Segregation phenomena in a shaker

ELSEVIER Powder Technology 93 (1997) 83-88

Segregation phenomena in a shaker

S.S. Hsiau *, H.Y. Yu Department of Mechanical Engineering, National Central Universi~. , Chung-Li 32054, Taiwan

Received 5 June 1996; revised 29 January 1997; accepted 24 April 1997

Abstract

The segregation phenomena of different binary mixtures were studied experimentally in a vertical shaker. The larger particles tend to move upwards in the shaker in a certain range of vibrational accelerations. The segregation effect was more significant for the mixture with a larger size difference. The segregation coefficient was measured and found to increase with vibrational acceleration until reaching a maximum and then to decrease with acceleration. The bed expansion height was also measured. It was found that the greatest segregation effect occurred when the bed transformed from a dense state to a loose state.

Keywords: Segregation; Shakers; Expansion; Granular material; Vibrational acceleration

1. Introduction

A granular material is an assembly of a large number of discrete solid particles under various states of consolidation, either under static conditions or in some state of motion. The storage and transport of ore, sand or food products are some applications. In this decade, there has been a great deal of fundamental research into granular flows [ 1-3]. The related studies can be found in Campbell's review paper [41. Mixing and heat transfer problems have also received attention recently [5-8].

Shakers are important industrial devices to mix and dry granular materials [9-11 ]. They are also used to sort particulate materials according to particle size in the pharmaceu- tical, powder metallurgy, and food industries. Jaeger and Nagel [ 12 ] presented a good review of the related studies. Recently the particle mixing phenomenon in a vibrated granular bed was studied experimentally by Hunt et ai. [ 13]. In the current study, the segregation aspects of vibratory particulate systems are investigated experimentally.

Segregation may result from differences in particle size, particle density, properties and angle of repose of the materials [ 14,15], and the granular temperature gradient [ 16]. Savage and Lun [ 17 ] proposed and analyzed two segregation mechanisms due to size differences: the 'random fluctuating sieve' mechanism and the 'squeeze expulsion' mechanism. Segregation is important and is broadly discussed in industrial fields involving powders and granular maLerials [ 15]. Some

* Corresponding author.

0032-5910/97/$17.00 © 1997 Elsevier Science S.A. All rights reserved P!! S0032-59 ! 0 (97) 03263-4

studies about this complicated phenomenon have been reviewed by Williams [ 14] and Savage [18]. Segregation caused by granular thermal diffusion was also studied theoretically by Hsiau and Hunt [ 16].

Rosato et al. [19-21] used a Monte Carlo algorithm to simulate and explain that segregation phenomena occurred in a shaker. Jullien and Meakin [22] developed a three- dimensional model and concluded that no segregation occurred when the ratio of particle diameters of the binary mixture was less than a critical value Or. Knight et al. [23]

linear bearing

[ !

D.C.motor

i

L_.

shafts ~amp 1

nk i

link

base

i~:L vibrated plate

i

Fig. 1. Schematic drawing of the shaker.

S,S. Hsiau, H. E Yu / Prowler Technoh~gy 93 (1997) 83--88

found ~ a t ~ convective motion of particles resulted in segregation, Duran et at. [24,25] established an arching effect model to analyze the segregation effect. Recently, POscbei ~ d H e n m ~ [26] analyzed the effect of convective motion on segregation by large-scale molecular-dynamic simula- tions. The current study is based on experimental studies of ~ ~gregafion ~ d e x ~ s i o n pbenomena of bina~ mixtures in ashaker.

~ d m n ~

In this study, the particle segregation experiments are per- formed in a rectangular box driven by an eccentric drive

100

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Z 5 0

0

2S

0

0,0

" ' ' ' I . . . . I . . . . I . . . . I ' ' ' ' I t t t t m m t m t t t t I

ZomSmm

G l a s s B e a d s

m = 0 . 1 6 k g

8 v

v

.... i = = • = l i

© Imm&~mm

I mm&Smm

o x I m m & 4 m m 0

~ V 2 m m & $ m m

,, ~ 2 m m & 4 m m

A 3 m m & 4 m m ¢

0

o ,'. v

o

A

OV O^

@V V ^

~v 8

V O 0

v •

• • • • O • • • • • O00m

i . . . I . . . . I . , , , I . . , . I , , . . I , , , , I , , , , I

0.5 1,0 I ,S 2.0 2,1S 8.0 3,5

VIBRATIONAL ACCELERATION (g) Fig, 2, Segregation coefficient a s , function of vibrational acceleration at a v ib ra t iona l amp l i t ude of 5 m m ,

t O0

m

0 - - " 75

8

m

O~

0,0

i ' ' " " I " " " " I . . . . . I " " " " I " " " " I " " " " I " " " " I l l l i l l l l l i • t i I • i • i •

