The granular mixing in a slurry rotating drum

Transcription

1 The granular mixing in a slurry rotating drum C. C. Liao and S. S. Hsiau Department of Mechanical Engineering National Central University Jhong-Li, Taiwan 321, R.O.C. Abstract The mixing dynamics of granular materials immersed in a liquid was experimentally studied in a quasi-2d rotating drum. A DV (SONY DCR-TRV9 NTSC) motion corder analyzer was used to record the motions of granular materials. The effects of interstitial fluid viscosity and filling degree on the mixing index, mixing rate constant, and dynamic repose angle in the rotating drum were investigated and discussed in this paper. The experimental results show that the interstitial fluid viscosity has almost not influence on the final stable mixing index but has significantly effects on the mixing rate constant and dynamic repose angle in slurry granular flows. The results show that the mixing rate and dynamic repose angle increase with increasing the interstitial fluid viscosity. The results also indicate that the filling degree plays an important role in mixing dynamics in slurry granular flows. The mixing rate constant is demonstrated to be decreased with increasing the filling degree. The dynamic repose angle is not altered by the filling degree. Finally, we find that the dynamic repose angle and the mixing rate constant increase slightly at high Stokes number and increase dramatically at low Stokes number with decreasing Stokes number. Keywords: rotating drum, granular mixing, interstitial fluid, mixing rate, filling degree sshsiau@cc.ncu.edu.tw; phone: ; fax: ; 1. INTRODUCTION Granular materials (e.g. sand, glass, coffee beans, pills, salt, etc.) are widely found in nature and it is important to understand granular materials in many environmental problems such as landslides, sediment transport, dune migration, and debris flow. Granular materials are also used in many industries extensively, such as pharmaceutical engineering, polymer, and chemical engineering. Rotating drums are used in chemical, pharmaceutical, and mechanical industrial engineering for processing granular materials, such as for mixing, granulation, segregation, coating and drying. Rotating drums are also widely used to investigate the mechanics and physical properties of granular flows in the past years [1-6]. There are two important flow regions existing in the rotating drum: the thin flowing layer region and the fixed bed region. The physical mechanisms mainly occur in the flowing layer. Depending on the rotation speed, filling degree, drum diameter, six different flowing regimes may occur: slipping, slumping, rolling, cascading, cataracting and centrifuging [4-5]. When a drum partially filled with granular materials is rotated around its horizontal axis, the particles participate in this rotating as a part of a rigid body until they reach their maximum angle of repose θ m then roll down the pitched surface. Continually the particles return into the fixed bed region and a new cycle starts when they reach their dynamic repose angle θ r < θ m. The dynamic repose angle is influenced by the size of drum, the size of particle, the rotating speed, the cohesive force between particles and the roughness of particles [6-1]. The mixing dynamics of granular materials is important in many industries. Better knowledge of mixing mechanism could ensure how to choose the optimal operating conditions, therefore saving time, energy, and obtaining the better products. Thus, it is important to understand the mixing mechanism. Lu and Hsiau [11] indicated that the mixing rate constants increase with the increasing electrostatic force in a vertical vibration bed by DEM (Discrete Element Method). Jain et al. [12] studied the mixing and segregation by combining the size and density effects of particles in the rotating drum. The mechanism of mixing in dry granular systems has been widely discussed and indicated that the rotating speed, filling ratio, shape of particles and shape of the rotating drum had significant influence on the mixing dynamics [13-17]. The cohesive force resulting from liquid bridges between particles strongly affect the mixing dynamics in wet granular materials [18].

