass beads (6.1 Am),

the normalized bed pressure drop attains approximately unity

when the gas velocity reaches around 0.1 cm/s, as shown in

Fig. 4a, indicating a thorough fluidization. The incipient or

minimum fluidization velocity (umf) is determined by the

conventional means [14], as illustrated in Fig. 4a. It should be

0.01 0.1 1 100.01

0.1

1umf

(b)

(a)

Superficial gas velocity (cm/s)


Ave

rag

e b

ed v

oid

age

(-)

TiO2 (5.2µm) Al2O3 (4.8µm) GB-S (6.1µm)

No

rmal

ized

pre

ssu

re d

rop

(-)

0.01 0.1 1 100.60

0.65

0.70

0.75

0.80

0.85

0.90

Solid symbols: 50Hz/0.3mmOpen symbols: No vibration

Fig. 4. Effects of mechanical vibration on hydrodynamic behaviours of typical

Geldart group C particles of TiO2 (5.2 Am), Al2O3 (4.8 Am) and glass beads

(6.1 Am): (a) the normalized bed pressure drop and (b) the average bed voidage.

noted that for all the cases shown in Fig. 4a, except for the

6.1 Am glass beads under vibration, the umf obtained, should

be more appropriately called the apparent minimum fluidiza-

tion velocity, since the fluidization of an entire bed is not

achieved in the testing range of ug. Meanwhile, the vibration

causes consolidation of the particle bed at a lower gas

velocity, resulting in much smaller values of (b than those

without vibration, as shown in Fig. 4b. Similar observations

of the consolidation effect of mechanical vibration have been

reported in some previous studies [4,13,15,16]. It is shown in

Fig. 4b that for TiO2 (5.2 Am), the consolidation phenomenon

appears essentially in the whole range of the gas velocities

(0¨5 cm/s) tested. As for the other two powders, namely

Al2O3 (4.8 Am) and glass beads (6.1 Am), there exists a

transition point of superficial gas velocity at about 0.4 cm/s,

beyond which the average bed voidages under vibration will

exceed those without vibration. It should be noted that all of

these three powders belong to Geldart group C powders and

there is no clear trend in the Hausner ratio, AOR, moisture

level or particle shape that would suggest the TiO2 should be

different in bed expansion behaviors under vibrated condi-

tions from the other powders. A possible reason is that the

TiO2 powder (5.2 Am) used in this study has a much wider

size-distribution compared with those of the other two

powders, as shown in Fig. 2. This assertion may be further

proven by comparing the bed expansion behaviors between

the 39 Am smooth glass beads of a narrow size-distribution

and the 39 Am irregular-shaped glass beads of a wider size-

distribution, as will be shown later in Fig. 7.

The effects of mechanical vibration on the fluidization

behaviour of glass beads (10, 65 and 216 Am), pertaining to

typical Geldart groups C, A and B, are shown in Fig. 5. The

pressure drops across the bed are significantly increased for all

types of particles under vibration, leading to a much smaller

umf than that without vibration. The umf for 10 Am glass beads

becomes the lowest after vibration is applied, in comparison to

being the highest among the three powders without vibration.

The vibration appears to have ‘‘rectified’’ the trend to that umf

decreases with particle size. In addition, similar to that formerly

shown in Fig. 4b for Al2O3 (4.8 Am) and glass beads (6.1 Am),

there is a transition gas velocity at about 0.1 cm/s for the 10Amglass beads, beyond which the average bed voidage under

vibration exceeds that without vibration. For the other two

powders of larger sizes, i.e., glass beads (65 and 216 Am),

however, the particle beds are consolidated almost in the whole

range of gas velocities tested and the consolidation is more

remarkable at lower gas velocities, as illustrated in Fig. 5b.

3.2. Influencing factors

The factors that may influence the performance of mechan-

ical vibration on fine particle fluidization are the properties of

the primary particles (e.g., Geldart type, size-distribution and

shape) and the vibration parameters (e.g., frequency, amplitude

and angle), among which the effects of particle shape and size-

distribution on the fluidization behaviour of fine particles under

vibration are studied for the first time.

0.01 0.1 1 10

0.01

0.1

1umf

(b)

(a)



Ave

rag

e b

ed v

oid

age

(-)

GB-S (10µm)

GB-S (65µm)

GB-S (216µm)

No

rmal

ized

pre

ssu

re d

rop

(-)

0.01 0.1 1 100.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

Solid symbols: 50Hz/0.3mmOpen symbols: No vibration

Fig. 5. Effects of mechanical vibration on hydrodynamic behaviours of glass

beads (10, 65 and 216 Am): (a) the normalized bed pressure drop and (b) the

average bed voidage.