, z0=3mm Glass Beads m = 0 . 1 6 k 9

C) t m m l ~ . m m

o ~ El 1 m m & 3 m m 0 o o o x l m m & 4 m m

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- . . , I . , , , 1 . . . , I . . . . I . , , , I . . . . I , , • , 1

0.5 1,0 1 ,S 2 ,0 2 ,~ 3 .0 3.5

V I B R A T I O ~ L ACCELERATION (g) Fig. 3. Segregation coefficient as a function of vibrationai acceleration at a vibrational amplitude of 3 ram.

system in the vertical direction. The schematic drawing of the apparatus is shown in Fig. 1. The box is made of Plexiglas for visualization purposes. The width of the box is 20 cm, the depth 1.9 cm and the height 29 cm. The bed is driven by a radial bearing that is eccentric to the shaft extension of the variable-speed d.c. motor. The vibrational amplitude Zo can be changed by using different radial bearings. Amplitudes of 3 and 5 mm are used in the present study. The vibrational frequency is adjusted by changing the rotational speed of the motor. The highest vibrational frequency f is 17 Hz. The rotational speed of the motor is measured by a HT-4000 OND SKKI tachometer. The amplitude of the vibrational acceleration ao is found from ao-zo<o 2, where e0 is the angular frequency, eo = 2 ~rrf. The magnitude of the acceleration amplitude in this experiment covers up to 4 g, where g is the gravitational acceleration.

Glass soda lime beads with a density of 2490 kg/m 3 were used as the sample particles. The diameters of the beads were i, 2, 3 and 4 mm. To analyze the size effect on segregation,

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'~ 0 lmm&2mm

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V 2mm&Smm

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. . . . ' • • • I I • " , " I • • , I I 1.0 2.0 8.0 4.0

VIBRATIONAL ACCELERATION (9)

• " " " I " " " " I " " " " I " " " " I

c o , ,oooooooooo { b )

v v ~vv,,vv~vvvv~, za=~mm

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<> 2mm&4mm ^ v A 3mm&4mm " [[ 8 8 8 8 8 8 ~ 8"

& A 6 A LI A 6a

0.20 . . . . e . . . . I . . . . , • • , , I =

0.0 1.0 2.0 3.0 4.0

VIBRATIONAL ACCELERATION (g) Fig. 4. Maximum bed expansion height (a) and solid fraction (b) as a function of vibrational acceleration at a vibrational amplitude of 5 ram.

S.S. Hsiau, H.Y. Yu I Powder Technology 93 (I 997) 83-88 85

different combinations of the binary mixture were employed. From the experimental report from Hunt et al. [ 13], the surface conditions of the particles and the walls could influ- ence the motion of the vibrated granular bed. If the particles are roughened or dyed with colors, wave phenomena may occur on the top surface of the bed [ 13,27 ]. Therefore, the box and the soda lime balls were cleaned after every two experimental runs to provide really smooth internal wall conditions and very smooth particles with low surface friction.

Let at and/3 denote the larger and smaller sizes, respectively, of the particles. Before the experiments, equal amounts (0.08 kg) of particles of sizes at and/~ were well mixed in the box. After the shaker was started at a preset frequency, the motion of the bed was digitally recorded by an image processing system, including a Deisa CCD image sensor (up to 110 frames per second) with a 55 mm Micro-Nikkor f/2.8 lens, an image grabber board (Dipix P360F Power Grabber), and a 150 W tungsten halogen light source.

