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A study of the axial segregation in a rotating drum using deformable particles
Powder Technology 166 (2006) 161 – 166 www.elsevier.com/locate/powtec
A study of the axial segregation in a rotating drum using deformable particles H.P. Kuo ⁎, Y.C. Hsiao, P.Y. Shih Department of Chemical and Materials Engineering, Chang Gung University, Tao-Yuan, 333, Taiwan Received 29 September 2004; received in revised form 1 April 2006 Available online 7 June 2006
Abstract A binary mixture of particles is utilized to investigate size-induced and non-size-induced axial segregation in a rotating drum using deformable 1 mm rubber particles as the key component. In the size-induced segregation studies, the dimensionless band width (width of segregation band divided by particle size) of the small particles (WB/dp) increases in proportion to the rotational speed in the range of 10 rpm to 40 rpm when the fill level is between 10% and 36%. WB/dp increases as the fill level increases from 10% to 36% with a particle size ratio 2 and has a maximum value with a particle size ratio 3. In the non-size-induced segregation studies, segregated bands are observed in (3 mm rubber–3 mm glass) and (4 mm rubber–4 mm glass) systems with low fill levels. There is no axial segregation when 1 mm and 2 mm rubber particles are mixed with 1 mm and 2 mm glass particles, respectively. The non-size-induced segregation bands were different from the size-induced segregation bands. The bands are less pure and the interfaces are less distinct. The results suggest that trajectory segregation is the dominant segregation mechanism in axial segregation in drums. © 2006 Elsevier B.V. All rights reserved. Keywords: Segregation; Rotating drum; Binary mixture; Non-size-induced segregation
1. Introduction Solids mixing is a common operation in many industries, for example, in the manufacture of pharmaceuticals, food, ceramics and polymers. The rotating drum is one of the most common devices for solids mixing, especially for the mixing of brittle particles due to the gentle particle motion in the drum and for the requirement of limited contamination between different batch operations due to its ease of cleaning. Other applications of rotating drums include granulation, drying and reaction. However, when particles of different properties are processed in a rotating drum, particle segregation often occurs and causes nonuniformity of the products. Williams and Khan [1] reported that particles of different sizes, densities, shapes, roughness, and elasticity showed segregation when they are mixed. Most of the previous studies focused on size-induced segregation. When a binary mixture of two sizes of glass beads was mixed in a tumbler, detectable segregation occurred for a diameter ratio of 1.2 to 2.5 [1]. Size segregation in a rotating drum typically occurs in two ⁎ Corresponding author. Tel.: +886 3 2118800x5488; fax: +886 3 2118668. E-mail address: [email protected] (H.P. Kuo). 0032-5910/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2006.05.016
stages: first, large particles rapidly segregate radially, fine particles producing a central core and are surrounded by large particles; next, particles in the core migrate along the axial direction of drum until the core extends axially for the length of the drum [2]. Radial size segregation and radial density segregation in a drum have been studied. Radial segregation usually results in the small (or high density) particles concentrating in a central core and the large (or low density) particles in the periphery [1,3]. In the radial direction, the flow consists of a thin surface flow zone and a rotating solid body bed zone. Savage and Lun [4] proposed a radial segregation mechanism based on different particle motion in two flow zones. Small particles percolate in the surface flow zone. A constant bulk density upward flux assumption resulting in a net downward flux of the small particles and a net upward flux of the large particles. The differences in the net flux between the particles of difference sizes cause radial segregation. Radial segregation pattern could reverse at high rotational speed [5]. Thomas [6] proposed that reverse segregation occurs when the large particles are massive enough to move down by pushing aside the small particles. Khakhar et al. [7] applied the hard sphere theory to model radial
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segregation in a drum and reasonable predicted density segregation in a drum, but the prediction on size segregation disagreed with the experimental observation. They proposed a new model based on dynamic variation of flow, composition and surface angle, which gave a qualitative description of the radial segregation process. Axial size segregation shows that the individual species segregate into alternate bands of relatively pure single concentrations (note: the conclusion was obtained using rigid particles) [1]. The formation of these axially segregated bands of binary mixtures of different sizes in a rotating drum was first reported by Oyama [8] and has been confirmed by many later studies [9–12]. The visual observations reported that initially, in the vicinity of the ends of the drum, the probability for smaller particles to move toward the centre of the drum is higher than that of larger particles. As the process proceeds, the larger particles tend to remain in the end region while a band of smaller ones moves away from it. As noted experimentally, the origin of the band formation is in the vicinity of the two end walls. The time-dependent evolution of the segregated bands is complicated and the initiating mechanisms are poorly understood [13]. Lloyd et al. [14] reported that the equilibrium concentration distribution of the band depended on the particle system and operating conditions. The band formation mechanisms have been proposed by previous researchers. Donald and Roseman [9] proposed a theory based on the surface velocity gradients of the beads along the axial direction of the mixer and the higher acceleration of the larger particles down the slope of the bed. The surface velocity gradients of the beads originate from the different angles of repose of the components of the mixture. If the static angles of repose of the small particles are greater than that of the large particles, the axial banding occurs. They also qualitatively studied the effect of the level of fill and the speed of rotation on particle axial segregation in rotating drums using binary mixtures of rigid particles. Bridgwater et al. [10,15] suggested that the interparticle percolation and differences in void fraction are probable reasons for the formation of the bands. Fan and Shih [11] used a probability theory and the Kolmogorov diffusion equation to model the band formation. Although the concentration of the key component of the binary mixture along the axial direction of the drum was well modelled, two modelling parameters (i.e., the diffusion coefficient and drift velocity) had to be obtained experimentally and their dependencies on the operating variables were not clear. Hill and Kakalios [13] proposed a similar approach of that of Donald and Roseman [9], but they used the dynamic angles of repose to relate to the particle velocity gradients along the drum instead of the static angles of repose. They reported three classes of behaviour resulting from systematic variation of the relative diameters of the components, including no segregation, a non-reversible axial segregation and an axial segregation at high speeds (∼15 rpm) which reverses back into the mixed state at low speeds (∼5 rpm). Although informative data were obtained, the range of the rotational speed tested is relatively low for industrial applications. Computational simulation has become a useful tool to investigate segregation mechanisms in drums. However, due to the limitation of computational power, most simulation studies using the discrete element method (DEM) focused on segregation studies at a certain