From the discussion in the previous section regarding Figs.

4 and 5, the performance of vibration varies significantly with

the types of particles. The influence of the Geldart type on fine

particle fluidization can be further revealed from Fig. 6, where

10 100

0.10

1.00

10.00

30050.05

Glass Beads (6.1-216 µm)

No vibration 50Hz/0.3mm

um

f (cm

/s)

dp (µm)

Fig. 6. umf as a function of particle size for glass beads with and without

vibration.

the results of umf for glass beads fluidized with and without

vibration (50 Hz/0.3 mm) are plotted against the mean particle

size. It is shown that the vibration leads to a decrease in umf for

all types of the glass bead samples. Such effect is particularly

remarkable for the group C particles. However, the effective-

ness of vibration decreases with the particle size. It thus

suggests that the effect of vibration on fluidization of fine

particles strongly depends on the Geldart type of particles.

In addition to Geldart type, the influence of particle shape

on the performance of vibration has also been investigated by

using two glass bead samples of the same mean diameter at 39

Am but different shapes, spherical and irregular. Fig. 7 shows

the comparison of the average bed voidage for the two samples

fluidized with and without vibration. Although these two

powders are in the same category (group A) according to

Geldart classification [3], the irregular shaped sample has a

much higher bed voidage in fluidization and shows a larger bed

expansion ratio. The difference may be ascribed to the

differences in surface properties and hence the change in

interparticle forces. In addition to the van der Waals force being

considered as the dominant interparticle force for most fine

particles [1], mechanical forces due to interlocking of re-entrant

surfaces can be significant for the particles of irregular shapes

[2]. As given in Table 1, the Hausner ratio (qbt /qba=1.68) and

the angle of repose (AOR=44.7-) for the irregular glass beadsare much higher than those for the spherical one, suggesting an

increased interparticle force due to the irregular shape. In term

of the Hausner ratio and the angle of repose, the 39 Amirregular shaped glass beads are more likely classified as the

group C powder according to the new criteria of Geldart et al.

[17] and Zhao et al. [18]. Although it is obviously not true to

conclude that a group C powder will exhibit higher bed

expansions than a group A powder, the theory of Jaraiz et al.

[5] do suggest that for group A particles, an increased

interparticle force will result in an enhancement in tensile

0.0 1.0 2.0 3.0 4.0 5.00.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

Glass Beads (39 µm)

Spherical

Irregular

Open symbols: No vibrationSolid symbols: 50Hz/0.3mm

Ave

rag

e b

ed v

oid

age

(-)


Fig. 7. Dependency of bed voidage on particle shape for glass beads (39 Am)

fluidized with and without vibration.

10 20 30 40 500.0

0.1

0.2

0.3

Glass Beads (10 µm) Glass Beads (39 µm)

um

f (cm

/s)

Frequency (Hz)

0.0

1.0

2.0

3.0

4.0

Λ (

-)

Fig. 9. Dependencies of umf and K on vibration frequency for glass beads (10

and 39 Am).

0.4 1.0


strength of the particle bed and lead to a larger bed expansion

ratio in fluidization. On the other hand, the increased

interparticle forces appear also to cause difficulty in fluidiza-

tion of the particles and result in a higher umf as shown in Fig.

8, where it is shown that vibration (50 Hz/0.3 mm) leads to a

remarkable decrease of about 50% in umf for the spherical

sample, but only a slight reduction in umf for the irregular

shaped one. In addition to different shapes, another difference

between these two types of glass beads is the size-distribution.

As revealed in Fig. 2, the smooth glass beads have a narrow

size-distribution while the irregular-shape sample has a much

wider size-distribution. Such a difference in particle size

distribution, as well as particle shape, may both contribute to

their different behaviors in bed expansion.

Other influencing factors are the vibration parameters

including frequency, amplitude and angle. Because of the

nature of the mechanical vibration system, it is difficult to vary

only the frequency while maintaining the same amplitude,

although it is obviously advantageous to keep the other

parameters such as the vibration amplitude unchanged when

examining the influence of vibration frequency. Given fixed

conditions of the vibrator, e.g., the unbalanced weight, the

amplitude of vibration is strongly dependent on the frequency

used. With a fixed unbalanced weight of the vibrator, for

instance, the vibration amplitudes are measured at 0.62, 0.34,

0.29, 0.27 and 0.30 mm at the frequency of 10, 20, 30, 40 and

50 Hz, respectively. By taking both frequency and amplitude

into account, a vibration strength (K) is adopted in this work to

characterize the intensity of mechanical vibration. K is a

dimensionless parameter defined as the ratio of acceleration of

vibration to that of gravity, i.e.,

K ¼ A 2pfð Þ2=g: ð1Þ

A same definition of the vibration strength can be found in

other works of Noda et al. [8] and Wang et al. [15].

