本文主要是探討不同密度之顆粒體於類二維剪力槽系統中，因密度分離效應所造成之顆粒環的沉降行為。並以實驗的方式，分析剪力槽內底盤速度之快慢、粒子體積佔有比之大小以及浮力效應對顆粒環沉降行為的影響。其中浮力效應意指不同密度之顆粒體因重力效應的影響，而形成密度大之顆粒向下擠壓，密度小之顆粒向上堆積的顆粒分層現象。另外，為了更清楚地分析及比較不同條件下顆粒環沉降的狀況，故本文特別定義了無因次沉降深度及沉降速率兩個參數，分別針對顆粒環位置的變化及速率進行討論。
本研究的實驗結果顯示，無因次沉降深度與沉降速率兩者，皆會隨著粒子體積佔有比與底盤轉速的增加而提升，且兩者之間為正比的關係。另一方面，於相同實驗配置下，無因次沉降深度的值會隨著密度比的增加而上升。而於不同的實驗配置下，顆粒環的沉降行為則是會受到追蹤粒子整體重量的大小以及顆粒之間力鏈(Force Chain)結構的影響。此外，當密度比較大時，沉降速率也會隨之增加，這是由於不同密度之顆粒所受重力效應的差異較大的原故。最後本實驗也發現，當密度比小於1.57時，顆粒環會因為密度分離效應的不足而產生崩散，使得系統內之輕重顆粒產生均勻混合的狀態。

This study investigates the sinking behavior of particle ring due to the density segregation effect in a quasi-2D Couette shear cell device. The influences of bottom wall velocity, solid fraction of granular material and buoyancy effect are studied experimentally. Here the “Buoyancy effect” means the heavier particles sink to lower levels in the flowing layer while lighter ones rise due to the effects of gravity. Additionally, the parameters of the dimensionless sinking depth and sinking rate are defined to describe the change of particle ring’s position and quantify the sinking speed of the particles respectively.
The experimental results show that both the dimensionless sinking depth and the sinking rate increase with increasing the bottom wall velocity and solid fraction, and the linear relation is also observed between the dimensionless sinking depth and the sinking rate. On the other hand, in the case of the same experimental configuration, the dimensionless sinking depth will increase as the density ratio increases. However, the sinking behavior of particle ring will be affected by the overall weight of tracking particles and the force chains inter particles in different experimental configuration. The result also show that the sinking rate increase with increasing the density ratio due to the gravity effect. Finally, we found that the particle ring structure cannot be maintained due to the weak density segregation effect when density ratio is less than 1.57, and the binary mixture becomes the homogeneous mixing state in the granular system.

Aidanpää, J. O., Shen, H. H., and Gupta, R. B., “Experimental and Numerical Studies of Shear Layers in Granular Shear Cell,” Journal of Engineering Mechanics, Vol. 122, No.3, pp. 187-196, 1996
Bagnold, R. A., “The Physics of Blown Sand and Desert Dunes,” Methuen, London, 1941
Bagnold, R. A., “The shearing and dilation of dry sand and the ''singing'' mechanism,” Proceedings of the Royal Society, A295, pp. 219-232, 1966
Campbell, C. S., “Rapid granular flows,” Annual Review of Fluid Mechanics, Vol. 22, pp. 57-92, 1990
Dantu, P., “A contribution to the mechanical and geometrical study of non-cohesive,” Proceeding if the 4th International Conference on Soil Mechanics and Foundation Engineering (London: Butterworth), Vol. 133, pp. 144-148, 1957
Duran, J., “Sands, Powders, and Grains：An Introduction to the Physics of Granular Materials,” Springer Verlag, 2000
Elliott, K.E., Ahmadi, G., and Kvasnak, W., “Couette flows of a granular monolayer an experimental study,” Journal of Non-Newtonian Fluid Mechanics, Vol. 74, pp. 89-111, 1998
Faraday M., “On a peculiar class of acoustical figures; and on certain forms assumed by a group of particles upon vibrating elastic surfaces,” Philosophical Transactions of the Royal Society (London), Vol. 121, pp. 299-318, 1831
Fenistein, D., and van Hecke, M., “Kinematics - Wide shear zones in granular bulk flow,” Nature, Vol. 425, pp. 256, 2003
Gerald, H., “Pattern Formation in Granular Materials,” Springer Verlag, 1999
Goldhirsch, I., “Rapid granular flows,” Annual Review of Fluid Mechanics, Vol. 35, pp. 267-293, 2003
Golick, L. A., and Daniels, K. E., “Mixing and segregation rates in sheared granular materials,” Physical Review E, Vol. 80, 042301, 2009
Hirshfeld, D., and Rapaport, D. C., “Molecular Dynamics Studies of Grain Segregation in Sheared Flow,” Physical Review E, Vol. 56, pp. 2012-2018, 1997
Hogg, R., “Mixing and Segregation in Powders: Evaluation, Mechanisms and Processes,” KONA Powder and Particle Journal, No.27, 2009
Hsiau, S. S., and Jang H. W., “Measurements of velocity fluctuations of granular materials in a shear cell,” Experimental Thermal and Fluid Science, Vol. 17, pp. 202-209, 1998
Hsiau, S. S., and Shieh Y. M., “Effect of soild fraction and self-diffusion of sheared granular flows,” Chemical Engineering Science, Vol. 55, pp. 1969-1979, 2000
Hsiau, S. S., and Yang W. L., “Stresses and transport phenomena in sheared granular flows with different wall conditions,” Physics of Fluids, Vol. 14, pp. 612-621, 2002
Hsiau, S. S., and Yang W. L., “Transport property measurements in sheared granular flows,” Chemical Engineering Science, Vol. 60, pp. 187-199, 2005