Table 1 The packing and surface frictional properties for the rigid glass (G) particles and deformable rubber (R) particles Particle type
Loose density (kg/m3)
Tapped density (kg/m3)
Hausner ratio
Working density (kg/m3)
Void fraction
Friction coefficient
1 mm-G 1 mm-R 2 mm-G 2 mm-R 3 mm-G 3 mm-R 4 mm-G 4 mm-R
1495 765 1388 764 1491 767 1481 788
1607 802 1486 803 1555 800 1527 845
1.075 1.048 1.071 1.051 1.043 1.043 1.031 1.072
1503 767 1394 766 1494 768 1482 792
0.40 0.37 0.45 0.37 0.41 0.37 0.41 0.35
0.40 0.48 0.38 0.42 0.28 0.48 0.54 0.52
level of fill and at a certain rotational speed with a fixed particle size ratio (e.g., Shinbrot et al. [16]) and most of the simulation studies also considered the effect of particle size. Although as early as 1973, Williams and Khan [1] reported that particles of different sizes, densities, shapes, roughness, and elasticity showed segregation when they are mixed, most of the previous experimental studies focused on size-induced axial segregation using rigid glass beads, e.g., [11–13] and neglected the influences of other particle properties. Although some studies focused on the effect of the particle shape, for example [17,18], there is little work on density-induced, roughness-induced or non-size-induced axial segregation in the rotating drum (note: most of the density-induced segregation studies were carried out in fluidised beds and radial segregation in drums). In this work, we studied both size-induced and non-size-induced axial segregation in a rotating drum using deformable rubber particles. Non-rigid particles are common in many industries, for example, biological cells and polymer pellets. A systematic study on the equilibrium band width in a rotating drum was carried out by considering both the operational conditions and the particle properties. 2. Experimental Two cylinders made of “Perspex” acrylic were used to investigate axial segregation in the drum. In the size-induced segregation studies, the cylinder was 300 mm in length and 110 mm in internal diameter. A cylinder of length 194 mm and internal diameter 99 mm was used to study the non-size-induced segregation. The partially filled drum was placed horizontally on a pair of rollers, in a similar way to a ball mill. The rotational speed of the drum was directly controlled by the rollers. Deformable rubber particles were used to study the sizeinduced segregation. Particles of different sizes were classified and dyed with different colours. The rubber particles were classified into three size groups: 0.9–1.1 mm, 1.9–2.1 mm and 2.9–3.1 mm. The density of the particles was 1213 kg/m3 and the shore A value is 45 (i.e., the measurement of the softness of the particles frequently used in the polymer industry, from 0: completely soft; to 100: completely rigid; ASTM D2240). In the non-size-induced segregation studies, a binary mixture of the rubber particles and glass particles (density = 2521 kg/m3) of the same sizes (1, 2, 3, 4 or 5 mm) were mixed in the drum. Table 1
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observed [19–21], the quasi-steady segregated patterns after the initial growth stage are perhaps the interests of most engineers. Hence, the quasi-steady segregated patterns for 10– 20 min are used for current analysis. The band widths and locations may differ between the two reproducibility-testing runs, the average band width of each component was similar. The difference of the average band width between the two runs is typically within 0.5 cm. The widths of the bands were then measured and the average width of the band containing a high concentration of small or soft particles (i.e., the key component), WB, was obtained. The interfaces of the segregated bands were determined by eye and the errors were within approximately 1.0 cm, mainly resulting from the determination of the positions of the non-sharp interfaces. WB was divided by the diameter of the small particle and the dimensionless band width, WB/dp, was used for further comparison. 3. Results and discussion For simplification, the mixing system uses the following notation. For example, a (1 mm-R/2 mm-G) system represents a 50:50 v/v binary mixture with 1 mm rubber particles and 2 mm glass particles.
Fig. 1. Size-induced axial segregation in the rotating drum at 20% fill level and 20 rpm. Particles of light grey represent 1 mm rubber spheres and particles of dark grey represent 2 mm rubber spheres. (a) The evolution of the band formation as a function of time. (b) The distribution of the segregated particles at equilibrium.
shows the packing properties for the particles measured from a Hosokawa Powder Tester together with the surface frictional properties of the particles. The values of the void fraction are calculated from the working densities and the true densities of the particles. In a typical run, the drum was filled with a 50:50 v/v binary mixture of particles with different properties. Four speeds of rotation (i.e., 10, 20, 30 and 40 rpm) and four levels of fill were tested (i.e., 10%, 20%, 30% and 36% fill in the size-induced studies and 10%, 20%, 30% and 40% fill in the non-sizeinduced studies). A randomly mixed condition was selected as the initial state. Each operating condition was run for 30 min and repeated once to test its reproducibility. The evolution of the segregated bands was recorded by a video camera. The recording of the band formation as a function of time of a typical run is shown in Fig. 1. Although band movement and merging was observed for the binary mixtures of granular media at the beginning of each run, a quasi-steady state was obtained. In Fig. 1, after the quasi-steady segregated state was reached (i.e., 3 min after the beginning of the run), no change in the segregated pattern was observed before the end of the run. Since the long-lasting instability takes several hours to be
Fig. 2. Dimensionless band width of the key component as a function of the rotational speed of the drum at different fill levels. (a) A 50:50 v/v mixture of 1 mm and 2 mm particles; (b) a 50:50 v/v mixture of 1 mm and 3 mm particles.
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3.1. Size-induced segregation Fig. 1(a) and (b) show a typical result of a size-induced segregation run. The solid lines in Fig. 1(a) represent the evolution of the interfaces between the bands. The bands are initially observed at ca. 45 s after the beginning of the run and the steady state was reached after the first 3 min. The light grey particles are 1 mm rubber spheres and particles of dark grey indicate 2 mm rubber spheres. The bands close to the two end walls are large-particle-rich bands and this phenomenon is consistent with previous work using rigid glass beads [9,11,12]. Apparently, the total width of the small-particle-rich bands is smaller than the total width of the large-particle-rich bands. Since a 50:50 v/v binary mixture of particles with different sizes was filled in the drum and from the mass balance on the small particles, there must be small particles in the large-particle-rich bands. This is a difference from the results of rigid glass beads. In previous reports [1,12,13], the alternating bands consisted of relatively pure single concentrations. Fig. 2(a) and (b) show the dimensionless band width of the key component, WB/dp, as a function of the rotational speed of the drum at different levels of fill in the (1 mm-R/2 mm-R) system and the (1 mm-R/3 mm-R) system, respectively. There is no segregation observed at 10% level of fill in the (1 mm-R/ 3 mm-R) system. Within the error of the band width mea-
Fig. 3. Dimensionless band width of the key component as a function of the level of fill at different rotational speeds of the drum. (a) A 50:50 v/v mixture of 1 mm and 2 mm particles; (b) a 50:50 v/v mixture of 1 mm and 3 mm particles.