2 The liquid bridges force and the electrostatic force have significant influences on the mechanism of granular materials and cause serious problems in many industries. However, the effect of liquid bridges force and the electrostatic force are less important in slurry systems. In technological and industrial processes, there are many applications include the handling of dredging slurries and fresh concrete using slurry granular materials with liquid as the interstitial fluid. However the slurry system received relatively less attention in past years especially the study of the influence of interstitial fluid on mixing dynamics. Finger and Stannarius [19] investigated the effect of the interstitial fluid viscosity in a horizontally rotating mixer. They found that the interstitial fluid viscosity played a crucial role in the pattern dynamics and the structure of the segregation patterns. They also indicated that the density effect of interstitial fluid does not influence the formation and evolution of segregation patterns of the granular materials. Pont et al. [2] studied the dynamics of granular avalanches in fluids. They found that the amplitudes of avalanches were constant at high Stoke number and decrease at low Stoke number. Liao and Hsiau [21] demonstrated that the self-diffusion coefficients and granular temperatures were smaller as the interstitial fluid was more viscous resulting in the larger viscous force. However, Jain et al. [22] indicated that the flow behavior of granular materials in a quasi-2d rotating drum remained similar with interstitial fluids of air, pure water, and glycerin-water mixtures and demonstrated that the viscosity of the interstitial fluid had very little influence on the physical mechanisms of the granular flow. In this paper we have performed an extensive series of experiments to investigate the influence of the interstitial fluid viscosity on the mixing dynamics in a slurry rotating drum. The effect of filling degree on the mixing dynamics in slurry systems is also studied. The time evolutions of mixing index, mixing rate constant and dynamic repose angle are discussed in this study. 2. EXPERIMENTAL PROCEDURE The quasi-2d rotating drum is shown schematically in Fig. 1(a), where the diameter of the drum is 2 cm, the axial gap width of the drum is 2.5 cm, the dynamic repose angle is denoted by θ r in Fig. 1(a). The dimensionless axial thickness of the drum, defined as the ratio of the axial gap width of the drum and the particle diameter, was set to 8.33 to avoid wall effect in this study [2]. We used mono sized glass beads as granular materials and the diameter of glass beads is 3 mm with standard deviation of.9 mm and the glass bead density ρ p of g/cm 3. The volume fraction of the white and black glass beads was 5% - 5%. The snapshot of initial loading of particles is shown in Fig. 1(b). The white glass beads are on the bottom and black glass beads are on the top. The front and back faceplates of the rotating drum were made of transparent plexiglass to permit optical access. A black paper was adhered to the back surface of the rotating drum to minimize the optical noise effect in the digital images. (a) (b) Figure 1(a). The skeleton diagram of the rotating drum, (b) the snapshot of the initial loading particle. In this study, we used water-glycerin mixture as the interstitial fluid in slurry systems and the weight concentration of glycerin ranged between % and 85%. The corresponding interstitial fluid viscosity µ varies from 1 to 19 cp at room temperature (2 ). There was a small hole in the top of rotating drum to permit liquid to be injected into the drum. After the rotating drum is completely filled with the interstitial liquid, the hole is sealed. A dry system using air as the interstitial fluid is a reference test in this study. The rotating speed of the drum is driven by a server motor. The rotating speed was fixed as 2.3 rpm and corresponding to a Froude number, F r = Rω 2 / g, where ω is the rotating speed of the

