Segregation processes of a binary granular mixture

in a shaker

SHU-SAN HSIAU and JING-I WANGNational Central University, Department of Mechanical Engineering, Chung-Li, Taiwan32054, ROC

Received 25 September 1998;accepted 4 December 1998

Abstract The segregation phenomena of a binary mixture in a vertical vibrated bed were investi- gated experimentally by using image technology. The larger particles tend to move upwards and the smaller particles move downwards due to particle reorganization. The maximum segregation ratios at different vibration acceleration amplitudes were measured and analyzed. The segregation coefficientsand the vertical velocities of the larger and the smaller particles were also measured. The segregationcoefficient is increased with time until reaching a maximum value. The segregation rate and the ve- locities (absolute values) of the larger and the smaller particles are decreased with time, and finallybecome zero.

Keywords:Segregation; binary mixture; granular material; shaker; vibrated bed; vibrational accelera- tion.

NOMENCLATURE

a amplitude of vibrational acceleration (cm/s2)

CS segregation coefficient (%)

Cs,max maximum segregation ratio (%)

f vibrational frequency (Hz)Nl number of larger particle in the lower half of the bed

Nu number of larger particle in the upper half of the bed

0 N the difference of the numbers of larger particles in the higher andthe lower beds, AN = N" - N,

T vibrational period (s)t vibrational time (s)

Greek

(0 vibrational radian frequency, w = 2n f (rad/ s)

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1. INTRODUCTION

Shakers are important devices to mix and dry granular materials in industry [1-4].Shakers are also used to sort granular materials according to particle size in the pharmaceutical, powder metallurgy, and food industries. Many mechanismscontribute to segregation, e.g. differences in particle size, particle density, propertiesand angle-of-repose of the materials [5, 6], and granular temperature gradient [7].The segregation phenomenon occurs for a binary mixture in a shaker due to the

reorganization and the convection of particles [8-12]. The larger particles tend to move upwards in the shaker over a certain range of vibrational accelerations [12].Williams [5] and Savage [ 13] have produced very good review papers about these

segregation processes.Most experiments and computer simulations about segregation in a vertical shaker

used only one larger ball with a background of smaller particles [11, 14-19]. The

purpose is to study the segregation process microscopically. However, for most

practical applications, there is not only one larger particle in the mixture. Recently,Hsiau and Yu [12] used equal-mass and well-mixed binary mixtures to study thesize effect on segregation in a vertical shaker. The binary mixtures were of the same material (glass beads) with the same total masses but different sizes. Theymeasured the segregation coefficient and the solid fraction during bed expansionin the bed at different amplitudes of vibrational accelerations. They found that the

segregation effect was increased with the vibrational acceleration until reaching amaximum and then to decrease with the acceleration [12]. The bed is in a dense state and does not expand seriously when the acceleration is low. The bed starts to

expand quickly after the acceleration is greater than a critical value [4, 12, 20]. The

expansion height is increased with the vibration acceleration amplitude. When the acceleration amplitude is greater than the other critical values, the bed expansionheight remains constant and the bed is in a loose state. Hsiau and Yu [12] found that the greatest segregation effect occurs when the bed transformed from a dense state to a loose state.

2. EXPERIMENTAL SET-UP

This study experimentally investigates the segregation processes at different vibra- tion intensities. The current experimental setup is shown in Fig. 1. A TechronVTS-100 electromagnetic vibration test system is used as the vertical shaker. The vibration test system is vertically driven by sinusoidal signals which are produced bya Meter DDS FG-503 function generator through a Techron 5530 power amplifier. The amplitude of vibrational acceleration a and the vibrational radian frequency coare measured by a Dytran 3136A accelerometer which is connected to a Tektronix TDS 360 oscilloscope. A frequency f of 20 Hz is used ( f = o)/2.7r) throughout thecurrent experiments. A plexiglas tank with a width of 20 cm, height of 30 cm, and

depth of 2 cm, attached to an aluminum expander, is driven by the shaker. The well-mixed binary mixture with equal masses of glass beads (density = 2490 kg/m3) but

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Figure 1. Schematic drawing of the experimental apparatus.

with different sizes is put in the container. The present experiment uses 100 g of

larger particles with a diameter of 4 mm and 100 g of smaller particles with a diam- eter of 2 mm. About 20% of the larger and smaller particles are dyed with different colors to serve as tracers. The segregation processes are digitally recorded by an

image processing system, including a Dalsa CCD image sensor (120 f.p.s.), a DipixP360F power grabber and a 150 W tungsten halogen light source.