Table 2 The comparison of the dimensionless band width of the small particles between the rigid glass (G) beads and deformable rubber (R) beads at different operating conditions Binary system
Rotational speed
Fill level
1 mm-R/2 mm-R
WB/dp increases with rotational speed WB/dp increases with rotational speed WB/dp increases with rotational speed
WB/dp increases with respect to fill level WB/dp decreases with respect to fill level No segregation at 10% fill and WB/dp shows maximum at ca. 30% No segregation at 10%, 20%, 30% and 40% fill
1 mm-G/2 mm-G 1 mm-R/3 mm-R
1 mm-G/3 mm-G
No segregation
surement, the increase of WB/dp is proportional to the rotational speed of the drum. The influence of the fill level on the dimensionless band width of the key component, WB/dp, at different speeds of rotation in the (1 mm-R/2 mm-R) and (1 mm-R/3 mm-R) systems is shown in Fig. 3(a) and (b), respectively. WB/dp increases with the increase of the level of fill in the (1 mm-R/2 mm-R) system at 10, 20, 30 or 40 rpm. In the (1 mm-R/3 mm-R) system, there exists a fill level where WB/dp has a maximum value at 10, 20, 30 or 40 rpm. In this case, the maximum occurs at approximately 30% fill. The reason for the existence of such a maximum fill is not clear. However, the authors have found that 30% fill is a significant value. For example, in previous work, the rate of mixing in the V-mixer was reported to be at its highest when the level of fill was approximately 27% using rigid particles [22,23]. Table 2 shows the comparison between the results in Figs. 2 and 3 and those obtained using rigid glass beads of the same sizes [12]. In the (1 mm-G/2 mm-G) system, WB/dp increases with increase of the rotational speed of the drum. The dependence of the dimensionless band width of the key component on the rotational speed is similar for rigid and non-rigid particles. Nevertheless, WB/dp decreases dramatically when the level of fill increases from 10% to 20% and is independent of the fill level at levels between 20% and 40% at 10, 20, 30 or 40 rpm. In the (1 mm-G/3 mm-G) system, no segregation was observed at fill levels between 10% fill and 40% fill with rotational speed in the range between 10 rpm and 40 rpm. Segregation mechanisms include, at least, percolation, trajectory and vibrational segregation [1]. The vibrational segregation involves the rising of the large particles in a vibrator and therefore places a minor role in the drum segregation. The trajectory mechanism in the drum indicating that particles are projected with the intention of spreading them over the surface of a particle bed. The mechanism proposed by [9,13] indicating that the main reason causing particles of different angles of repose to segregate may also be regarded as the trajectory mechanism. The percolation mechanism describes the smaller particles moving downwards through the interstitial voids in a particle bed. The percolation mechanism is enhanced with the increase of the size of the interstitial voids. When non-rigid rubber particles are used, the particles deform and the interstitial voids are smaller compared to those of a rigid glass particle assembly (see Table 1). Since the sizes of the particles and the
H.P. Kuo et al. / Powder Technology 166 (2006) 161–166 Table 3 The summary of the elasticity-induced segregation in the rotating drum B Binary system
Fill level (%)
Rotational speed (rpm)
Bed configuration
1 mm-R/1 mm-G 2 mm-R/2 mm-G 3 mm-R/3 mm-G
10–40 10–40 10
10, 20, 30, and 40 10, 20, 30, and 40 10 20 30 40 10
R-rich R-rich R/G/R = 7:8:3 R/G/R = 8:8:3 R/G = 9:9 R/G = 9:9 R/G/R/G/ R = 2:2:5:2:2 R/G/R/G/R⁎ R/G/R/G/R⁎ M R-rich R-rich M M R-rich R-rich M M R/G = 9:9 R/G/R = 7:8:3 R/G/R = 7:8:3 R/G/R = 7:8:3 R/G/R/G/R* M M M M M M M M M M M
20
30
40
4 mm-R/4 mm-G
10
20
30
40
20 30 40 10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40
165
the surface of the bed (i.e., the R-rich cases) as shown in Fig. 4(a). The non-size-induced axial segregation occurs only at certain operating conditions using 3 mm or 4 mm beads at low levels of fill. When the number of the bands is 2 and 3, the interfaces between the segregated bands can be distinguished as shown in Fig. 4(b) and (c), respectively. In Fig. 4(d), five segregated bands are observed at 10 rpm. From the top view, three are rubber-rich bands and two are glass-rich bands. The rubber-rich bands are close to the two end walls, which are analogous to the largeparticle-rich bands in the size-induced segregation (Fig. 1(b)). However, the segregation patterns are different from those of sizeinduced segregation. The interfaces between the bands are less distinct. The glass particles are surrounded by the rubber particles in the (surface) rubber-rich bands. The non-size-induced segregation clearly shows a weaker segregation potential than that of the size-induced segregation using particles of similar sizes. When the speed of rotation increases, the interfaces become
R: rubber beads; G: glass beads; M: mixed; ⁎Difficult to determine the interface between segregated bands.
experimental conditions are the same, the (1 mm-R/3 mm-R) system segregates while the (1 mm-G/3 mm-G) system does not segregate suggest that large voids suppress the formation of the segregation bands in a (1 mm-G/3 mm-G) system. The results in the current study imply that percolation may not be the dominant segregation mechanism for the formation of the bands in a rotating drum. 3.2. Non-size-induced segregation Although particles with different properties other than size segregate in solids handling processes was known as early as 1973 [1], to the authors' knowledge, no published work systematically discusses non-sized-induced segregation in rotating drums. Table 3 summarises the results of the non-size-induced segregation (here, the elastiaty-induced segregation was studied) experiments using rubber particles and glass particles of 1, 2, 3, or 4 mm. When 1 or 2 mm particles are used, there is no non-sizeinduced axial segregation observed, although radial segregation is observed and the rubber particles appear at higher concentration at
Fig. 4. Elasticity-induced segregation. (a) 1 mm-R (dark grey)/1 mm-G (light grey), 10% fill, 20 rpm; (b) 3 mm-R (blue)/3 mm-G (red), 10% fill, 20 rpm; (c) 3 mm-R (blue)/3 mm-G (red), 20% fill, 20 rpm; (d) 3 mm-R (blue)/3 mm-G (red), 10% fill, 40 rpm; (e) 3 mm-R (blue)/3 mm-G (red), 20% fill, 10 rpm.