Fig. 9 shows dependencies of umf and K on vibration

frequency ( f) for glass beads (10 and 39 Am). At lower

frequencies ( f�35 Hz), umf decreases with increasing fre-

0.0

0.2

0.4

0.6

0.8

1.0Glass Beads (39 µm)

Spherical shapeIrregular shape

No vibration50Hz/0.3mm

um

f (cm

/s)

Fig. 8. Dependency of umf on particle shape for glass beads (39 Am) fluidized

with and without vibration.

0.00.0 0.1 0.2 0.3 0.4 0.5

0.1

0.2

0.3

Frequency at 20 Hz

Glass beads (10 µm) Glass beads (39 µm)

um

f (c

m/s

)

Amplitude (mm)

0.0

0.2

0.4

0.6

0.8

Λ (

-)

Fig. 10. Dependencies of umf and K on vibration amplitude for glass beads (10

and 39 Am).

quency for both types of particles, whereas the decreasing

tendency is levelled off at about 30 Hz. At f >35 Hz, however,

umf increases slightly with frequency, suggesting that 35 Hz

could be the optimum frequency to achieve the best perfor-

mance of the vibration for the current vibrated fluidized bed

system. On the other hand, a monotonous increasing trend is

shown for the vibration strength with frequency. K increases

relatively slowly with f prior to 35 Hz while more sharply after

this point, also suggesting the frequency of 35 Hz being a

critical point in the relationship between K and f. The

experimental results on the influence of vibration amplitude

on umf are depicted in Fig. 10, where the dependencies of umf

and K on vibration amplitude are plotted at a fixed frequency

(20 Hz) for glass beads (10 and 39 Am). Clearly, for both

powders, umf decreases with both amplitude and the vibration

intensity. It should be noted that although the frequency of 35

0.1100

1000

500

0.40.05

σσσ σmsg/S

ε0=0.605

ε0=0.647

ε0=0.678

Glass Beads (6.1 µm)

Bed

pre

ssu

re d

rop

(P

a)

Superficial gas velocity (mm/s)

ε0=0.704

Fig. 12. Pressure drops across the bed for tensile strength tests for glass beads

(6.1 Am).


Hz is shown to be a critical point for umf And K in Fig. 9, the

results illustrated in Fig. 10 are for a fixed frequency at 20 Hz.

The reason why the frequency was fixed at a value other than

the critical value (35 Hz) in examining the effects of vibration

amplitude is to avoid the possible predominance of the

frequency over the amplitude.

In addition to the influences of vibration frequency and

amplitude, the effect of vibration angle (or direction) on

fluidization is also investigated with glass beads (39 Am) under

frequencies of 10–50 Hz, and the results are shown in Fig. 11.

As expected, the effect of vibration on the fluidization of the

powder changes greatly with the vibration angle. For most

frequencies tested, the best performance (leading to lowest umf

values) is observed at the vibration angle of 0- (horizontal

vibration), worse at 45- and the worst at 90- (vertical

vibration). One possible reason is that the horizontal vibration

could disrupt the channels formed or reduce the tensile strength

of the particle bed more efficiently than the vertical vibration.

In addition, the influence of frequency shown in Fig. 9 can also

be observed in Fig. 11: umf decreases with the frequency at

lower frequencies and levels off at about 35 Hz. Like in many

other mechanical vibration systems, the horizontal vibration

generated by the present vibrator-system may inevitably

contain a minor component of vertical vibration that may also

contribute to the improvement of fluidization quality. Due to

the limited length of the paper, however, this effect is not

discussed.

3.3. Tensile strength of a particle bed

Tensile strength is a fundamental property of materials. In a

particle bed, the value of tensile strength provides a terminal

point of the yield loci of failure for samples in given states of

compaction. It presents the inherent interparticle attractive

forces developed when a mass of particles is compacted. In this

10 20 30 40 500.05

0.10

0.15

0.20

0.25Glass Beads (39 µm)

90° (Vertical)

0° (Horizontal)

45°

Vabration angle:

um

f (cm

/s)

Frequency (Hz)

Fig. 11. Effect of vibration angle on umf for glass beads (39 Am) fluidized under

various frequencies.

study, the following method is applied to determine the tensile

strength of a powder bed with and without vibration. The bed

of fine particles is first consolidated to obtain a compacted bed

of different states of compaction by vibration for different

lengths of time before being subject to the tensile strength tests.