Under vibrating conditions, the larger particles tend to move upwards and the

segregation phenomenon occurs. The segregation coefficient Cs at time t was measured by counting particles from the recorded images. With the numbers of

NU and N, larger particles located in the upper and the lower half parts in the bed,the segregation coefficient is defined by [5, 12]

By definition, a segregation coefficient of 1 means complete segregation conditionand no larger particles in the lower bed; a segregation coefficient of 0 denotes that the material is fully mixed and the larger particles are still equally distributed in the whole bed. For the particle size ratio of 2 used in this experiment, the binary mixture

may not be completely segregated [12]. The maximum segregation ratio Cs,roaXismeasured from the images. The particles in the lower levels are denser than those in the upper part during the bed expansion [4, 20, 21]. 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 synchronizewith the vibration so that the images could always be recorded when the bed is in a state of compression. The interfaces between the higher and lower half of the bedwere decided from the recorded images for every cycle by dividing the bed in to

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two equal-height beds. The interface may not be horizontal due to the existence of heaping phenomena [21 ].

The shifts of particle tracers could be found by identifying the positions of tracers in consecutive images. The velocities of the larger and the smaller particles couldhence be calculated from dividing the corresponding shifts by the time delay ofthe two consecutive images. The vertical mean velocities of the larger and the smaller particles are calculated from averaging the tracers' vertical velocities in theimages. Note that the average velocity calculated here was the so-called long-termaverage [22], which was determined from the particle displacements per vibrationcycle (at the same phase angle).

3. RESULTS AND DISCUSSIONS

Figure 2 shows that the maximum segregation ratio C;,max varied with the vibra-tional acceleration amplitude. There is no segregation effect for an acceleration less than 1 g (g is gravitational acceleration) since the kinetic energy received by themixture is not enough to generate any relative particle movements in the bed. The segregation phenomena exist when the vibrational acceleration amplitude is greaterthan 1 g. The segregation of particles is due to the reorganization of particles. Whenparticles get sufficient energy from the shaker, the bed expands and contracts peri-odically, resulting in the relative motions of particles. When the bed expands, thevoids among particles are rearranged and some larger voids are formed. Therefore

Figure 2. The maximum segregation ratio as a function of the vibrational acceleration amplitude.

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the smaller particles fall more easily down through the bed and the segregation phe- nomenon occurs. The higher the acceleration, the more larger voids are formed,which results in a greater segregation ratio. The maximum segregation ratio is con-

tinually increased with the acceleration and reaches a maximum value when the acceleration is 2.2 g. When the acceleration is greater than 2.2 g, the particle mo-tion becomes significant and the bed expands quickly. The bed motions are much more random and even larger voids are formed in the bed. Hence the probabilityfor the larger particles to fall through the voids in the bed increases. Therefore it becomes more difficult for the particles to segregate, causing the decrease of the maximum segregation ratio.

The maximum segregation ratio C,,r"aX is influenced by the total mass of particlesin the shaker. The maximum segregation ratio is higher for the case with smaller

particles since more energy is received by each particle from the bed plate. However,the maximum segregation ratio occurs at the same acceleration amplitude, providedthe size ratio and the concentration remain the same. A related study can be foundin Hsiau and Yu [12] and is not discussed here.