S . 0 " ' ' ; ' ' 1 ' ' " ' 1 ' ' ' ' 1 ' ' ' ' 1

7 .0

A

E 8 .0

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(a)

z 0 = 3 m m

Glass Beads

m=0.16kg

~ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 O"

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4 .0

9 ® L (-~ I m m & 2 m m

C] I m m & 3 m m

x l m m & 4 m m

~ 8 V 2 m m & $ m m

<> 2 m m & 4 m m

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8 ,~ 88a88858~

3 ' 0 / . . . . . . • , I . . . . I . . . .

0 0 1,0 2.0 3,0 4.0 VIBRATIONAL ACCELERATION (g)

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. ° . . . . . .

0 , 5 0 o ,~ooooooo= AA~AA~A Z ^ ~ Glass Beads

0 m=0.16kg m

< IT 0.40 g,o U,.

a " cJ

, - - I ~ =

0 ~,~) I m m & 2 m m v

^ ° ~ v ~ ' ® ® o o ® o o o e o ® • • • • er 0,30 I m m & 3 m m

x ! m m & 4 m m ^ o r, q

'.'~ £ 1 f l n l & 4 m m "~ "' e, ... a

3 m m & 4 m m

0 . 2 0 i i i i I • • • , I , • • • l • • • • i "

0 0 1.0 2 . 0 3 . 0 4 .0

VIBRATIONAL ACCELERATION (g) Fig. 5. Maximum bed expansion height (a) and solid traction (b) as a function of vibrational acceleration at a vibrational amplitude of 3 ram.

Under the vibrating condition, the larger particles tend to move upwards and segregation occurs. The segregation coefficient C~ at time t was measured by counting particles from the image. If there are N. particles of at in the upper half of the bed and Ni particles of at in the lower half, the segregation coefficient C~ was defined by

C~=(N,,-N,)/(N.+NO

A segregation coefficient of I denotes complete segregation of the binary mixture and C~ = 0 shows that the material is fully mixed. The granular bed compresses and expands con- tinually when the bed is vibrated [ 13 ]. The particles in the lower levels are denser than those in the upper part during expansion. Therefore, it is difficult to decide the interface between the upper half and the lower half. In this experiment, the recording speed of the image processing system was adjusted to synchronize with the vibration so that the images could always be recorded when the bed is in a state of compression.

The solid fraction when the bed expanded was also measured. A light sheet of paper was placed above the bed and then the height of the bed could be measured from the image [ 13,28]. The solid fraction v could be calculated from the total mass of particles m divided by the particle density pp, the bed expansion height h and the bed cross-sectional area.

The maximum segregation coefficient of a binary mixture was called the maximum segregation ratio C,.m,,,. Some binary mixtures could segregate completely (C~. ,,,..,~ = l ) and the time when the mixture reached the completely segregated condition was called the segregation time T. Some binary mixtures could only segregate partially and the maximum segregation coefficient C,, ,,,,,~ was recorded.

3. Results and discussions

Fig. 2 shows the maximum segregation coefficient as a function of the vibrational acceleration ao for six combinations of the binary mixture of glass balls vibrated at an amplitude of 5 ram. When the acceleration is less than ! g, the kinetic energy received by the mixture is not enough for the particles to have any relative movement, so no segregation occurs. Binary mixtures can segregate for accelerations greater than i g, since they receive sufficient kinetic energy to generate relative movement between the particles. From the figure, the greater the size difference, the better the segregation effect. The I and 4 mm and the ! and 3 mm mixtures can segregate completely (C, = I ) with an acceleration rang- ing from 1 to 2.7 g. For the other types of mixtures with particle diameter ratios less than 3, the mixtures cannot segregate completely and the segregation coefficient increases with acceleration, reaching a maximum when ao = 1.75 g. For a vibrational acceleration greater than ! .75 g, particles receive even higher kinetic energy from the base plate, which results in the remixing of particles, hence the segregation effect decreases (C, decreases). When the acceleration is greater

&X Hsiau. H. E Yu l Powder Technolo&~' 93(1997) 83-88

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W 50. m=O.16kg 1 ~ t ",,

.~' "'~,, 0 .75

0 ~ - ~ o . . . . . ~; 'b- -o--~--~- o ~; -o'

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• .100 . . . . . . . . . . . . . . -0 .0 1.0 2.0 3.0 4.1

VIBRATIONAL ACCELERATION (g)

1.00

0.00

0.25

<

tt.