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more blurred, although the segregated bands can still be distinguished (Fig. 4(e)). Since the rubber particles and the glass particles are different in elasticity, density and surface roughness, the axial segregation may be caused by the differences in any of these properties. In order to determine the important factor(s), we mixed the rigid glass beads (density = 2521 kg/m3) with rigid stainless steel beads (density = 7700 kg/m3) of the same sizes (2, 3 or 4 mm), which have similar surface friction coefficients. No axial segregation was observed in the drum at the operating conditions listed in Table 3. The difference in elasticity is therefore the most probable cause of segregation. Although there may be other factors that cause such a phenomenon, for example, dynamic angles of repose and surface electrical charges, we can conclude that particles of the same size can show axial segregation in the drum if their elasticity values are sufficiently different. The non-size-induced segregation observation provides important information and supports our previous argument. In the size-induced experiments, we conclude that percolation may not be the dominant segregation mechanism for the formation of the bands in a rotating drum. Since the interstitial voidage of a glass–rubber mixture is smaller than that of a glass bead bed, the percolation mechanism, which is suppressed by the reduction of the interstitial voidage in the glass–rubber mixture, is even less likely to be the dominant axial segregation mechanism in a rotating drum. The existence of the non-size-induced axial segregation of the particles suggests that there must be other segregation mechanisms apart from the percolation mechanism causing the formation of the bands in a rotating drum. According to the segregation mechanisms proposed by Williams and Khan [1] and our current observation, the trajectory mechanism is considered to be the dominant axial segregation mechanism in the rotating drum. When the particles which are different in elasticity are mixed in a drum and trajectory mechanism is the dominant segregation mechanism, particles of different elasticity are spread via different paths over the surface of a particle bed. This argument is similar to the conclusions of Donald and Roseman [9] and Hill and Kakalios [13] obtained from size-induced axial segregation experiments. They suggested that the different angles of repose of the particles causes the surface velocity gradients of the beads in the axial direction of the mixer and the higher acceleration of the larger particles down the slope of the bed. In the current study, the different paths of the rubber particles and glass particles in the axial direction cause axial segregation to occur. However, because the rubber particles have a high coefficient of restitution, their paths over the surface of the particle bed are less regular compared to that of the glass beads. Therefore, the interfaces between the elasticity-induced segregation bands in the drum are less distinct compared to the interfaces between the size-induced segregation bands in the drum. 4. Conclusions Size-induced and non-size-induced segregation in a rotating drum were studied at different operating conditions using de-
formable rubber particles. Similarly to the results for rigid glass beads, the bands close to the two end walls are rich in large particles and the dimensionless band width of the small particles increases with increasing rotational speed of the drum. However, the configuration of each band is not as pure as that using rigid glass beads and the dependence of the dimensionless band width of the small particles on the fill level is different. Nonsize-induced segregation is reported using rubber beads and glass beads of the same sizes. Segregated bands are observed at low levels of fill using 3 mm or 4 mm particles. The rubber-rich bands are close to the two end walls and the interfaces between the bands are not distinct. The glass particles are surrounded by the rubber particles in the (surface) rubber-rich bands. Non-sizeinduced segregation clearly shows a weaker segregation potential than that of size-induced segregation using particles of similar sizes. The size-induced and the non-size-induced axial segregation studies imply that percolation may not be the dominated segregation mechanism for the formation of the bands in a rotating drum. According to the segregation mechanisms proposed by Williams and Khan [1], trajectory segregation is considered to be the dominant axial segregation mechanism in this case. Acknowledgement The authors are grateful for the financial support from National Science Council of the Republic of China (NSC91-2218-E-182007). References [1] J.C. Williams, M.I. Khan, Chem. Eng. (Jan 1973) 19. [2] T. Shinbrot, F.J. Muzzio, J. Phys. Today (Mar 2000) 25. [3] H. Henein, J.K. Brimacombe, A.P. Watkinson, Metall. Trans., B, Process Metall. 16B (1985) 763. [4] S.B. Savage, C.K.K. Lun, J. Fluid Mech. 189 (1988) 311. [5] N. Nityanand, B. Manley, H. Henein, Metall. Trans., B, Process Metall. 17B (1986) 247. [6] N. Thomas, Phys. Rev., E 62 (2000) 961. [7] D.V. Khakhar, A.V. Orpe, S.K. Hajra, Physica, A 318 (2003) 129. [8] Y. Oyama, Bull. Inst. Phys. Chem. Res. (Tokyo), Rep. 5 (1939) 600. [9] M.B. Donald, B. Roseman, Chem. Eng. 7 (1962) 749. [10] J. Bridgwater, N.W. Sharpe, D.C. Stocker, Trans. IChemE 47 (1969) T114–T119. [11] L.T. Fan, S.H. Shih, Chem. Eng. Sci 34 (1979) 811. [12] H.P. Kuo, R.C. Hsu, Y.C. Hsiao, Powder Technol. 153 (2005) 196. [13] K.M. Hill, J. Kakalios, Phys. Rev., E 52 (1995) 4393. [14] P.J. Lloyd, P.C.M. Yeung, D.C. Freshwater, J. Soc. Cosmetic Chem. 21 (1970) 205. [15] J. Bridgwater, Powder Technol. 15 (1976) 215. [16] T. Shinbrot, M. Zeggio, F.J. Muzzio, Powder Technol. 116 (2001) 224. [17] M. Furuuchi, K. Gotoh, Powder Technol. 54 (1988) 31. [18] M. Furuuchi, C. Yamada, Powder Technol. 75 (1993) 113. [19] O. Zik, D. Levine, S.G. Lipson, S. Shtrikman, J. Stavans, Phys. Rev. Lett. 73 (1994) 644. [20] K. Choo, T.C.A. Molteno, S.W. Morris, Phys. Rev. Lett. 79 (1997) 2975. [21] H. Caps, R. Michel, N. Lecocq, N. Vandewalle, Physica, A 326 (2003) 313. [22] G. Metcalfe, T. Shinbrot, J.J. McCarthy, J.M. Ottino, Nature 374 (1995) 39. [23] H.P. Kuo, A.S. Burbidge, D.J. Parker, Y. Tsuji and J.P.K. Seville, AIChE Journal. submitted for publication.
