本文主要是以實驗方法探討不同密度顆粒體於類二維旋轉鼓系統中，因物理性質的差異所造成之條紋狀分離現象。並分析旋轉鼓轉速之快慢、密度比之不同、安息角角度之大小，以及粒子填充率之高低對分離圖案所造成的影響。實驗過程中，以高畫質數位攝影機與高速攝影機拍攝顆粒體在旋轉鼓中因密度差異所造成之分離現象，並以影像分析方法及粒子追蹤技術計算分離現象達到穩態後的條紋數目及顆粒體的傳輸性質，其後也計算條紋圖形的面積以及周長，進而求得該圖形之形狀指標。本文更引用了該指標來量化分離圖案變化的過程，並進行分析與比較。
本研究的實驗結果顯示，我們成功的以實驗方法做出由密度分離效應所產生之條紋狀分離現象，這在之前的文獻中並沒有被探討過。且由實驗結果發現，若要在密度效應下形成規律且穩定的條紋狀分離圖案，所需要的是兩顆粒間差異較大的安息角與密度。而最重要的一點是，顆粒體的密度差異並不是造成條紋狀分離形成的主要原因。因此，我們可以根據不同之實驗結果，並利用無因次安息角差值及密度比值畫出一相圖區間。將所有條件分成條紋狀分離、核心狀分離及混合三個部份，用以表示顆粒體在不同條件下之分離圖形。我們也發現到，無因次安息角差值、密度比以及旋轉鼓轉速皆會嚴重影響到條紋形成的花瓣數目。而最後本實驗也發現，在相同的配置且改變不同粒子填充率的情況下，條紋的圖形以及形狀指標都會明顯受到旋轉鼓內填充率高低的影響。

Granular segregation in a rotating drum occurs due to the differences in either particle size or density. This study investigates experimentally the streak segregation patterns in binary mixtures of different density particles (D-system) in a circular thin rotating drum. The influences of rotational speed, density ratio, angle of repose and fill level on streak segregation are studied. The particles motions are recorded by the high definition DV and high-speed camera. Image processing technology and particle tracking method are employed to determine the number of petals, granular transport properties and shape index of streak patterns. Additionally, the parameter of shape index is defined to quantify the process of formation of segregation patterns.
The streak segregation patterns due to density effect are successful measured in this paper. The result is interesting and not be studied in the previous literatures. The results show that the binary mixtures require significant difference of repose angles and density ration to generate a regular and stabilization streak patterns. We also find that the density ratio of particle is not the dominate parameter to influence the formation of streak segregation patterns. A phase diagram is determined to identify three regimes about segregation patterns. Additionally, we also find that the dimensionless difference of repose angle, density ratio, rotational speed and fill level all play crucial roles in the number of petals in the streak segregation patterns.

[1] H.J. Herrmann, “Physics of granular media,” Chaos, Solitons and Fractals, Vol. 6, pp. 203-212, 1995.
[2] B.J. Ennis, J. Green, and R. Davies, “The legacy of neglect in the U.S.,” Chem. Eng. Prog., Vol. 90, pp. 32-43, 1994.
[3] S.M. Chaudeur, H. Berthiaux, and J.A. Dodds, “Experimental study of the mixing kinetics of binary pharmaceutical powder mixtures in a laboratory hoop mixer,” Chem. Eng. Sci., Vol. 57, pp. 4053-4065, 2002.
[4] R.A. Bagnold, “The physics of blown Sand and Desert Dunes,” Methuen, pp. 265, 1941.
[5] P.A. Shamlon, “Handling of Bulk Solids: Theory and Practice ,” Butterworth, pp. 193, 1998.
[6] P. Richard, “Slow relaxation and compaction of granular systems,” Nature Materials 4, pp. 121–128, 2005.
[7] C.S. Campbell, “Rapid granular flows,” Annu. Rev. Fluid Mech., Vol. 22, pp. 57-92, 1990.
[8] H.M. Jaeger, S.R. Nagel, and R.P. Behringer, “Granular solids, liquids and gases,” Rev. Mod. Phys., Vol. 68, pp. 1259-1273, 1996.
[9] J. Duran, “Sands, Powders, and Grains：An Introduction to the Physics of Granular Materials,” Springer Verlag, 2000.
