Shape separation of particulates by a rotating horizontal sieve drum

Powder Technology, 75 (1993) 113-118

113

Shape separation of particulates by a rotating horizontal sieve drum M. Furuuchi*, C. Y a m a d a a n d K. G o t o h Department of Energy Engineering, Toyohashi University of Technology, Tempaku-cho, Toyohashi 441 (Japan) (Received August 15, 1991; in revised form February 25, 1992)

Abstract Shape separation of elongated particles is conducted by a rotating horizontal sieve drum with equal circular holes of diameter 0.4 mm, through which all particles placed in the interior can flow out. The drum is 100 mm in diameter and 500 mm in length. The residence time of particles in the drum relates to the particle shape. Hence particles can be separated according to the aspect ratio. The residence time of particles is measured and related to the particle shape, the initial hold-up and the rotational frequency of drum. The particle flow through the drum is modeled to discuss the influence of the operating conditions on the residence time. It is found that the residence time increases with the aspect ratio and hold-up. The residence time distribution of the mixture of multi-shaped particles is made obtainable by a modified perfect mixing model. The particles are successfully separated according to the aspect ratio and the separation efficiency is discussed.

Introduction

Experimental

Since particle shape significantly affects bulk properties of powder, it is important to control not only size but also shape to improve the quality and function of powder products. Various types of shape separators have been proposed [1] so that a wide range of particles can be separated according to shape by choosing the most effective one. Most of the separators utilize the difference in the rolling motion of particles so that they are limited for use to the particles larger than several hundreds micrometers; sieve methods [2-8] may be applicable for smaller particles. In this study, zinc particles with a wide distribution in their elongation are separated according to the aspect ratio by a rotating cylindrical sieve and the influence of the operating conditions on the separation performance is investigated experimentally. The cylindrical sieve has such merits that the separation can be conducted both in batch and continuous modes, and clogging particles can be easily removed during the operation. First, the residence time of particles in a horizontal cylindrical sieve is measured and related to the aspect ratio of particles, the initial particle hold-up, and the rotational speed of the drum. Next, the shape separator is modeled to discuss the operating conditions and the shape separation efficiency is explained.

A schematic diagram of the experimental apparatus is shown in Fig. 1. The stainless steel drum (100 mm diameter; 500 mm length; 0.3 mm thickness) has circular holes of 0.4 mm diameter with number density 1.136 holes mm-K The inside of the cylinder is sectioned by transparent acrylic and a copper plates. Initial amount W0 of particles was fed into the central section of 150 mm length through the input port of the acrylic plate. The drum was rotated by an AC motor, and particles passed through mesh holes were collected at time intervals. In order to prevent the fed particles from leaking before the test run, the drum was covered with a paper sheet. Although not dealt with in the present paper, continuous separation can be conducted by removing the sectioning plates and tilting the drum [9], where the particles continuously fed from the upper end of the drum are separated according to the distance traveled. 500

1

dl) O& ~ 1 - , ~

175

150

175

Z Input fort

*Current address: Dept. of Civil Engineering, Faculty of Engineering, Kanazawa University, Kodatsuno 2-40-20, Kanazawa 920 (Japan).

0032-5910/93/$6.00

Sectioningplate (Acrylic)

Sectioningplate (Copper)

Fig. 1. Sieve drum.

© 1993- Elsevier Sequoia. All rights reserved

114 TABLE 1. Particle sizes

Length Width Thickness

1 Average [/~m]

o'* [/xm]

642 296 192

230 58 37

k~ '~

eqn.(7)

X~ ~\~ ~

I

\

o

*Standard deviation. 1.0

i

I

'

0.5

o7

wo,, -\

_X\ \

fuuuuu~J~

9' ~I

N=3Olrpm] a=O. 451s-11 b=2.3X10-31g-~l n:1.55[-I

0

a= 7[-I ~ = el

°/E N = 1-~1-exp(-~ R)'-(~R)j /o/ j--0 j! .~, I , I , 0 I 2 3 R/ [-] Fig. 2. Cumulative number fraction Er~.

