在傳統流體力學裡，一般流體的流動為連續運動，由微觀的角度來看，流體流動分子間的相對位移不超過一個特徵長度。而在粒子流的領域裡，粒子的流動屬於不連續運動，受到粒子間吸引力較為薄弱的影響，粒子間的相對位移大於一個特徵長度。在流體動力學中，那維爾-史托克方程式常用來描述黏性流體在平板、斜管等不同環境下的流體運動。在粒子流中，粒子受到外界能量的作用下，粒子群的型態可以像固體、液體和氣體般的狀態存在，並且可以以多相的形態存在。因此，由於粒子間複雜的碰撞行為，一般的理論方程不適用於描述粒子的運動行為。
在本篇論文中，探討在二維環型剪力槽中，不同邊壁運動形式對於粒子動態行為的影響。在內、外邊壁單獨轉動系統中，由實驗結果可得知，粒子受到剪力的作用下，粒子切向速度以類指數型態分佈，隨著和剪力邊壁距離的增加，粒子切向速度呈現遞減的分佈。在相同邊壁速度參數下，因不同局部占有率的影響，在外邊壁轉動的系統中，接近剪力邊壁處有較高的局部粒子占有率，因此存在較大的切向速度值。在本論文中，也將探討內、外邊壁同時同向和反向運動，對於粒子動態行為的影響。

In fluid dynamics, liquid flow is continuous flow. In microcosmic, the relative displacement is not yet one characteristic length. In granular flow, the flow is not continuous flow, the weak attraction around particle will let relative placement over one characteristic length. In fluid dynamics, Navier-Stokes equation is usually used to describe the flow behaviors in tube flow, plate flow and draft flow. In granular flow, multiphase flow behaviors may exist as granular materials are driven by external force. Granular materials may behave solid, liquid and gas depending on the processing conditions. Thus, general theory is still poor to describe the granular flows due to the complex flow behavior.
In this thesis, the two-dimensional annular shear cell is used to investigate the dynamic properties of granular flow with different rotational types. Through experiment analyze, we know the velocity profile is roughly exponential decay from shearing boundary with only inner wall or outer wall rotation. The tangential velocity of particles with rotating outer boundary is larger than rotating inner boundary under the same rotating tangential velocity. Pass by analyze, the results show that the local solid fraction is different near inner and outer shear boundary, particles collision violently when solid fraction is higher. In this thesis, we also discuss the flow behaviors by rotating both walls with the same direction rotation and inverse direction rotation.

[1] Ennis, B. J., Green, J. and Davies, R. , 1994, “The Legacy of Neglect in The U.S.,” Chemical engineering progress, Vol. 90, pp. 32-43.
[2] Campbell, C. S., 1990, “Rapid Granular Flows,” Annual Review of Fluid Mechanics, Vol. 22, pp. 57-92.
[3] Campbell, C. S., and Brennen, C. E., 1985, “Choutte flows of granular material：some computer simulations”, Transactions of the ASME, Vol. 52, pp. 172-178.
[4] Reynolds, O., 1885, “On the Dilatancy of Media Composed of Rigid Particals in Contact,” Phill.Mag, Vol. 20, pp. 469-481.
[5] Renolds, O., 1887, “Experiments Showing Dilutency,A Property of Granular Materials Possibly Connected with Gravitation,” Proceedings of the Royal. Institution of Great Britain, Vol. 51, pp. 218-227.
[6] Coulomb, C., 1773, “Memoir de Mathématique et de Phy-sique,” Academie des Sciences, l''Imprimerie Royale, Paris Vol. 7 , p. 343-382.
[7] Rajchenbach, J., 1990, “Flow in powders：from discrete avalanches to continuous regime,” Physical Review Letters, Vol. 65, pp. 2221-2225.
[8] Santomaso, A., Olivi, M., and Canu, P., 2005, “Mixing kinetics of granular materials in drums operated in rolling and cataracting regime”, Powder Technology, Vol. 152, pp. 41-51.
[9] Savage, S. B. and Sayed, M., 1984, “Stresses developed by drycohesionless granular materials sheared in an annular shear cell”, Journal of Fluid Mechanics, Vol. 142, pp. 391-430.
[10] Hanes, D. M., and Inman, D. L., 1985, “Observations of rapidly flowing granular fluid materials”, Journal of Fluid Mechanics, Vol. 150, pp. 357-380.
[11] Elliott, K. E., Ahmadi, G., and Kvasnak, W., 1998, “Couette flows of a granular monolayer-an experiment study,” Journal of Non-Newtonian Fluid Mech, Vol. 74 , pp. 89-111.
