在本研究中二維顆粒碰撞模擬程式被運用在研究二元圓-橢圓乾燥顆粒混合物於垂直振動下因不同形狀所導致的顆粒分層現象。尤其我們模擬由相同體積圓和不同長短徑比橢圓組成之乾燥顆粒混合物的分層現象。兩種顆粒的質心位置在模擬中被連續的紀錄，從中可推論振動振幅和橢圓長短徑比對分層的影響。研究中發現振動振幅和頻率對分層現象都有影響。當上述兩種因素的值增加時，兩顆粒之間質心位置的差距更加明顯。假如特別專注在二元圓-橢圓乾燥顆粒混合物上，分層現象僅發生在橢圓長短徑比達到其臨界值時。在充分的振動振幅和頻率時，橢圓朝著混合物的自由面移動，同時圓形顆粒朝著容器底部聚集。

In the present study the 2-D particle collision simulation program is employed to study the particle segregation phenomenon induced by the shape-difference in a binary sphere-ellipsoid dry granular mixture under vertical vibration. In particular, we simulate the segregation phenomenon for a dry granular mixture consisting of the same-volume spheres and ellipsoids with different aspect ratios. The Locations of the mass centers of the two types of particles are continuously recorded in the simulations, from which the influences of the vibration amplitude and the aspect ratio on the segregation can be deduced. It is found that both the vibration amplitude and frequency have influence on the segregation phenomenon. As the values of these two factors increase, the departing between the mass centers of the two types of particles becomes more significant. If particular interest is that for a binary sphere-ellipsoid dry granular mixture, the segregation can only occur when the aspect ratio of the ellipsoids reaches its critical value. It is found that under sufficient vibration amplitude and frequency the ellipsoid particles move toward the free surface of the mixture, while the spheric particles gather themselves at the bottom of the vessel.

[1] Jacque Duran：Sands, Powders, and Grains：An Introduction to the Physics of Granular Materials, Springer, 1999
[2] 潘國樑，環境地質與防災科技，地景企業股份有限公司，169-176，民國94年。
[3] Gerald H. Ristow：Pattern Formation in Granular Materials, Springer, 1999
[4] Clément, E. and Rajchenbach, J., Fluidization of a bidimensional powder. Europhys. Lett. 16, 133, 1991.
[5] E. Guazzelli and L. Oger, eds., Mobile Particulate Systems (Dordrecht：Kluwer Academic, 1995.
[6] R.L. Brown, The fundamental principles of segregation, J. Inst. Fuel 13, 15, 1939.
[7] R. Jullien, P. Meakin and A. Pavlovitch：Jullien, Meakin, and Pavlovitch reply, Phys. Rev. Lett., VOLUME 70, 2195, 1993.
[8] J. Duran, J. Rajchenbach, and E. Clément, Arching Effect Model for Particle Size Segregation, 1993.
[9] 黃俊豪，「剪力流中分離現象研究」，國立中央大學機械工程研究所碩士論文，9-12，民國95年7月。
[10]Das Gupta, S., Khakhar, D. V., and Bathia, S. K., Axial segregation of particles in a horizontal rotating cylinder. Chem. Engineering Science 46, 1513, 1991.
[11]Yanagita, T., Three-dimensional cellular automaton model of segregation of granular materials in a rotating cylinder. Phys. Rev. Lett. 82, 3488, 1999.
[12]Alder, B. J. and Wainwright, T. E. J. Chem. Phys. 27, 1208, 1957.
[13]Alder, B. J. and Wainwright, T. E. J. Chem. Phys. 31, 459, 1959.
[14]Stillinger, F. H. and Rahman, A. J. Chem. Phys. 60, 1545, 1974.
[15]J.M.Haile, Molecular Dynamics Simulation , John Wiley&Sons, Inc, 1992.
[16]T. Pöschel and T. Schwager: Computation Granular Dynamics, Springer, 13-17, 2005.
[17]Y. C. Fung, A First Course In Continuum Mechanics Second Edition, 1-6, 1981.
[18]Cundall P A, A computer model for simulating progressive large scale movements in blocky rock systems, ISRM Symp., Nancy, France, Proc. 2, 129-136, 1971.
[19]J.R. Williams, G. Hocking and G.G.W, Mustoe, The theoretical basis of the Discrete Element Method, Proc. NUMETA`85, A.A. Balkena, 1985.
[20]林立欣，「離散元素模擬之帄行策略」，碩士論文摘要，國立台灣大學土木工程學系，1-2，2004。
80
[21]Lee, Y., Fang, C., Tsou, Y.R., Lu, L.S., Yang, C.T. (2009): A packing algorithm for three-dimensional convex particles. Granul. Matt. (in press)(DOI 10.1007/s10035-
009-0133-7).
[22]Dantzig, G. B., Linear programming and extensions., Princeton, N.J.: Princeton University Press, 1963.
[23]Cormen, T.H., Leiserson, C.E., Rivest, R.L., Introduction to algorithms., Cambridge, Mass.: MIT Press, 2001.