A study of the axial segregation in a rotating drum using deformable particles H.P. Kuo ⁎, Y.C. Hsiao, P.Y. Shih Department of Chemical and Materials Engineering, Chang Gung University, Tao-Yuan, 333, Taiwan Received 29 September 2004; received in revised form 1 April 2006 Available online 7 June 2006
Abstract A binary mixture of particles is utilized to investigate size-induced and non-size-induced axial segregation in a rotating drum using deformable 1 mm rubber particles as the key component. In the size-induced segregation studies, the dimensionless band width (width of segregation band divided by particle size) of the small particles (WB/dp) increases in proportion to the rotational speed in the range of 10 rpm to 40 rpm when the fill level is between 10% and 36%. WB/dp increases as the fill level increases from 10% to 36% with a particle size ratio 2 and has a maximum value with a particle size ratio 3. In the non-size-induced segregation studies, segregated bands are observed in (3 mm rubber–3 mm glass) and (4 mm rubber–4 mm glass) systems with low fill levels. There is no axial segregation when 1 mm and 2 mm rubber particles are mixed with 1 mm and 2 mm glass particles, respectively. The non-size-induced segregation bands were different from the size-induced segregation bands. The bands are less pure and the interfaces are less distinct. The results suggest that trajectory segregation is the dominant segregation mechanism in axial segregation in drums. © 2006 Elsevier B.V. All rights reserved. Keywords: Segregation; Rotating drum; Binary mixture; Non-size-induced segregation
1. Introduction Solids mixing is a common operation in many industries, for example, in the manufacture of pharmaceuticals, food, ceramics and polymers. The rotating drum is one of the most common devices for solids mixing, especially for the mixing of brittle particles due to the gentle particle motion in the drum and for the requirement of limited contamination between different batch operations due to its ease of cleaning. Other applications of rotating drums include granulation, drying and reaction. However, when particles of different properties are processed in a rotating drum, particle segregation often occurs and causes nonuniformity of the products. Williams and Khan [1] reported that particles of different sizes, densities, shapes, roughness, and elasticity showed segregation when they are mixed. Most of the previous studies focused on size-induced segregation. When a binary mixture of two sizes of glass beads was mixed in a tumbler, detectable segregation occurred for a diameter ratio of 1.2 to 2.5 [1]. Size segregation in a rotating drum typically occurs in two ⁎ Corresponding author. Tel.: +886 3 2118800x5488; fax: +886 3 2118668. E-mail address: [email protected] (H.P. Kuo). 0032-5910/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2006.05.016
stages: first, large particles rapidly segregate radially, fine particles producing a central core and are surrounded by large particles; next, particles in the core migrate along the axial direction of drum until the core extends axially for the length of the drum [2]. Radial size segregation and radial density segregation in a drum have been studied. Radial segregation usually results in the small (or high density) particles concentrating in a central core and the large (or low density) particles in the periphery [1,3]. In the radial direction, the flow consists of a thin surface flow zone and a rotating solid body bed zone. Savage and Lun [4] proposed a radial segregation mechanism based on different particle motion in two flow zones. Small particles percolate in the surface flow zone. A constant bulk density upward flux assumption resulting in a net downward flux of the small particles and a net upward flux of the large particles. The differences in the net flux between the particles of difference sizes cause radial segregation. Radial segregation pattern could reverse at high rotational speed [5]. Thomas [6] proposed that reverse segregation occurs when the large particles are massive enough to move down by pushing aside the small particles. Khakhar et al. [7] applied the hard sphere theory to model radial
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segregation in a drum and reasonable predicted density segregation in a drum, but the prediction on size segregation disagreed with the experimental observation. They proposed a new model based on dynamic variation of flow, composition and surface angle, which gave a qualitative description of the radial segregation process. Axial size segregation shows that the individual species segregate into alternate bands of relatively pure single concentrations (note: the conclusion was obtained using rigid particles) [1]. The formation of these axially segregated bands of binary mixtures of different sizes in a rotating drum was first reported by Oyama [8] and has been confirmed by many later studies [9–12]. The visual observations reported that initially, in the vicinity of the ends of the drum, the probability for smaller particles to move toward the centre of the drum is higher than that of larger particles. As the process proceeds, the larger particles tend to remain in the end region while a band of smaller ones moves away from it. As noted experimentally, the origin of the band formation is in the vicinity of the two end walls. The time-dependent evolution of the segregated bands is complicated and the initiating mechanisms are poorly understood [13]. Lloyd et al. [14] reported that the equilibrium concentration distribution of the band depended on the particle system and operating conditions. The band formation mechanisms have been proposed by previous researchers. Donald and Roseman [9] proposed a theory based on the surface velocity gradients of the beads along the axial direction of the mixer and the higher acceleration of the larger particles down the slope of the bed. The surface velocity gradients of the beads originate from the different angles of repose of the components of the mixture. If the static angles of repose of the small particles are greater than that of the large particles, the axial banding occurs. They also qualitatively studied the effect of the level of fill and the speed of rotation on particle axial segregation in rotating drums using binary mixtures of rigid particles. Bridgwater et al. [10,15] suggested that the interparticle percolation and differences in void fraction are probable reasons for the formation of the bands. Fan and Shih [11] used a probability theory and the Kolmogorov diffusion equation to model the band formation. Although the concentration of the key component of the binary mixture along the axial direction of the drum was well modelled, two modelling parameters (i.e., the diffusion coefficient and drift velocity) had to be obtained experimentally and their dependencies on the operating variables were not clear. Hill and Kakalios [13] proposed a similar approach of that of Donald and Roseman [9], but they used the dynamic angles of repose to relate to the particle velocity gradients along the drum instead of the static angles of repose. They reported three classes of behaviour resulting from systematic variation of the relative diameters of the components, including no segregation, a non-reversible axial segregation and an axial segregation at high speeds (∼15 rpm) which reverses back into the mixed state at low speeds (∼5 rpm). Although informative data were obtained, the range of the rotational speed tested is relatively low for industrial applications. Computational simulation has become a useful tool to investigate segregation mechanisms in drums. However, due to the limitation of computational power, most simulation studies using the discrete element method (DEM) focused on segregation studies at a certain