C3 t a m s _ J

0

Fig. 6. Segregation coefficient and solid fraction of the bed as a function of vibrational acceleration for a I and 2 mm glass mixture with a vibrational amplitude of 5 ram.

than 2.7 g, the mixture is random, andno segregation appears for the six combinations of the binary mixture.

Fig. 3 shows the segregation coefficient as a function of acceleration for the same six combinations of the binary mixture but using the vibrational amplitude of 3 mm. Fig. 3 is very similar to Fig. 2: the materials can segregate partially at an acceleration between I and 2.7 g, and the most favorable segregation condition occurs at ao - 1.75 g. This indicates that the acceleration is an appropriate factor to correlate segregation phenomena. However, the magnitude of the vibrational amplitude is still an important factor, since it must be in the same order as the particle diameter to generate the bed motion.

The granular bed expands when the bed is vibrating. The maximum bed height was measured by the image processing system and then the solid fraction v could be calculated. Fig. 4(a) shows the maximum expansion height of the bed as a function of the vibrational acceleration with a vibrational amplitude of 5 ram. When the acceleration is less than 1.8 g, the bed height remains the same and the bed is in a 'solid- like' condition, The height begins to increase rapidly when the acceleration is greater than 1.8g. The bed volume expands quickly during this stage. The bed height stops increasing for accelerations greater than 2.7 g and the bed is transformed to a 'liquid-like' regime. Fig. 4(b) shows the solid fraction as a function of acceleration for the corresponding case.

Fig. 5(a) and (b ) shows the height and solid fraction as a function of the vibrational acceleration with an amplitude of 3 ram. Fig. 5 is simil~ to Fig. 4, but the range of acceleration for the most rapid expansion is different. From Fig. 5(a) and (b), the bed expands significantly when ao is between 1.2 and 1.8g.

It is interesting to plot the variations of both the segregation coefficient and the solid fraction with acceleration in the same figure. Fig. 6 shows the segregation coefficient and the solid fraction of the bed for a 1 and 2 mm glass mixture with a vibrational amplitude of 5 ram. When the acceleration is below I g, particles have no relative motion, so the bed is not in an expanding condition and no segregation occurs. When the acceleration is between ! and 1.75 g, there is some small relative motion between particles. This relative motion causes reorganization of the voids among particles but the energy is not high enough to expand the bed. During this range of vibrational acceleration, some larger voids are formed, therefore the smaller particles fall more easily down through the voids, resulting in segregation. The higher the acceleration, the more voids are formed and the larger they are, and thus the segregation coefficient is increased. When the acceleration is higher than ] ,75 g, the particle motion becomes significant and the bed Starts to expand quickly, causing the solid fraction to decrease. The motion of particles becomes more random, so larger voids are formed in the bed. At this stage, the probability for larger particles to fall through the voids in the bed increases. Therefore, the material becomes more difficult to segregate and the segregation coefficient decreases. When the acceleration increases to 2.7 g, the voids are so large that the probabilities for larger and smaller particles to fall down through voids are equal, the segregation phenomenon does not exist and the material is in a well-mixed condition. The bed also stops expanding, indicating that the material has already transformed from a 'solid-like' state to a 'liquid-like' state. The transformation could also be described as the transition from a 'dense' state to a 'loose' state.

S.S. Hsiau, H.Y. Yu / Powder Technology 93 (1997) 83-88 87

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1-- 75

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(b) G,.. m=0.16kg

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o 013

r,

v

~ og~ s8 § ea • =o =o

• , • • | , • • • | t • • • i , • • •

0 1 ,§ 2.0 2.6 8.9

VIBRATIONAL ACCELERATION (g) Fig. 7, Segregation time (a) and nun)her of cycles (b) as a function of vibrational acceleration.

As shown in Figs. 2 and 3, for I and 4 mm and i and 3 mm binary mixtures, the materials can completely segregate for accelerations between I and 2.7 g. Fig. 7(a) shows the segregation time needed for these binary mixtures at different accelerations. As discussed above, for higher acceleration, the material is easier to segregate and the segregation time is shorter. For the same vibrational acceleration, the segregation time is shorter for the I and 4 mm mixture due to the greater particle diameter ratio. Dividing the segregation time by the period of vibration, Fig. 7(b) shows the number of cycles needed to reach the completely segregated condition as a function of the acceleration. The number of cycles needed for complete segregation is smaller for the I and 4 mm mixture; it is also smaller for a higher acceleration.