Then, the fluidizing gas is introduced to the bed at a flow rate

increased slowly with a very small step at 1–5 ml/min, with the

bed pressure drop recorded simultaneously, until the eventual

rapture of the compacted bed. The tensile strength can then be

determined from the plot of the bed pressure drop in a similar

manner to that reported by Watson et al. [19], as shown in Fig.

12 for 6.1 Am glass beads. The tensile strength is the extra

pressure drop over and above the normal pressure drop

corresponding to the particle weight, required to rupture the

bed. This ‘‘extra force’’ is needed to overcome the interparticle

force, so that it can be another measure of the interparticle

force. The tensile strength thus obtained for all the group C

particles without vibration and for TiO2 (5.2 Am) particles with

and without vibration are shown in Fig. 13. In all cases, the

tensile strength reduces dramatically in a linear relationship

with the initial bed voidage. As the initial bed voidage

increases, the bed compaction becomes less and so does the

interparticle force. This obviously leads to much lower tensile

strength. More importantly, it is shown that vibration can

dramatically lower the tensile strength of the particle bed.

3.4. Roles of vibration in the fluidization of fine particles

Despite the vital importance, a comprehensive understand-

ing on the roles of vibration in the fluidization of fine particles

has not yet been reported in the literature. Therefore, a general

discussion is presented here for the possible roles of vibration

with respect to bed voidage, pressure drop, agglomeration and

tensile strength of a particle bed.

The bed voidage (or the bed expansion ratio) and the

pressure drop across the bed are the most commonly used

parameters to characterize the fluidization behaviours of

0.5 0.6 0.7 0.8 0.90

50

100

150

200

250

300

350

TiO2 (5.2 µm) (10Hz/0.3mm)

Glass Beads (6.1 µm)

TiO2 (5.2 µm)

CaCO3 (5.5 µm)

Al2O3 (4.8 µm)

Ten

sile

str

eng

th, σ

σ (P

a)

Initial bed voidage, ε0 (-)

Fig. 13. Tensile strengths for group C particles and the effect of vibration.

Fig. 14. Agglomerate formation in fluidization of the 5.5 Am CaCO3 powder at 9

agglomerates, (b) the middle-bed agglomerates and (c) the bottom-bed agglomerate


particles. Results from the previous section (Figs. 4 and 5) have

indicated a decrease in bed voidage and an increase in bed

pressure drop at a low gas velocity for all the particles with

vibration. Obviously, consolidation effect of the vibration may

account for the decrease in bed voidage. The cause for the

increase in bed pressure drop may lie in two aspects. First, from

the well-known Ergun equation [20],

DP

L

� �drag

¼ 150 1� ebð Þ2

e3b

lglg

/sd̄p� �2 þ 1:75 1� ebð Þ

e3b

qgu2g

/sd¯p

ð2Þ

a decrease in bed voidage ((b) due to vibration may lead to an

increase in bed pressure drop. Second, it has been observed that

vibration can efficiently eliminate the formation of channels,

which also leads to more uniform fluidization, and therefore

also an increase in pressure drop.

To examine the self-agglomeration of fine particles during

fluidization, a method to sample the agglomerates out of the

.5 cm/s for 3 h with and without vibration (45 Hz/0.45 mm): (a) the top-bed

s.


bed without disruption is crucial. This is very challenging due

to the fragile structure of the agglomerates. In this work, a

novel ‘‘on-line sampling’’ method has been developed to

prevent the agglomerates from being disrupted while main-

taining their size and shape during sampling. The on-line

sampling method has been introduced in Xu et al. [16] and

described in more detail in another paper by Xu and Zhu [21].

In brief, the agglomerates are sampled in situ, i.e., without

stopping the fluidizing gas or making any other changes to the

fluidizing conditions (e.g. vibration) by using a sampling ladle

from the top of the column. To sample the agglomerates in the

upper region of the bed, the ladle is used to pick up the

agglomerates directly. To sample the agglomerates in the

middle and bottom regions, an intensity-controllable vacuum

is used to carefully remove all the particulate materials above

the sampling plane before a sample is taken. Fig. 14 shows the

microscopic images of agglomerates sampled from both the

top and the bottom of the bed of the CaCO3 particles (5.5 Am)

after being ‘‘fluidized’’ in air at 9.5 cm/s for 3 h with and

without mechanical vibration (45 Hz/0.45 mm). Under no

vibration, the maximum size of the top-bed agglomerates is

around 500 Am and the bottom-bed agglomerates around 6000

Am, suggesting a very severe segregation of agglomerate size.