[12] Zheng, X. M., and Hill, J. M., 1998, “Molecular dynamics simulation of granular flows：Slip along rough inclined planes”, Computational Mechanics, Vol. 22, pp 160-166.
[13] Drake, T. G., 1991, “Granular flow：physical experiment and their implications for microstructural theories”, Journal of Fluid Mechanics, Vol. 225, pp. 121-152.
[14] Hsiau S. S. and Jang H. W., 1998, “Measurements of velocity fluctuations of granular materials in a shear cell”, Experimental Thermal and Fluid Science, Vol. 17, pp. 202-209.
[15] Kim H. and Rosato A. D., 1992, “Particle simulations of the flow of smooth spheres between bumpy boundaries,” Micromechanics of Granular Materials Elsevier, pp. 91-100.
[16] Howell, D., and Behringer R. P., 1998, “Stress Fluctuations in a 2D Granular Couette Experiment：A Continuous Transition”, Physical Review Letters, Vol. 82, pp. 5241-5244.
[17] Veje, C. T., 1998, “Kinematic of a two-dimentional granular Couette experiment at the transition to shearing”, Physical Review E, Vol.59, pp 739-745.
[18] Campbell, C. S., and Wang, D. G., 1992, “Renolds Analogy for a Shearing Granular Masterials”, Journal of Fluid Mechanics, Vol. 244, pp 527-546.
[19] Hsiau, S. S., and Yu H. Y., 1997, “Segregation phenomena in a shaker,” Powder Technology, Vol. 93, pp. 83-88.
[20] Gabriel, l. T., 2005, “Wet-Granulation Research with Application to Scale-up,” China Particuology, Vol. 3, pp191-195.
[21] Hvorslev, M. J., 1936, “A Ring Shearing Apparatus for the Determination of the Shearing Resistance and Plastic Flow of Soil” In Proc. Intl Conf. Soil Mech. Found. Engng, Cambridge, Mass., Vol. 2, pp. 125-129.
[22] Hvorslev, M. J., 1939. “Torsion Shear Tests 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.
[23] Novosad, J., 1964, “Apparatus for Measuring the Dynamic Angles of Internal Friction and External Friction of a Granular Material,” Collection Czech. Chen. Commun., Vol. 29, pp. 2697-2701.
[24] Carr, J. F., and Walker, K. M., 1967, “An Annular Shear Cell for Granular Materials,” Powder Technology, Vol. 1, pp. 369-373.
[25] Scarlett, B., and Todd, A. C., 1968, “A Split Ring Annular Shear Cell for Determination of the Shear Strength of a Powder,” Scientific Instruments, Vol. 1, pp. 655-656.
[26] Cambell, C. S., and Brennen, C. E. 1983, “Computer simulation of shear folws of granular material”, Mechanics of Granular Materials, pp. 313-325.
[27] Ahmadi, G., and Abu-Zaid, S., 1990, “A rate-dependent thermodynamical model for rapid granular flow”, Journal of Fluid Mechanics, Vol 35, pp 15-35.
[28] Jasti, V., and Higgs, C., 2008, “Experiment study of Granular Flows in a rough annular shear cell,” Physical Review E, Vol 78, pp. 0413061-0413067.
[29] Jasti, V., and Higgs, C., 2010,“ A fast first order model of a rough annular shear cell using cellular automata,” Granular Matter, Vol 12, pp. 97-106.
[30] Wang, D. M., and Zhou Y. H., 2009, “Shear Profiles and Velocity Distribution in Dense Shear Granular Flow,” Chinese Physics Letters, Vol. 26, pp. 0245011-0245014.
[31] Schöllmann, S., 1999, “Simulation of a two-dimentional shear cell,” Physical Review, Vol. 59, pp. 889-896.
[32] Koval, G., Roux, J., Corfdir, A., and Chevoir, F., 2009, “Annular shear of cohesionless granular materials：From the inertial to quasistatic regime,” Physical Review E, Vol. 59, pp. 0213061-02130616.
[33] Uttera, B., and Behringer, R.P., 2004, “Transients in sheared granular matter,” Europe Physics, Vol. 14, pp 373-380.
[34] Mueth, D. M., 2003, “Measurements of particle dynamics in slow, dense granular Couette flow,” Physical Review E., Vol. 67,　pp. 0113041-01130413.
[35] May, B. H., and Daniels, K. E, 2009, “Shear-driven size segregation of granular materials：Modeling and experiment,” Physical Review E, Vol. 81, pp. 0513011-05130117.