Fig. 8 shows that the segregation coefficients increase with time t until the materials of the I and 4 mm and I and 3 mm binary mixtures reach the completely segregated condition at accelerations of 1.08 and I. ! 8 g, respectively, with an amplitude of 5 mm. The corresponding plot for an amplitude of

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50

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I ' " " " I " • " • I " " " • I • • • • I • " "

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0 25 50 75 100 125

TIME (see) Fig. 8. Segregation coefficient as a function of time at a vibrational amplitude of 5 mm for accelerations of 1.08 and I. 18 g.

w m

0 7s LI. t.L. UJ

oo Z 50

o

I i i 25

I " ' ' " I " " " " I " ' ' " I " " " " I " " " "

100 " o o o o o o o- z0=3mm , °

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m = 0 . 1 6 k g ~ o

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¢ V ZX

&

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0 25 50 ?5 100 12B

TIME (see) Fig. 9. Segregation coefficient as a function of time at a vibrational amplitude of 3 mm for accelerations of !.08 and I. 18 g.

3 mm is shown in Fig. 9. As seen from the figures, the segregation speed is faster in the beginning and becomes slower for higher segregation coefficients. The increasing curves seem to be close to exponential curves, indicating that the segregation might be a diffusion process. However, more experiments and analyses are necessary to make this conclusion.

The above results show that the amount of energy received by the mixture is very important for the segregation. Choosing equal masses of I and 4 mm glass beads as the mixture, the total mass was changed for different experiments. Fig. 10 shows the maximum segregation coefficient as a function of the vibrational acceleration for total masses of 0.16, 0.32,

~+ &S, ltsiou, H, E Yu / Powder Technology 93 (1997) 83-88

100 +

Z 50 0

I

++" ": " " I " " " " I " + ' ' " I " " " " I " " " " I " " " " I " ' ' ' I

0 0 0 0 0 0 0 0 0 0 0 0 O ,,

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~t (+]

m

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V

0 m,.O.16kg m-O.a2k9

x m-O.48kg V m=O.64k9

v v n i • Q

9 V

n • • Q

o • v v • o

0 • O 0 0 0 o + v v v v • • O 0 0 Q ~

l l l . l . , . , l , , . . l . . . . l . . . . l . . . . l . . , , l

0.0 0,5 1.0 1.5 2.0 2.5 3.0 3.5 VIBRATIONAL ACCELERATION (g)

Fig. 10. Segregation coefficient as a function of acceleration for different mas,~s of the binary mixture ( I and 4 mm glass beads).

0,48 and 0.64 kg. For the same acceleration, the segregation coefficient is greater for the case of smaller total mass, because more energy could be received by each particle to generate greater movement. The range of acceleration amplitude causing the segregation effect becomes narrower if more particles are in the bed. However, the most favorable acceleration for mixtures to segregate is 1.75 g. Note that only for the case of the smallest total mass (m =0.16 kg) could the bed reach the fully segregated condition.

4. Conclusions

The greatest segregation effect of binary mixtures occurs for a brutal collapse of the solid fraction when the bed is transformed from a dense state to a loose state. The larger the size difference in the mixture, the greater the segregation of the materiM: The material needs an appropriate amount of vibrational energy to segregate. If the energy is too small, it is not enough to segregate the material. However, too much energy results in the remixing of the material and the segregation effect might disappear. The appropriate vibrational acceleration for the material to segregate ranges from I to 2.7 g, and it reaches the most segregated condition at a vibrational acceleration of 1.75 g. In the future, the granular temperature

generated from the vibration should be studied in order to gain a theoretical understanding of segregation.

Acknowledgements

The authors would like to acknowledge the support from the National Science Council of the Republic of China for this work through Grants NSC83-0410-008-018 and NSC84- 2211-E-008-036.

References

!11 121

131 141 151 161

171 181 [91

I IOl

1111

II21 !i31 1141 1151 1161 1171 1181

1191 1201

11211

[22] [231

1241

1251

1261 1271 1281

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Segregation phenomena in a shaker