With vibration, however, the maximum agglomerate sizes

from the bottom-bed are reduced to about 500 Am and become

similar to that from the top bed at around 400 Am. Obviously,

vibration can substantially reduce both the average size and

the segregation of agglomerates in the bed, both very

important for improving the fluidization quality of cohesive

particles.

Since tensile strength is a fundamental property of a particle

bed, representing the inherent interparticle attractive forces

developed when a mass of particles is compacted, the role of

vibration may also be evaluated with respect to the tensile

strength of a particle bed. As shown formerly in Fig. 13, for the

particle bed of TiO2 (5.2 Am), the tensile strength is

dramatically reduced when vibration is applied. It therefore

suggests that vibration can overcome the interparticle forces of

fine particles and improves their fluidization quality.

Therefore, the roles of mechanical vibration in fluidization

of fine particles may be summarized as follows: the consoli-

dation effect of vibration causes lower bed voidages, the

disruption of the channels and agglomeration leads to more

uniform fluidization and thus higher bed pressure drops as well

as a lower umf, and the vibration also reduces interparticle

forces and thus the tensile strength. In one words, the external

energy introduced by vibration helps the fluidization of

cohesive particles by disrupting channels, breaking the

agglomerates and reducing the tensile strength of the particle

bed.

4. Conclusions

(1) For all the powders examined, the fluidization quality

can be enhanced by mechanical vibration, leading to

higher bed pressure drops at low superficial gas

velocities and lower values of umf.

(2) The effectiveness of vibration is strongly dependent on

the particle properties (Geldart particle type, size-

distribution and shape). The effectiveness is found to

be more significant for group C powders or smaller

particles than for groups A and B powders or larger

particles. In comparison with the spherical particles, the

irregular particles exhibit higher expansion ratios or

larger bed voidages, but are more difficulty in becoming

fluidized (leading to a higher umf) probably due to the

enhanced interparticle forces.

(3) Vibration parameters also show strong influence on fine

particle fluidization. At low vibration intensities, umf

decreases as the vibration intensity increases (by increas-

ing either frequency or amplitude) but levels off when the

intensity reaches a critical value. For the first time, the

effectiveness of mechanical vibration is demonstrated to

strongly depend on the vibration angle or direction, with

the best performance being observed at 0- (horizontal

vibration) and the worst at 90- (vertical vibration).(4) Vibration can dramatically lower the tensile strength of

the particle bed, suggesting that vibration can overcome

the interparticle forces of fine powders and improve their

fluidization quality.

(5) The possible roles of mechanical vibration in fluidization

of fine particles are examined with respect to bed

voidage, pressure drop, agglomeration and tensile

strength of the particle bed. The decrease in bed voidage

at a lower gas velocity (caused by the consolidation

effect of the vibration) and the elimination of the

channels by vibration may account for the increase in

bed pressure drops. Vibration can also significantly

reduce both the average size and the segregation of

agglomerates in the bed, both vitally important for

improving the fluidization quality of cohesive particles.

Nomenclature

A Amplitude of vibration (m)

AOR Angle of repose (-)D Inner diameter of the fluidized bed column (m)

dp Mean particle size (m)

f Frequency of vibration (Hz)

g Gravity acceleration (9.81 m/s2)

L0 Static (unexpanded) bed height (m)

L Bed height (m)

ms Weight of solids in the fluidized bed (kg)

DP Pressure drop across the fluidized bed (Pa)

RH Hausner ratio (=qbt /qba) (–)

S Cross sectional area of the fluidized bed column (m2)

ug Superficial gas velocity (m/s)

umf Minimum fluidization velocity (m/s)

Greek letters

(b Average bed voidage (–)

(0 Initial average bed voidage (–)

K Vibration strength (–)

qba Aerated bulk density of the particles (kg/m3)


qbt Tapped bulk density of the particles (kg/m3)

qg Gas density (kg/m3)

qp Particle density (kg/m3)

r Tensile strength of the particulate bed (Pa)

lg Gas viscosity (kg/m/s)

/s Particle sphericity (–)

Acknowledgements

The authors are grateful to the Ontario Research and

Development Challenge Fund for supporting this study.

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