~

a 200

50

00

t Is]

Fig. 3. Time change of particle hold-up WR for rotational speed N=30 rpm. 1

I

--

eqn.(7)

I O

N=60[rpml 0=0.67[s -~] b=1. I X10-31g-I] n=2.6[-] Wo [gl

t~

Elongated zinc particles (density 3 639 kg m -a) were used as the test sample. They were obtained by sieving for 1 h with a vibrator, operated at amplitude about 2 mm and frequency 60 Hz. 50 g of particles were sieved for each run. Microscope images of the particles on a slide glass were analyzed by a TV image processing system to obtain their size and shape; while the particle thickness was measured by a micrometer. Sizes of the particles are listed in Table 1. The distribution of particle length is broader than those of width and thickness. Hence the particle length may be a dominant factor in the subsequent experiment of the shape separation. The cumulative distribution EN(R)of the aspect ratio, R = (length)/(width), is shown in Fig. 2, where (R) denotes the average aspect ratio. The solid curve depicts the gamma distribution [10] in which the parameter a is adjusted so as to give the best fit to the experiment.

/' 100 [] 200

I

I

I

i

I

i

i

i

i

0

50 O0 t Is] Fig. 4. Time change of particle hold-up WR for rotational speed N=60 rpm. N : 3 0 [rpm]

Wo:400 [g]

R e s i d e n c e time of particles in sieve d r u m

Figures 3 and 4 show the time change of the particles retained in the sieve drum, where Wo is the initial particle hold-up and N is the rotational speed of the drum. When 14Io is small, the flow rate of particles through the mesh holes decreases with increasing N owing to the slipping motion of particles on the drum wall. At higher Wo, a circulatory motion of the particle bed occurs so that it becomes hard for the interior

(a) (b) Fig. 5. Pictures of particles sampled at time t = (a) 0 ~ 5 and (b) 65 ~ 95 s. particles to reach the sieve surface. The drum rotation enhances agitation of the particle bed, giving rise to an increase in the particle flow through the sieve. Figures 5(a) and (b) respectively depict pictures of particles sampled at t = 0 ~ 5 and 65~95 s, showing

115

that more elongated particles are collected at later period. The time changes of the aspect ratio R of the particles which have left the drum are plotted in Figs. 6 and 7 respectively for N = 30 and 60 rpm, where R at time t, defined as (maximum length)/(perpendicular width), was measured and averaged for 100 particles. It is seen that the longer the particle, the longer the residence time. Hence one can separate the particles according to their aspect ratio R. The influence of the initial hold-up W0 on the residence time is significant for N = 30 rpm. The peaks in Fig. 6 were caused by the fact that some disk-like particles with diameters close to the size of the mesh holes were in the sample, and they were unable to flow out of the drum. If the particle concentration is so low that the interaction between particles is negligible, the rate of outflow of the particle mixture with different aspect ratios may be expressed as follows [11]: 6 5 4 T

5

J

N= 30[rpml W0 [g] o 50 100 v 200 400

¢y

2 1 0

!itt lo

t

t

5o l bo

560 looo

t Isl Fig. 6. Time change of aspect ratio R of particles flown out of drum for N = 30 rpm. The vertical bars show the range of standard deviation of the data for W0=50 g.

dW.i & or

e~

WR = ffw(R) exp( - kt)dR = ~, wi exp(-k,t)

w0

i

where WR is the hold-up of particle mixture in the drum at time t, WR~ is that of component i, Wo is the initial particle hold-up, fw(R) is the weight distribution function of the aspect ratio R, k is the rate constant related to R and the operating conditions, wi = fw(R)z~2 and kl is the rate constant of i component. Here, ki is assumed as follows [12, 13],

kl =aRi-"

(3)

where a and n are constants. Figure 8 shows the time change of WR/Wo. The solid curves denote eqn. (2) with eqn. (3), where a and n are adjusted so as to give the best fit to the experiment. The number distribution of particles was measured and transformed into the weight distribution by regarding the test particles as being cylindrical. Equation (2) is in good agreement with the experiments so that the particle interaction may be negligible for Wo=50 g. As the particle hold-up increases, however, the interaction becomes significant, giving rise to an increase in the residence time as already shown in Figs. 3 and 4. In order to explain the particle interaction, the above mentioned perfect mixing model is modified in the following way. If the probability for particle i to leave its assembly in the drum is assumed to be an exponential function of the total particle hold-up WR, then the flow rate of particle i through the drum becomes

i

(It

N= 60[rpm]

(4)

k , WR, exp( - (, WR)

-

5

Wo 50lgl " 100 • 200

t

•

4

1

* 400 --

I

/32

2

J

m ~

t

3

,

i

i

I

Wo=50Ig!

i

i

i

i

N Irprn__~l o 30

T 3=

0

I

5

I

10

50

100

?