Table 1 The packing and surface frictional properties for the rigid glass (G) particles and deformable rubber (R) particles Particle type
Loose density (kg/m3)
Tapped density (kg/m3)
Hausner ratio
Working density (kg/m3)
Void fraction
Friction coefficient
1 mm-G 1 mm-R 2 mm-G 2 mm-R 3 mm-G 3 mm-R 4 mm-G 4 mm-R
1495 765 1388 764 1491 767 1481 788
1607 802 1486 803 1555 800 1527 845
1.075 1.048 1.071 1.051 1.043 1.043 1.031 1.072
1503 767 1394 766 1494 768 1482 792
0.40 0.37 0.45 0.37 0.41 0.37 0.41 0.35
0.40 0.48 0.38 0.42 0.28 0.48 0.54 0.52
level of fill and at a certain rotational speed with a fixed particle size ratio (e.g., Shinbrot et al. [16]) and most of the simulation studies also considered the effect of particle size. Although as early as 1973, Williams and Khan [1] reported that particles of different sizes, densities, shapes, roughness, and elasticity showed segregation when they are mixed, most of the previous experimental studies focused on size-induced axial segregation using rigid glass beads, e.g., [11–13] and neglected the influences of other particle properties. Although some studies focused on the effect of the particle shape, for example [17,18], there is little work on density-induced, roughness-induced or non-size-induced axial segregation in the rotating drum (note: most of the density-induced segregation studies were carried out in fluidised beds and radial segregation in drums). In this work, we studied both size-induced and non-size-induced axial segregation in a rotating drum using deformable rubber particles. Non-rigid particles are common in many industries, for example, biological cells and polymer pellets. A systematic study on the equilibrium band width in a rotating drum was carried out by considering both the operational conditions and the particle properties. 2. Experimental Two cylinders made of “Perspex” acrylic were used to investigate axial segregation in the drum. In the size-induced segregation studies, the cylinder was 300 mm in length and 110 mm in internal diameter. A cylinder of length 194 mm and internal diameter 99 mm was used to study the non-size-induced segregation. The partially filled drum was placed horizontally on a pair of rollers, in a similar way to a ball mill. The rotational speed of the drum was directly controlled by the rollers. Deformable rubber particles were used to study the sizeinduced segregation. Particles of different sizes were classified and dyed with different colours. The rubber particles were classified into three size groups: 0.9–1.1 mm, 1.9–2.1 mm and 2.9–3.1 mm. The density of the particles was 1213 kg/m3 and the shore A value is 45 (i.e., the measurement of the softness of the particles frequently used in the polymer industry, from 0: completely soft; to 100: completely rigid; ASTM D2240). In the non-size-induced segregation studies, a binary mixture of the rubber particles and glass particles (density = 2521 kg/m3) of the same sizes (1, 2, 3, 4 or 5 mm) were mixed in the drum. Table 1
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observed [19–21], the quasi-steady segregated patterns after the initial growth stage are perhaps the interests of most engineers. Hence, the quasi-steady segregated patterns for 10– 20 min are used for current analysis. The band widths and locations may differ between the two reproducibility-testing runs, the average band width of each component was similar. The difference of the average band width between the two runs is typically within 0.5 cm. The widths of the bands were then measured and the average width of the band containing a high concentration of small or soft particles (i.e., the key component), WB, was obtained. The interfaces of the segregated bands were determined by eye and the errors were within approximately 1.0 cm, mainly resulting from the determination of the positions of the non-sharp interfaces. WB was divided by the diameter of the small particle and the dimensionless band width, WB/dp, was used for further comparison. 3. Results and discussion For simplification, the mixing system uses the following notation. For example, a (1 mm-R/2 mm-G) system represents a 50:50 v/v binary mixture with 1 mm rubber particles and 2 mm glass particles.
Fig. 1. Size-induced axial segregation in the rotating drum at 20% fill level and 20 rpm. Particles of light grey represent 1 mm rubber spheres and particles of dark grey represent 2 mm rubber spheres. (a) The evolution of the band formation as a function of time. (b) The distribution of the segregated particles at equilibrium.
shows the packing properties for the particles measured from a Hosokawa Powder Tester together with the surface frictional properties of the particles. The values of the void fraction are calculated from the working densities and the true densities of the particles. In a typical run, the drum was filled with a 50:50 v/v binary mixture of particles with different properties. Four speeds of rotation (i.e., 10, 20, 30 and 40 rpm) and four levels of fill were tested (i.e., 10%, 20%, 30% and 36% fill in the size-induced studies and 10%, 20%, 30% and 40% fill in the non-sizeinduced studies). A randomly mixed condition was selected as the initial state. Each operating condition was run for 30 min and repeated once to test its reproducibility. The evolution of the segregated bands was recorded by a video camera. The recording of the band formation as a function of time of a typical run is shown in Fig. 1. Although band movement and merging was observed for the binary mixtures of granular media at the beginning of each run, a quasi-steady state was obtained. In Fig. 1, after the quasi-steady segregated state was reached (i.e., 3 min after the beginning of the run), no change in the segregated pattern was observed before the end of the run. Since the long-lasting instability takes several hours to be
Fig. 2. Dimensionless band width of the key component as a function of the rotational speed of the drum at different fill levels. (a) A 50:50 v/v mixture of 1 mm and 2 mm particles; (b) a 50:50 v/v mixture of 1 mm and 3 mm particles.
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3.1. Size-induced segregation Fig. 1(a) and (b) show a typical result of a size-induced segregation run. The solid lines in Fig. 1(a) represent the evolution of the interfaces between the bands. The bands are initially observed at ca. 45 s after the beginning of the run and the steady state was reached after the first 3 min. The light grey particles are 1 mm rubber spheres and particles of dark grey indicate 2 mm rubber spheres. The bands close to the two end walls are large-particle-rich bands and this phenomenon is consistent with previous work using rigid glass beads [9,11,12]. Apparently, the total width of the small-particle-rich bands is smaller than the total width of the large-particle-rich bands. Since a 50:50 v/v binary mixture of particles with different sizes was filled in the drum and from the mass balance on the small particles, there must be small particles in the large-particle-rich bands. This is a difference from the results of rigid glass beads. In previous reports [1,12,13], the alternating bands consisted of relatively pure single concentrations. Fig. 2(a) and (b) show the dimensionless band width of the key component, WB/dp, as a function of the rotational speed of the drum at different levels of fill in the (1 mm-R/2 mm-R) system and the (1 mm-R/3 mm-R) system, respectively. There is no segregation observed at 10% level of fill in the (1 mm-R/ 3 mm-R) system. Within the error of the band width mea-
Fig. 3. Dimensionless band width of the key component as a function of the level of fill at different rotational speeds of the drum. (a) A 50:50 v/v mixture of 1 mm and 2 mm particles; (b) a 50:50 v/v mixture of 1 mm and 3 mm particles.