[10] I. Goldhirsch, “Rapid granular flows,” Annu. Rev. Fluid Mech., Vol. 35, pp. 267-293, 2003.
[11] H.M. Jaeger, and S.R. Nagel, “Physics of the Granular State,” Science, Vol. 255, pp. 1523-1531, 1992.
[12] H. Henein, J.K. Brimacomble, and A.P. Watkinson, “Experimental study of transverse bed motion in rotary kilns,” Metall. Trans. B, Vol. 14, pp. 191-205, 1983.
[13] J. Rajchenbach, “Flow in powders: from discrete avalanches to continuous regime,” Phys. Rev. Lett., Vol. 65, pp. 2221-2224, 1990.
[14] J. Mellmann, “The transverse motion of solids in rotating cylinders-forms of motion and transition behavior,” Powder Technol., Vol 118, pp. 251-270, 2001.
[15] A.A. Boateng, and B.V. Barr, “Modeling of particle mixing and segregation in the transverse plane of a rotary kiln,” Chem. Eng. Sci., Vol. 51, pp. 4167-4181, 1996.
[16] A. Ingram, J.P.K. Seville, D.J. Parker, X. Fan, and R.G. Forster, “Axial and radial dispersion in rolling mode rotating drums,” Powder Technol., Vol. 158, pp. 76-91, 2005.
[17] A.A. Boateng, “Boundary layer modeling of granular flow in the transverse plane of a partially filled rotating cylinder,” Int. J. Multiphase flow, Vol. 24, pp. 499-521, 1998.
[18] A.V. Orpe, and D.V. Khakhar, “Scaling relations for granular flow in quasi-two-dimensional rotating cylinders,” Phys. Rev. E, Vol. 64, pp. 031302 1-13, 2001.
[19] X.Y. Liu, E. Specht, O.G. Gonzalez, and P. Walzel, “Analytical solution for the rolling-mode granular motion in rotary kilns,” Chem. Eng. Process., Volume 45, Issue 6, Pages 515-521, 2006.
[20] M.B. Donald, and B. Roseman, “Mixing and de-mixing of solid particles. Part I. Mechanisms in a horizontal drum mixer,” Br. Chem. Eng., Vol. 7, pp. 749-753, 1962.
[21] H. Henein, J.K. Brimacombe, and A.P. Watkinson, “An experimental study of segregation in rotary kilns,” Metall. Trans. B, Vol. 16, pp. 763-774, 1985.
[22] M. Alonso, M. Satoh, and K. Miyanami, “Optimum combination of size ratio, density ratio and concentration to minimize free surface segregation,” Powder Technol., Vol. 68, pp. 145-152, 1991.
[23] F. Cantelaube, and D. Bideau, “Radial segregationina 2d drum: an experimental analysis,” Europhys. Lett., Vol. 30, pp. 133-138, 1995.
[24] D.V. Khakhar, J.J. McCarthy, and J.M. Ottino, “Radial segregation of granular materials in rotating cylinders,” Phys. Fluids, Vol. 9, pp. 3600-3614, 1997.
[25] C.M. Dury, and G.
H. Ristow, “Radial segregation in two-dimensional rotating drum,” J. Phys. France I, Vol. 7, pp. 737-745, 1997.
[26] L. Prigozhin, and H. Kalman, “Radial mixing and segregation of a binary mixture in a rotating drum: model and experiment,” Phys. Rev. E, Vol. 57, pp. 2073-2080, 1998.
[27] D. Eskin, and H. Kalman, “A numerical parametric study of size segregation in a rotating drum,” Chem. Eng. Process., Vol. 39, pp. 539-545, 2000.
[28] A. Rosato, K.J. Strandburg, F. Prinz, and R.H. Swendsen, “Why the Brazil nuts are on top: size segregation of particulate matter by shaking,” Phys. Rev. Lett., Vol. 58, pp. 1038-1040, 1987.
[29] N. Nityanand, B. Manley, and H. Henein, “An analysis of radial segregation for different sized spherical solids in rotary cylinders,” Metall. Trans. B, Vol. 17, pp. 247-257, 1986.