Hvorslev, M. J., “A Ring Shearing Apparatus for the Determination of the Shearing Resistance and Plastic Flow of Soil,” Proceedings, International Conference on Soil Mechanics and Foundation Engineering, Cambridge, Mass, Vol. 2, pp. 125-129, 1936
Hvorslev, M. J., “Torsion Shear Test and Their Place in the Determination of Shearing Resistance of Soils,” Proceedings of the American Society of Testing and Materials, Vol. 39, pp. 999-1022, 1939
Jaeger, H. M., and Nagel, S. R., “Physics of the Granular State,” Vol. 255, pp. 1523-1531, 1992
Jaeger, H. M., Nagel, S. R., and Behringer, R. P., “Granular solids, liquids and gases,” Reviews of Modern Physics, Vol. 68, pp. 1259-1273, 1996
Jain, N., Ottino, J. M., and Lueptow, R. M., “Effect of interstitial fluid on a granular flowing layer,” Journal of Fluid Mechanics, Vol. 508, pp. 23-44, 2004
Jain, N., Ottino, J. M., and Lueptow, R. M., “Regimes of segregation and mixing in combined size and density granular systems: an experimental study,” Granular Matter, Vol. 7, pp.69-81, 2005
Jha, A. K., and Puri, V. M., “Percolation segregation of multi-size and multi-component particulate materials,” Powder Technology, Vol. 197, pp. 274-282, 2010
Klein, M., Tsai, L. L., Rosen, M. S., Pavlin, T., Candela, D., and Walworth, R. L., “Interstitial gas and density segregation of vertically vibrated granular media,” Physical Review E, Vol. 74, 010301, 2006
Kudrolli, A., “Size separation in vibrated Granul,” Reports on Progress Physics, Vol.67, pp. 209-247, 2004
Li, H. M., and McCarthy, J. J., “Cohesive particle mixing and segregation under shear,” Powder Technology, Vol. 164, pp. 58-64, 2006
Liao, C. C., Hsiau, S. S., Tsai, T. H., and Tai, C. H., “Segregation to mixing in wet granular matter under vibration,” Chemical Engineering Science, Vol. 65, pp. 1109-1119, 2010
Liao, C. C., Hsiau, S. S., and Kiwing, To., “Granular dynamics of a slurry in a rotating drum,” Physical Review E, Vol. 82, 010302, 2010
Lovoll, G., Maloy, K. J., and Flekkoy, E. G., “Force measurements on static granular materials,” Physical Review E, Vol. 60 pp. 5872-5878, 1999
May, L. B. H., Golick, L. A., Phillips, K. C., Shearter, M., and Daniels, K. E., “Shear-driven size segregation of granular materials: Modeling and experiment,” Physical Review E, Vol. 81, 051301, 2010
Möbius, M. E., Lauderdale, B. E., Nagel, S. R., and Jaeger, H. M., “Brazil-nut effect Size separation of granular particles,” Nature, Vol. 414 pp.270, 2001
Mueth, D. M., Jaeger, H. M., and Nagel, S. R., “Force distribution in a granular medium,” Physical Review E, Vol. 57 pp. 3164-3169, 1998
Ogawa, S., “Multi-temperature Theory of Granular Materials,” In Proceedings of US-Japan Seminar on Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Materials, Tokyo, 1978
Ottino, J. M., and Khakhar, D. V., “Mixing and segregation of granular materials,” Annual Review of Fluid Mechanics, Vol. 32, pp. 55-91, 2000
Reynolds, O., “On the Dilatancy of Media Composed of Rigid Particles in Contact,” Philosophical Magazine, Vol. 20, pp. 469-481, 1885
Richard, P., “Slow relaxation and compaction of granular systems,” Nature Materials 4, pp. 121–128, 2005
Rosato, A., Strandburg, K. J., Prinz, F., and Swendsen, R. H., “Why the Brazil nuts are on top: size segregation of particulate matter by shaking,” Physical Review Letters, Vol. 58, pp. 1038-1040, 1987
Sanfratello, L., and Fukushima, E., “Experimental studies of density segregation in the 3D rotating cylinder and the absence of banding,” Granular Matter, Vol.11 pp. 73-78, 2009
Shamlon, P. A., “Handling of Bulk Solids,” Butterworth, London, 1988
Shi, Q. F., Sun, G., Hou, M., and Lu, K. Q., “Density-driven segregation in vertically binary granular mixture,” Physical Review E, Vol. 75, 061302, 2007
Silbert, L. E., Grest, G. S., and Landry, J. W., “Statistics of the contact network frictional and frictionless granular packings,” Physical Review E, Vol. 66, 061303, 2002
Taguchi, Y., “New origin of a convective motion: Elastically induced convection in granular materials,” Physical Review Letters, Vol. 69, pp. 1367-1370, 1992
Utter, B., and Behringer, R. P., “Transients in sheared granular matter,” European Physical Journal E, Vol.14 pp.373-380, 2004
Voivret, C., Radjai, F., Delenne, J. Y., and Youssoufi, M. S. EI, “Multiscale Force Network in Highly Polydisperse Granular Media,” Physical Review Letters, Vol.102, 178001, 2009
Wang, D. M., and Zhou, Y. H., “Particle dynamics in dense shear granular flow,” Acta Mechanica Sinica, Vol. 26, pp 91-100, 2010
Yang, W. L., and Hsiau, S.S., “The effect of liquid viscosity on sheared granular flows,” Chemical Engineering Science, Vol. 61, pp. 6085-6095, 2006
Yu, Y. S., Hu, L., Gone, C., and Zhang, G. H., “Effect of boundary condition on the movement of spheres on a granular medium,” Journal of Shandong University(Natural Science), Vol. 45, No. 9, 2010