3 drum, R is the radius of the drum and g is the acceleration of gravity are Four different filling degrees (4%, 5%, 6%, 75%) were also used to study the mixing dynamics in the slurry rotating drum. A DV (SONY DCR-TRV9 NTSC) motion corder analyzer was used to record the flow motions inside the drum with a grabbing speed of 3 frames per second and a resolution of 8 6 pixels. Employing image processing technology, the frames were digitized to gray levels ranging from to 255 due to the different colors of the tracer particles and background particles [23]. The frames are analyzed by thresholding of the intensities to identify each type of particles [25]. The local concentrations and the mixing index are then calculated. The mixing index was defined as: M = N i= 1 ( C C N 1 avg ) 2, (1) where N is the total bins occupied by the total particles (each bin size are 2 2 pixels in this study), C is the volume concentration of the white particles in each bin and C avg is the average volume concentration of the white particles in the entire area [24-27]. The intensity of mixing is between and.5. If the particles are completely mixed, the mixing index is. The mixing index is.5 for a completely segregated system. By tracing the variation of mixing index, we can get a clearly and completely about mixing dynamic evolution in the granular system. The Stokes number (St) is a dimensionless parameter which prescribes the relative importance of particle inertia and fluid viscous effects which govern the particle dynamics in fluids [2]. ( ρg sinθ ) 1/ 2 1/ 2 3/ 2 ρ p r d p St = (2) 18 2µ where ρ p is the particle density, ρ = ρ p ρ f and ρ f is the interstitial fluid density, g is the acceleration of gravity, d p is the particle diameter and µ is the viscosity of interstitial fluid. 3. RESULTS AND DISCUSSIONS Figure 2 shows the mixing index M variation with rotating time for different interstitial fluid viscosity using F r = and 5% filling degree. Due to the initially completely segregated loading configuration, the mixing index at t = is.5. It shows that the mixing index gradually decreases with time and reaches a stable value, M s for all cases. It also shows that the interstitial fluid viscosity has no influence on the final stable mixing index. M s are almost the same (about at.18) in different interstitial fluid viscosity. The interactions between particles are mitigated due to the viscous force using liquid as the interstitial fluid. The viscous force is larger with the more viscous liquid as the interstitial fluid resulting in the smaller particle motions and diffusions. However, the particle motions and diffusions are affected by the similar force in each case. Therefore the final stable mixing index is similar as observed in Fig. 2. From the time evolutions of mixing index in Fig. 2, we found that the mixing indexes decrease exponentially with time as they approach the final stable values for all cases.

4 Mixing index air pure water 6% glycerin 7% glycerin 75% glycerin 8% glycerin 85% glycerin Time (second) Figure 2. The variation of mixing index with rotating time for different interstitial fluid viscosity. The stage from initial completely segregating state to the stable mixing condition could be called as the initial mixing stage and we could analyze the mixing speed in this stage. From Fig. 2, the initial mixing stage could be fitted to the exponential equations of the form: M M = ( M M )exp( kt) (3) s s where M is the initial mixing index (M =.5 in this study), M s is the final stable mixing index, t is the rotating time and k is the mixing rate constant, which can be used to quantify the mixing speed in the initial mixing stage. The experimental data of -water and 85% glycerin-water in Fig. 2 was redrawn in Fig. 3(a) in which the mixing index M was plotted against time for different interstitial fluid viscosity in logarithmic-normal scale. In the initial mixing stage, the data were fitted to a straight line by the least-square method using eq. (3) for each case. The mixing rate constant k can be determined from the slopes of the straight lines in Fig. 3(a). The mixing rate constant is plotted against the interstitial fluid viscosity in Fig. 3(b). It shows that the mixing rate increases upon increasing the interstitial fluid viscosity. The result is interesting and non-trivial because the particle motions and interaction collisions are the strongest resulting in the strongest particle diffusions in the dry system and decreases with the increase of the interstitial fluid viscosity in the slurry system [21]. However, the mixing rate is the smallest using air as the interstitial fluid. From the previous study, the thickness of flowing layer is larger with using the more viscous interstitial fluid [22]. The particle diffusions and the flowing layer thickness both influence the mixing rate. The flowing layer thickness apparently plays a more significant role on the mixing rate in the slurry rotating drum systems. There are more interactions between particles due to the thicker flowing layer resulting in an increase of mixing rate. Therefore, the mixing rate constant is the smallest in the dry system for air as the interstitial fluid and increases with increasing the interstitial fluid viscosity using liquid as the interstitial fluid as observed in Fig. 3(b) % glycerin.5 Mixing index air pure water 6% glycerin 7% glycerin 75% glycerin 8% glycerin 85% glycerin Time (second) (a) Interstitial fluid viscosity (cp) (b)

