本論文研究顆粒體在不同的預先排列配置下，以不同的混合指標，對系統內顆粒體混合程度的分析，以及對於目前針對混合研究中常見的Lacey Mixing Index，提出另一新混合指標加以比較分析其優缺點。
研究結果顯示，在完全分離的狀態下，平均高度指標會較其他混合指標來的較為準確。而在混合過程中，平均高度混合指標，會因為系統內顆粒體分布的關係，對其所計算出之混合度發生影響。而Lacey Mixing Index 在某些特殊顆粒排列下會計算出較高的混合值，同時選取cell的大小對其後計算出的系統混合值亦有相當大之影響。
在本文中，沒有混合指標可準確的反應當下系統內顆粒體所處的真實混合度，混合指標間的優劣差異是在於能提供一相對穩定的混合趨勢指示。

This study represents the degree of mixing with different mixing index under the presetting particle system, and develops a new mixing index to compare with Lacey mixing index which is the most be used in granular mixing study and analyzed the performance of these two indices.
According to the results, the AVG. mixing index will indicate the best value in fully segregation and mixing state of system, but in the processing of mixing, the AVG. mixing value will be influenced by the distribution of particles in the system. And Lacey mixing will give higher mixing value while some special particle pattern, and the choice of cell size is a very important factor about the result of mixing value.
In this study no mixing indices can represent the degree of mixing of system precisely. To evaluate the degree of mixing of system depends on the feature of mixer or mixing mechanism, and the mixing index can give a relative accuracy and stable mixing values.

[1] Campbell, C. S. and Brennen, C.E. , 1895, “Chut flow of granular material: some computer simulations. ”J. Appl. Mech. Vol. 52, pp. 72-178.
[2] Faraday, M. , 1831, “On a peculiar Class of Acoustical Figures and on Certain Forms Assumed by Groups of Particles upon Vibrating Elastic Surfaces”. Philsosphical Transactions of the Royal Society of London, Vol. 121, pp. 299-340
[3] Reynolds, O. , 1885, “On the Dilatancy of Media Composed od Rigid Particle in Contact, with Experiment Illustration. ” Phil. Mag., Vol. 20, pp. 469-481.
[4] Hsiau, S. S. and Hunt, M. L. , 1993, “Kinetic Theory Analysis of Flow-induce Particle Diffusion and Thermal Conduction in Granular.
[5] Lacey P. M. C. , 1953, “Developments in the theory of particle mixing.”, J. Appl. Chem., Vol. 4 Issue 5, pp. 257 -268.
[6] Chandratilleke G. R., Yu A. B. , Stewart R.L., Bridgwater J. , 2009, “Effects of blade rake angle and gap on particle mixing in a cylindrical mixer.”, Powder Technol. Vol. 193 pp. 303–311 .
[7] Lu L. S. , Hsiau S. S. ,2008, “Mixing in a vibrated granular bed: Diffusive and convective effects. ” , Powder Technol. Vol. 184, pp.31-43.
[8] Troy S., Albert A., Maher M. and Fernando J. M., 1999, “Chaotic granular mixing.”, American Institute of Phy. , Vol. 9. pp. 611-620
[9] Weidenbaum, S. S., 1958, “Solids Mixing. ”Advances in Chemical Eng. II, pp. 211-321.
[10] Lacey, P. M. C. , 1943, “The Mixing of Solid Particles.” Tram. Inst. Chern. Engrs. , 21, pp. 53-59.
[11] Gayle, J. B., Lacey, 0. L., and Gary, J. H., 1958, “Mixing of Solids-x-quare as a Criterion,” Ind. Eng. Chem., pp. 1279-1282.
[12] Leggatt C. W., 1951 “Method of Making the Homogeneity Test,” 1951. Assoc. Official Seed Analysis News Letter. Vol. 25
[13] Venables, H. J. , Wells, J. I., 2001, “Powder mixing,” Drug Development and Industrial Pharm. , Vol. 27, No. 7, pp. 599-612.
[14] Rhodes, M., 1998, Introduction to Particle Technology. (John Wiley & Sons, London).
[15] Cooke, W. , Warr, S. , Huntley, J. M. and Ball, R. C., 1996, “Particle size segregation in a two-dimentional bed undergoing vertical vibration.” Phys. Rev. E. , Vol. 53, pp.2812-2822 .
[16] Knight, J. B., Ehrichs, E. E., Kuperman, V. Y., Flint, Jaeger, H. M and Nagel, S. R. ,1996, “An experimental study of granular convection.”Phys. Rev. E., Vol. 54, pp. 5726-5738 .
[17] Hsiau, S. S. and Tai, C. H. , 2004, “Dynanic Behavior of Powders in a Vibrating Bed.”Powder Technol. , Vol. 139 No. 3, pp.221-232
[18] Fan L. T. , Chen S. J. , And Watson C. A., 1970, “Solid Mixing. ” Industrial and Eng. Chem,.Vol. 62, No.7, pp.53-69.
[19] Alhwaige A. A., S. M. Tasirin, A. M. Sowedan, W. R. W. Daud, 2008, “Study The Homogeneity of Mixing a Binary Polyethylene Granular Mixture in Fluidised Bed Mixer. ”WCECS.
[20] L.S.Lu and S.S.Hsiau., 2006 “Study of granular mixing in vibrated beds and
sheared flows by DEM simulations”.,中央大學博士論文
[21] Shah R. , Manickam S.S. , Tomei J. , Bergman T.L., Chaudhuri B. 2009, “Mixing Study in a Multi-dimentional Motion Mixer. ”, Powder and Grains, pp.683-686.
[22] Kramer H . A., 1968 “Effect of Grain Velocity and Flow Rate Upon the Performance of a Diverter Type Sampler,” U.S. Dept. Agr. , ARS 51-25 .
[23] Weidenbaum, S. S., and Bonilla, C. F. , 1953, “ A Fundamental Study of the Mixing of Particulate Solids,” Ph.D. Thesis, Columbia Univ.
[24] Poux M, Fayolle P, Bertrand J, Bridoux D, Bousquet J, 1991, “Powder mixing
some practical rules applied to agitated systems. ”Powder-Technol.
.Vol. 68, issue3, pp. 213-234.
[25] Poole K. R. M. A., Taylor R. F. M.Sc., Wall G. P. , 1964, “Mixing Powders to fine-scale. homogeneity: studies of batch mixing. ”Chem. Eng. Research and Design.Vol. 42a, No.7, pp. 305-315.
[26] Deveswaran R. , Bharath S. , Basavaraj B. V. , Abraham S. , Furtado S. and Madhavan V. , 2009, “Concepts and Techniques of Pharmaceutical Powder Mixing Process: A Current Update. ”Research J. Pharm. and Tech2(2)., pp.245-249.
[27] Henrique, C., Batrouni, G. and Bideau, D., 2000, “Diffusion as a Mixing Mechanism in Granular Materials.” Phys. Rev. E., Vol. 63, No.1, pp. 1304-1311.
[28] Sahoo A. and Roy G.K. , 2005 “Mixing characteristic of homogeneous binary mixture of regular particles in a gas–solid fluidized bed.”Powder Technol. Vol. 159, Issue 3, pp. 150-154.
[29] S.S.Hsiau and H.Y.Yu., 1998 “Segregation phenomena in a shacker.”, Powder
Technol. , Volume 53, Number 6, June 1998 , pp. 35-35