Table 2 The comparison of the dimensionless band width of the small particles between the rigid glass (G) beads and deformable rubber (R) beads at different operating conditions Binary system
Rotational speed
Fill level
1 mm-R/2 mm-R
WB/dp increases with rotational speed WB/dp increases with rotational speed WB/dp increases with rotational speed
WB/dp increases with respect to fill level WB/dp decreases with respect to fill level No segregation at 10% fill and WB/dp shows maximum at ca. 30% No segregation at 10%, 20%, 30% and 40% fill
1 mm-G/2 mm-G 1 mm-R/3 mm-R
1 mm-G/3 mm-G
No segregation
surement, the increase of WB/dp is proportional to the rotational speed of the drum. The influence of the fill level on the dimensionless band width of the key component, WB/dp, at different speeds of rotation in the (1 mm-R/2 mm-R) and (1 mm-R/3 mm-R) systems is shown in Fig. 3(a) and (b), respectively. WB/dp increases with the increase of the level of fill in the (1 mm-R/2 mm-R) system at 10, 20, 30 or 40 rpm. In the (1 mm-R/3 mm-R) system, there exists a fill level where WB/dp has a maximum value at 10, 20, 30 or 40 rpm. In this case, the maximum occurs at approximately 30% fill. The reason for the existence of such a maximum fill is not clear. However, the authors have found that 30% fill is a significant value. For example, in previous work, the rate of mixing in the V-mixer was reported to be at its highest when the level of fill was approximately 27% using rigid particles [22,23]. Table 2 shows the comparison between the results in Figs. 2 and 3 and those obtained using rigid glass beads of the same sizes [12]. In the (1 mm-G/2 mm-G) system, WB/dp increases with increase of the rotational speed of the drum. The dependence of the dimensionless band width of the key component on the rotational speed is similar for rigid and non-rigid particles. Nevertheless, WB/dp decreases dramatically when the level of fill increases from 10% to 20% and is independent of the fill level at levels between 20% and 40% at 10, 20, 30 or 40 rpm. In the (1 mm-G/3 mm-G) system, no segregation was observed at fill levels between 10% fill and 40% fill with rotational speed in the range between 10 rpm and 40 rpm. Segregation mechanisms include, at least, percolation, trajectory and vibrational segregation [1]. The vibrational segregation involves the rising of the large particles in a vibrator and therefore places a minor role in the drum segregation. The trajectory mechanism in the drum indicating that particles are projected with the intention of spreading them over the surface of a particle bed. The mechanism proposed by [9,13] indicating that the main reason causing particles of different angles of repose to segregate may also be regarded as the trajectory mechanism. The percolation mechanism describes the smaller particles moving downwards through the interstitial voids in a particle bed. The percolation mechanism is enhanced with the increase of the size of the interstitial voids. When non-rigid rubber particles are used, the particles deform and the interstitial voids are smaller compared to those of a rigid glass particle assembly (see Table 1). Since the sizes of the particles and the
H.P. Kuo et al. / Powder Technology 166 (2006) 161–166 Table 3 The summary of the elasticity-induced segregation in the rotating drum B Binary system
Fill level (%)
Rotational speed (rpm)
Bed configuration
1 mm-R/1 mm-G 2 mm-R/2 mm-G 3 mm-R/3 mm-G
10–40 10–40 10
10, 20, 30, and 40 10, 20, 30, and 40 10 20 30 40 10
R-rich R-rich R/G/R = 7:8:3 R/G/R = 8:8:3 R/G = 9:9 R/G = 9:9 R/G/R/G/ R = 2:2:5:2:2 R/G/R/G/R⁎ R/G/R/G/R⁎ M R-rich R-rich M M R-rich R-rich M M R/G = 9:9 R/G/R = 7:8:3 R/G/R = 7:8:3 R/G/R = 7:8:3 R/G/R/G/R* M M M M M M M M M M M
20
30
40
4 mm-R/4 mm-G
10
20
30
40
20 30 40 10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40
165
the surface of the bed (i.e., the R-rich cases) as shown in Fig. 4(a). The non-size-induced axial segregation occurs only at certain operating conditions using 3 mm or 4 mm beads at low levels of fill. When the number of the bands is 2 and 3, the interfaces between the segregated bands can be distinguished as shown in Fig. 4(b) and (c), respectively. In Fig. 4(d), five segregated bands are observed at 10 rpm. From the top view, three are rubber-rich bands and two are glass-rich bands. The rubber-rich bands are close to the two end walls, which are analogous to the largeparticle-rich bands in the size-induced segregation (Fig. 1(b)). However, the segregation patterns are different from those of sizeinduced segregation. The interfaces between the bands are less distinct. The glass particles are surrounded by the rubber particles in the (surface) rubber-rich bands. The non-size-induced segregation clearly shows a weaker segregation potential than that of the size-induced segregation using particles of similar sizes. When the speed of rotation increases, the interfaces become
R: rubber beads; G: glass beads; M: mixed; ⁎Difficult to determine the interface between segregated bands.
experimental conditions are the same, the (1 mm-R/3 mm-R) system segregates while the (1 mm-G/3 mm-G) system does not segregate suggest that large voids suppress the formation of the segregation bands in a (1 mm-G/3 mm-G) system. The results in the current study imply that percolation may not be the dominant segregation mechanism for the formation of the bands in a rotating drum. 3.2. Non-size-induced segregation Although particles with different properties other than size segregate in solids handling processes was known as early as 1973 [1], to the authors' knowledge, no published work systematically discusses non-sized-induced segregation in rotating drums. Table 3 summarises the results of the non-size-induced segregation (here, the elastiaty-induced segregation was studied) experiments using rubber particles and glass particles of 1, 2, 3, or 4 mm. When 1 or 2 mm particles are used, there is no non-sizeinduced axial segregation observed, although radial segregation is observed and the rubber particles appear at higher concentration at
Fig. 4. Elasticity-induced segregation. (a) 1 mm-R (dark grey)/1 mm-G (light grey), 10% fill, 20 rpm; (b) 3 mm-R (blue)/3 mm-G (red), 10% fill, 20 rpm; (c) 3 mm-R (blue)/3 mm-G (red), 20% fill, 20 rpm; (d) 3 mm-R (blue)/3 mm-G (red), 10% fill, 40 rpm; (e) 3 mm-R (blue)/3 mm-G (red), 20% fill, 10 rpm.