[30] N. Thomas, “Reverse and intermediate segregation of large beads in dry granular media,” Phys. Rev. E, Vol. 62, pp. 961-974, 2000.
[31] G.H. Ristow, “Particle mass segregation in a two-dimensional rotating drum,” Europhys. Lett., Vol. 28, pp. 97-101, 1994.
[32] D.R. Van Puyvelde, B.R. Young, M.A. Wilson, and S.J. Schmidt, “Experimental determination of transverse mixing kinetics in a rolling drum by image analysis,” Powder Technol., Vol. 106, pp. 183-191, 1999.
[33] H.P. Kuo, R.C. Hsu, and Y.C. Hsiao, “Investigation of axial segregation in a rotating” Powder Technol., Vol. 153, pp. 196-203, 2005.
[34] N. Jain, J. M. Ottino, and R. M. Lueptow, “Regimes of segregation and mixing in combined size and density granular systems: an experimental study,” Granul. Matter, Vol. 7, pp. 69-81, 2005.
[35] H. A. Makse, S. Havlin, P. R. King, and H. E. Stanley, “Spontaneous stratification in granular mixtures,” Nature, Vol. 386, pp. 379-382, 1997.
[36] J. M. N. T. Gray, and K. Hutter, “Pattern formation in granular avalanches,” Continuum Mech. Thermodyn., Vol. 9, pp. 341-345, 1997.
[37] K.M. Hill, D.V. Khakhar, J.F. Gilchrist, J.J. McCarthy, and J.M. Ottino, “Segregation-driven organization in chaotic granular flows,” Proc. Natl. Acad. Sci., Vol. 96, pp. 11701-11706, 1999.
[38] K. M. Hill, G. Gioia, D. Amaravadi, and C. Winter, “Moon patterns, sun patterns, and wave breaking in rotating granular mixtures,” Complexity, Vol. 10, pp. 79-86, 2005.
[39] D.V. Khakhar, A. V. Orpe, and S.K. Hajra, “Segregation of granular materials in rotating cylinders,” Physica A, Vol. 318, pp. 192-136, 2003.
[40] D. V. Khakhar, A. V. Orpe, and J. M. Ottino, “Continuum model of mixing and size segregation in a rotating cylinder:concentration-flow coupling and streak formation,” Powder Technol., Vol. 116, pp. 232-245, 2001.
[41] K.M. Hill, G. Gioia, and D. Amaravadi, “Radial segregation patterns in rotating granular mixtures:waviness selection,” Phys. Rev. Lett., Vol. 93, 224301, 2004.
[42] I. Zuriguel, J.M.N.T. Gray, J. Peixinho, and T. Mullin, “Pattern selection by a granular wave in a rotating drum,” Phys. Rev. E, Vol. 73, 061302, 2006.
[43] S. W. Meier, D. A. M. Barreiro, J. M. Ottino, and R. M. Lueptow, “Coarsening of granular segregation patterns in quasi-two-dimensional tumblers,” Nature Physics, Vol. 4, pp. 244-248, 2008.
[44] I. Zuriguel, J. Peixinho, and T. Mullin, “Segregation pattern competition in a thin rotating drum,” Phys. Rev. E, Vol. 79, 051303, 2009.
[45] G.G. Pereira, S. Pucilowski, K. Liffman, and P.W. Cleary, “Streak patterns in binary granular media in a rotating drum,” Appl. Math. Model., Vol. 35, pp. 1638-1646, 2011.
[46] H.L. Gao, Y.Z. Zhao, G.S. Liu, Y.C. Chen, and J.Y. Zheng, “Effect of damping on segregation of size-type binary granular systems in a rotating horizontal drum” Acta Phys. Sin., Vol. 60, 074501, 2011.
[47] S. Ogawa, “Multi-temperature theory of granular materials” Proc. U. S.-Japan Symp. on Continuum Mechanics and Statistical Approaches in the Mechanics of Granular Materials., pp. 208-217, 1978.
[48] K.M. Hill, D.V. Khakhar, J.F. Gilchrist, J.J. McCarthy, and J.M. Ottino, “Segregation-driven organization in chaotic granular flows” Proc. Natl. Acad. Sci. U. S. A., Vol. 96, pp. 11701-11706, 1999.