5 Figure 3(a). The variation of mixing index with rotating time for and 85% glycerin as interstitial fluid using 5% filling degree, in which the lines are fitted by least-square method, (b) the mixing rate constant plotted against the interstitial fluid viscosity. The repose angle is an important parameter to investigate the physical mechanism and flow behavior of granular materials. The dynamic repose angle θ r, the angle between the free surface and the horizontal plane, as shown in Fig. 1(a), was measured by the 1 images after the granular flow in the drum reached the steady state in this study. In Fig. 4(a), the dynamic repose angle is plotted as a function of interstitial fluid viscosity using 5% filling degree. It indicates that the dynamic repose angle increasing with the increase of the interstitial fluid viscosity. The results consistent with previous results [22] but differs from the result [7-8] who indicated that the dynamic repose angle for dry system and slurry system was similar. The viscous force increases with the increase of interstitial fluid viscosity and increase hydrodynamic shear force when one particle slides past another resulting in the greater dynamic repose angle [22]. The mixing rate constant is plotted as a function of the dynamic repose angle and shows in Fig. 4(b). It shows that the mixing rate constant increases with the increase of dynamic repose angle. The thickness of flowing layer increases linear with increasing the dynamic repose angle [22]. More particle motions in the flowing layer with increasing the thickness of flowing layer and more granular mixing would be able to occur resulting in the greater mixing rate constant as observed in Fig. 4(b) Dynamic repose angle air pure water 6% glycerin 7% glycerin 75% glycerin 8% glycerin air pure water 6% glycerin 7% glycerin 75% glycerin 8% glycerin Interstitial fluid viscosity (cp) Dynamic repose angle (degree) (a) Figure 4(a). The variation of dynamic repose angle with interstitial fluid viscosity using 5% filling degree, (b) the mixing rate constant plotted against the dynamic repose angle. The influence of filling degree on the dynamics of the mixing process was investigated in the dry rotating drum in the previous studies. However, they focused on the low filling degree 5% [13, 17, 28]. Not only the low filling degree but also the high filling degree is used to investigate the mixing dynamics in the slurry rotating drum in this paper. Figure 5 shows the variation of mixing index with rotating time for four different filling degrees using µ = 35.5 cp. It shows that the mixing index gradually decreases and then reaches a stable value for each case. It also shows that M s is almost the same which is about at.18 in each filling degree. It means that M s is independent of the filling degree. The result is similar with Finnie et al. [17] and Gosselin et al. [28] for the air as the interstitial fluid. (b)

6 .5.4 4% filling degree 5% filling degree 6% filling degree 75% filling degree Mixing index Time (second) Figure 5. The variation of mixing index with rotating time for different filling degree using µ = 35.5 cp. The mixing rate constants k was measured with the same method mentioned in Fig. 3(a). The mixing rate constant is plotted as a function of the filling degree in Fig. 6(a). It indicates that the mixing rate constants k decreases dramatically with increasing the filling degree. The filling degree has a very little influence on the thickness of flowing layer. However, the fixed layer thickness increases significantly due to the increase of filling degree therefore reduces its relative thickness T (flowing layer thickness / fixed layer thickness) [28-29]. The mixing process occurred only in the flowing layer and the relative thickness T decreases with increasing the filling degree therefore results in the smaller mixing rate constant k as observed in Fig 6(a). The trend is similar to the dry system [17, 28]. Figure 6(b) shows the dynamic repose angle variation with the filling degree. It shows that the dynamic repose angle is independent on the filling degree using the same Froude number and interstitial fluid viscosity. The viscous force, inertia force, and gravity are similar with the four different