500 1000

t Is] Fig. 7. Time change of aspect ratio R of particles flown out of drum for N = 60 rpm. The vertical bars show the range of standard deviation of the data for Wo=50 g.

(2)

0

dW~, 6

(1)

= -- kiWRi

0

50 t Isl

100

Fig. 8. Time change of particle hold-up.

116

i

where W R i is the hold-up of particle i, kl is the rate constant defined by eqn. (3) and ~i is a constant assumed to be proportional to the aspect ratio Ri of particle i, that is,

~-bR~

(6)

where b is a constant. Hence, the total particle flow rate through the drum becomes dWR = E ( d W m ~ = _ E[k, Wm e x p ( - ~:,WR)]. dt \ dt ]

(7)

The solid curves in Figs. 3 and 4 depict eqn. (7) with eqn. (6), where the values of a and n obtained from the perfect mixing model in Fig. 8 are used and only b is adjusted so as to give the best fit to the experiments. Needless to say, b = 0 means that the particle interaction is negligible. Although the detailed motion of individual particles in the bed is disregarded in eqn, (7), the agreement with the experiments is good. Similar results were obtained for N = 20 rpm. In Figs. 9(a), (b) and (c), the constants a, b and n are respectively shown in relation to the rotational speed N. The exponent n increases with N, since the particles are oriented to be flat on the sieve surface so that the rate constant (eqn. (3)) becomes smaller. That is, n =2.6 at N = 60 rpm is close to n = 3 obtained for the horizontally vibrated sieve with the square mesh [10, 11], although the particle motion on the cylindrical sieve rotating at N= 60 rpm may be different from that on the vibrating sieve. The constant b decreases with N because the agitation by the drum rotation makes the particle bed

looser, giving rise to a decrease in the particle interaction. The value of a is almost constant and may be a factor related to the mesh geometry and particle size. Once the constants a, b, n are obtained, the residence time distribution of multi-shaped particles can be predicted from eqn. (7). It is observed that, under the present operating conditions, the motion of particle bed lies in the range from the cascading to the slipping motion.

Separation efficiency The recovery efficiency of the particles smaller than Re is defined as

(Wo- w~)4,Rc T]re¢

=

Wo~bRC

and the removal efficiency of the particles larger than Ro is defined as

Wo(¢Rc- ,~Rco) + w R 0 - ¢~c) Wo(1 - CRC0)

nrem =

97 =

'}~rec'l~rern.

The recovery efficiency ~?re¢ is plotted against time t in Figs. 10(a) and (b) respectively at the rotational speed N = 3 0 and 60 rpm for various values of Wo,

1.0

5

I

(o')

: 30'[rpm~/-

(e)

Rc= 3 / / / /

WO[g]

0.5

0.5

-g -g-d " 100 o 200

o

0 5 xi073

r

i

i

i

[

i

.

i

.

i

.

I

v 400

q-

i

(b)

-!f

i

-- oo

0

1.0

I

.

V/

(c) 2 T c

: 200

,'I

• •

I 0 0

I

'2~0 N[rpml

(9)

where Rc is the cut-point value of R, ¢RC is the cumulative mass fraction of the particles smaller than R~ and CRC0 is its initial value. Then the overall efficiency of the particles which are removed from the cylinder becomes

N

I

(8)

0

70

Fig. 9. Relations between rotational speed N and three constants: (a) a in eqn. (3), (b) b in eqn. (6) and (c) n in eqn. (3).

,

I

,

10

I

100

400 ,

1000

t [s] Fig; 10. Time change of recovery efficiency "O,~cof particles of aspect ratio R~