Figure 3 shows that the segregation coefficient varied with the vibrational time (t)non-dimensionalized by the vibrational period (T) for the vibrational acceleration

amplitudes of 1.5, 2.0, 2.5, 3.0, 3.5 and 4.0 g. From Fig. 3, the segregation rates(the slopes of the curves) are larger at the beginning stage of segregation. Thedeviations of the segregation effects for the six cases are not significant. However,the segregation effects are very different when the vibrational cycle is greater

Figure 3. The segregation coefficient varied with the vibrational cycle for the vibration acceleration amplitudes of 1.5, 2.0, 2.5, 3.0, 3.5 and 4.0 g.

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Figure 4. The segregation coefficient and the mean vertical velocities of the larger and the smaller particles varied with the vibrational cycle for the vibration acceleration amplitude of 2.0 g.

than 70. The segregation coefficients for the cases of a = 2.0, 2.5 and 3.0 gare continually increased with time and the segregation rates are getting slowercompared with the earlier segregation stage. For the other cases, the segregationcoefficients almost reach the maximum ratio when t/T = 70 and are not changedsignificantly since then.

Figure 4 shows the segregation coefficient and the mean vertical velocities of the larger and smaller particles as functions of time for the acceleration amplitudeof 2.0 g. The segregation coefficient-time curve was shown in Fig. 3. The velocity profiles show that the larger particles move upwards (with positive verticalvelocities) and the smaller particles fall down through the bed (with negativevertical velocities). The absolute values of both speeds are decreased with time. It can be explained as follows. The segregation rate is dependent on the current segregation ratio. If the bed is more mixed (ON = N" - N1 is smaller), thesegregation rate is quicker. This is similar to the diffusion phenomena which is influenced by the concentration difference. The segregation rate is reflected by theascendent velocity of the larger species and the descendent velocity of the smaller species. Therefore, with increased time, the segregation rate (the slope of the segregation coefficient-time curve) is decreased due to the increase of segregationratio (greater Nu and AN). Therefore, the speeds for the larger particles upwardsand for the smaller particles downwards are also decreased with time. When thesegregation coefficient reaches the maximum value (maximum Nu and AN), bothspeeds become zero, indicating that both species stop segregating. Note that the vertical velocities of the smaller particles and the larger particles are almost of the

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Figure 5. The segregation coefficient and the mean vertical velocities of the larger and the smaller particles varied with the vibrational cycle for the vibration acceleration amplitude of 3.5 g.

same value but with opposite signs. Since the masses of both species are equal, themean vertical velocity of the binary mixture in the bed is zero.

Figure 5 shows the same profiles as Fig. 4 but for the case of a = 3.5 g. Thecurves in Fig. 5 have the same trends as Fig. 4. As mentioned earlier, the speeds ofboth species reflect the segregation ratio. Because the former case (a = 2.0 g) hasthe greater maximum segregation ratio and the faster segregation rate, it results in

particle speeds of both species for a = 2.0 g (ranging between ± 0.25 cm/s) beinggreater than those for a = 3.5 g (ranging between 0.4 cm/s).

4. CONCLUSIONS

This paper experimentally studied the segregation processes of binary mixtures of 4 and 2 mm glass beads in a vertical shaker. The influence of the vibrational acceleration amplitude was investigated. The vibrational acceleration causes the relative movements of particles, and the rearrangements of the particles and the voids resulting in the segregation phenomena. The variance of the segregationcoefficient, the rising speed of the larger particles and the falling speed of the smaller particles with vibrational time were also studied. With the increase of time,the segregation coefficient is increased but the increased rate is decreased. The

rising speed of the larger particles and the falling speed of the smaller particles aredecreased with time. The influence of the granular temperature (particle velocityfluctuations) on the segregation processes will be studied in the future.

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Acknowledgements

The authors gratefully acknowledge the financial support from the National Science Council of the ROC for this work through grant NSC84-2211-E-008-036. Thanksalso go to IChemE for publishing our preliminary results in Proceedings of theWorld Congress on Particle Technology 3 (on CD-ROM), Brighton, UK, 1998.

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