filling degrees thus the dynamic repose angles for the four different filling degrees are similar % filling degree 5% filling degree 6% filling degree 75% filling degree Dynamic repose angle % filling degree 5% filling degree 6% filling degree 75% filling degree Filling degree (%) Filling degree (%) Figure 6(a). The mixing rate constant plotted against the filling degree using µ = 35.5 cp, (b) the variation of dynamic repose angle with filling degree using µ = 35.5 cp. The Stokes number, determined by Eq. (2), is commonly used to study the influence of interstitial fluid on the particle motions in granular flow. Figure 7 shows the dynamic repose angle and mixing rate constant plotted as a function of the Stokes number. It shows two behaviors that both the dynamic repose angle and mixing rate constant increase slightly with decreasing St at large Stokes number (St 1) whereas both the dynamic repose angle and mixing rate constant increase sharply with decreasing St at small Stokes number. At large St, the granular flow behavior is similar to the dry system and the particle motions are dominated by the interactive collisions between particles. Therefore, the dynamic repose angle and mixing rate constant are small at large St. The viscous fluid effect becomes important and could not be neglected at small St [21]. From above discussions, the dynamic repose angle and flowing layer thickness are larger with using the larger viscosity of interstitial fluid resulting in the greater viscous force at small St. The mixing rate constant is

7 larger due to the thicker flowing layer at small St. From the energy point of view, the kinetic energy of particles are dissipated by the interstitial fluid during the collision process resulting in the weak particle motions and diffusions when the higher viscosity liquid as the interstitial fluid and induces a decrease of mixing rate. However, the flowing layer is thicker when the higher viscosity liquid as the interstitial fluid [22]. There are more interactions between particles due to the thicker flowing layer resulting in an increase of mixing rate. The particle diffusions and flowing layer thickness both influence mixing rate. However, the flowing layer thickness plays a more significant role on the mixing rate in the slurry rotating drum systems. 5.1 Dynamic repose angle (degree) Dynamic repose angle Stokes number (St) Figure 7. The dynamic repose angle and mixing rate constant plotted against the Stokes number. 4. CONCLUSION This paper studies the mixing dynamics of granular materials immersed in a water-glycerin mixture in a quasi-2d rotating drum. The results demonstrate that the interstitial fluid viscosity has a significant influence on the mixing speed and dynamic repose angle. The mixing rate constant and dynamic repose angle increase with the increase of interstitial fluid viscosity. However, the viscosity of interstitial fluid plays no role in the final stable mixing index. The final mixing index is almost the same with the difference interstitial fluid viscosity. The effect of the filling degree on the mixing dynamics of granular materials is also investigated in the slurry rotating drum. The results show that the mixing rate constant decreases sharply with increasing the filling degree. However, the dynamic repose angle is almost constant regardless of the filling degree. The results also indicate that the filling degree have no influence on the final stable mixing index. Finally, we demonstrate that the dynamic repose angle and the mixing rate increase slightly at high St and increase dramatically at low St with decreasing Stokes number. REFERENCES 1. Vargas W. L., Hajra S. K., Shi D. and McCarthy J. J., Suppressing the segregation of granular mixtures in rotating tumblers, AIChE journal Papers 54, (28). 2. Lee J. and Ladd A. J. C., Particle dynamics and pattern formation in a rotating suspension, J. Fluid Mech. 577, (27). 3. Meier S. W., Lueptow R. M. and Ottino J. M., A dynamical systems approach to mixing and segregation of granular materials in tumblers, Adv. Phys. Papers 56, (27). 4. Henein H, Brimacomble J. K. and Watkinson A. P., Experimental study of transverse bed motion in rotary kilns, Metall. Trans. B, Process Metall. Papers 14B, (1983). 5. Mellmann, J., The transverse motion of solids in rotating cylinders forms of motion and transition behavior, Powder Technol. Papers 118, (21). 6. Liu X. Y., Specht, E., and Mellmann, J., Experimental study of the lower and upper angles of repose of granular materials in rotating drums, Powder Technol. Papers 154, (25).