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more blurred, although the segregated bands can still be distinguished (Fig. 4(e)). Since the rubber particles and the glass particles are different in elasticity, density and surface roughness, the axial segregation may be caused by the differences in any of these properties. In order to determine the important factor(s), we mixed the rigid glass beads (density = 2521 kg/m3) with rigid stainless steel beads (density = 7700 kg/m3) of the same sizes (2, 3 or 4 mm), which have similar surface friction coefficients. No axial segregation was observed in the drum at the operating conditions listed in Table 3. The difference in elasticity is therefore the most probable cause of segregation. Although there may be other factors that cause such a phenomenon, for example, dynamic angles of repose and surface electrical charges, we can conclude that particles of the same size can show axial segregation in the drum if their elasticity values are sufficiently different. The non-size-induced segregation observation provides important information and supports our previous argument. In the size-induced experiments, we conclude that percolation may not be the dominant segregation mechanism for the formation of the bands in a rotating drum. Since the interstitial voidage of a glass–rubber mixture is smaller than that of a glass bead bed, the percolation mechanism, which is suppressed by the reduction of the interstitial voidage in the glass–rubber mixture, is even less likely to be the dominant axial segregation mechanism in a rotating drum. The existence of the non-size-induced axial segregation of the particles suggests that there must be other segregation mechanisms apart from the percolation mechanism causing the formation of the bands in a rotating drum. According to the segregation mechanisms proposed by Williams and Khan [1] and our current observation, the trajectory mechanism is considered to be the dominant axial segregation mechanism in the rotating drum. When the particles which are different in elasticity are mixed in a drum and trajectory mechanism is the dominant segregation mechanism, particles of different elasticity are spread via different paths over the surface of a particle bed. This argument is similar to the conclusions of Donald and Roseman [9] and Hill and Kakalios [13] obtained from size-induced axial segregation experiments. They suggested that the different angles of repose of the particles causes the surface velocity gradients of the beads in the axial direction of the mixer and the higher acceleration of the larger particles down the slope of the bed. In the current study, the different paths of the rubber particles and glass particles in the axial direction cause axial segregation to occur. However, because the rubber particles have a high coefficient of restitution, their paths over the surface of the particle bed are less regular compared to that of the glass beads. Therefore, the interfaces between the elasticity-induced segregation bands in the drum are less distinct compared to the interfaces between the size-induced segregation bands in the drum. 4. Conclusions Size-induced and non-size-induced segregation in a rotating drum were studied at different operating conditions using de-
formable rubber particles. Similarly to the results for rigid glass beads, the bands close to the two end walls are rich in large particles and the dimensionless band width of the small particles increases with increasing rotational speed of the drum. However, the configuration of each band is not as pure as that using rigid glass beads and the dependence of the dimensionless band width of the small particles on the fill level is different. Nonsize-induced segregation is reported using rubber beads and glass beads of the same sizes. Segregated bands are observed at low levels of fill using 3 mm or 4 mm particles. The rubber-rich bands are close to the two end walls and the interfaces between the bands are not distinct. The glass particles are surrounded by the rubber particles in the (surface) rubber-rich bands. Non-sizeinduced segregation clearly shows a weaker segregation potential than that of size-induced segregation using particles of similar sizes. The size-induced and the non-size-induced axial segregation studies imply that percolation may not be the dominated segregation mechanism for the formation of the bands in a rotating drum. According to the segregation mechanisms proposed by Williams and Khan [1], trajectory segregation is considered to be the dominant axial segregation mechanism in this case. Acknowledgement The authors are grateful for the financial support from National Science Council of the Republic of China (NSC91-2218-E-182007). References [1] J.C. Williams, M.I. Khan, Chem. Eng. (Jan 1973) 19. [2] T. Shinbrot, F.J. Muzzio, J. Phys. Today (Mar 2000) 25. [3] H. Henein, J.K. Brimacombe, A.P. Watkinson, Metall. Trans., B, Process Metall. 16B (1985) 763. [4] S.B. Savage, C.K.K. Lun, J. Fluid Mech. 189 (1988) 311. [5] N. Nityanand, B. Manley, H. Henein, Metall. Trans., B, Process Metall. 17B (1986) 247. [6] N. Thomas, Phys. Rev., E 62 (2000) 961. [7] D.V. Khakhar, A.V. Orpe, S.K. Hajra, Physica, A 318 (2003) 129. [8] Y. Oyama, Bull. Inst. Phys. Chem. Res. (Tokyo), Rep. 5 (1939) 600. [9] M.B. Donald, B. Roseman, Chem. Eng. 7 (1962) 749. [10] J. Bridgwater, N.W. Sharpe, D.C. Stocker, Trans. IChemE 47 (1969) T114–T119. [11] L.T. Fan, S.H. Shih, Chem. Eng. Sci 34 (1979) 811. [12] H.P. Kuo, R.C. Hsu, Y.C. Hsiao, Powder Technol. 153 (2005) 196. [13] K.M. Hill, J. Kakalios, Phys. Rev., E 52 (1995) 4393. [14] P.J. Lloyd, P.C.M. Yeung, D.C. Freshwater, J. Soc. Cosmetic Chem. 21 (1970) 205. [15] J. Bridgwater, Powder Technol. 15 (1976) 215. [16] T. Shinbrot, M. Zeggio, F.J. Muzzio, Powder Technol. 116 (2001) 224. [17] M. Furuuchi, K. Gotoh, Powder Technol. 54 (1988) 31. [18] M. Furuuchi, C. Yamada, Powder Technol. 75 (1993) 113. [19] O. Zik, D. Levine, S.G. Lipson, S. Shtrikman, J. Stavans, Phys. Rev. Lett. 73 (1994) 644. [20] K. Choo, T.C.A. Molteno, S.W. Morris, Phys. Rev. Lett. 79 (1997) 2975. [21] H. Caps, R. Michel, N. Lecocq, N. Vandewalle, Physica, A 326 (2003) 313. [22] G. Metcalfe, T. Shinbrot, J.J. McCarthy, J.M. Ottino, Nature 374 (1995) 39. [23] H.P. Kuo, A.S. Burbidge, D.J. Parker, Y. Tsuji and J.P.K. Seville, AIChE Journal. submitted for publication.