8 7. Samadani, A. and Kudrolli, A., Segregation transitions in wet granular matter, Phys. Rev. Lett. Papers 85, (2). 8. Samadani, A. and Kudrolli, A., Angle of repose and segregation in cohesive granular matter, Phys. Rev. E. Papers 64, 5131 (21). 9. Pohlman, N. A., Severson, B. L., Ottino, J. M., and Lueptow, R. M. Surface roughness effects in granular matter: Influence on angle of repose and the absence of segregation, Phys. Rev. E. Papers 73, 3134 (26). 1. Lai, P. Y., Jia, L. C., and Chan, C. K., Friction induced segregation of a granular binary mixture in a rotating drum, Phys. Rev. Lett. Papers 79, (1997). 11. Lu L. S., and Hsiau S. S., Mixing in vibrated granular beds with the effect of electrostatic force, Powder Technol. Papers 16, (25). 12. Jain, N., Ottino, J. M., and Lueptow, R. M., Regimes of segregation and mixing in combined size and density granular systems: an experimental study, Granul. Matter Papers 7, (25). 13. Kwapinska M., Saage G., and Tsotsas E., Mixing of particles in rotary drums: A comparison of discrete element simulations with experimental results and penetration models for thermal processes, Powder Technol. Papers 161, (26). 14. Dury, C. M. and Ristow, G. H., Competition of mixing and segregation in rotating cylinders, Phys. Fluid Papers 11, (1999). 15. Cleary, P. W., DEM simulation of industrial particle flows: case studies of dragline excavators, mixing in tumblers and centrifugal mills, Powder Technol. Papers 19, (2). 16. Lemieux, M., Bertrand, F., Chaouki, J., and Gosselin, P., Comparative study of the mixing of free-flowing particles in a V-blender and a bin-blender, Chem. Eng. Sci. Papers 62, (27). 17. Finnie, G. J., Kruyt, N. P., Ye, M., Zeilstra, C., and Kuipers, J. A. M., Longitudinal and transverse mixing in rotary kilns: A discrete element method approach, Chem. Eng. Sci. Papers 6, (25). 18. Chaudhuri, B., Mehrotra, A., Muzzio, F. J., and Tomassone, M. S., Cohesive effects in powder mixing in a tumbling blender, Powder Technol. Papers 165, (26). 19. Finger, T., Stannarius, R., Influences of the interstitial liquid on segregation patterns of granular slurries in a rotating drum, Phys. Rev. E Papers 75, 3138 (27). 2. du Pont, S. C., Gondret, P., Perrin, B., and Rabaud, M., Granular avalanches in fluids, Phys. Rev. Lett. Papers 9, 4431 (23). 21. Liao, C. C., and Hsiau, S. S., Influence of interstitial fluid viscosity on transport phenomenon in sheared granular materials, Chem. Eng. Sci. Papers 64, (29). 22. Jain, N., Ottino, J. M., and Lueptow, R. M., Effect of interstitial fluid on a granular flowing layer, J. Fluid Mech. Papers 58, (24). 23. Hsiau, S. S., and Shieh, Y. H., Fluctuations and self-diffusion of sheared granular material flows, J. Rheol. Papers 43, (1999). 24. Danckwerts, P. V., The definition and measurement of some characteristics of mixtures, Appl. Sci. Res. Papers 3, (1952). 25. Li, H. and McCarthy, J.J., Cohesive particle mixing and segregation under shear, Powder Technol. Papers 164, (26). 26. Shi, D., Abatan, A.A., Vargas, W.L. and McCarthy, J.J., Eliminating segregation in free-surface flows of particles, Phys. Rev. Lett. Papers 99, 1481 (27). 27. McCarthy, J.J., Khakhar, D.V. and Ottino, J.M., Computational studies of granular mixing, Powder Technol. Papers 19, (2). 28. Gosselin, R., Duchesne, C. and Rodrigue, D., On the characterization of polymer powders mixing dynamics by texture analysis, Powder Technol. Papers 183, (28). 29. Woodle, G. R. and Munro, J. M., Particle motion and mixing in a rotary kiln, Powder Technol. Papers 76, (1993).