本論文主要針對不同間隙流體黏度及顆粒大小對於旋轉儀中潛變流的核心動態行為及顆粒傳輸性質進行探討。首先，利用不同比例的水及甘油調配出不同黏度的液體，並使用黏度計測量其黏度大小，接著藉由搖篩機篩出我們所需的顆粒尺寸範圍，最後進行三種顆粒尺寸及六種間隙流體黏度的實驗。實驗結果的部分首先使用攝影機進行長時間影像紀錄，藉此可分析計算出核心侵蝕率及相位領先率，再利用高速攝影機拍攝其運動過程並透過PTV進行傳輸性質之分析。
實驗結果顯示出間隙流體黏度及顆粒尺寸對於核心區域的顆粒潛變行為的影響是很大的。在核心動態行為的部分可以發現到，當間隙流體黏度越大時核心侵蝕率是越大的，同時相位領先率也會越快，且於乾系統時有較高的相位領先率。而於相同間隙流體黏度不同顆粒直徑時，顆粒越大侵蝕率會下降，相位領先率則會較快。至於在顆粒傳輸性質方面的結果則顯示，當間隙流體黏度越大，顆粒的平均速度、擾動速度和粒子溫度都會越來越小，同時在速度的變化趨勢方面也會越來越小，但在安息角角度及流動層厚度方面則會越來越大。當相同間隙流體黏度不同顆粒大小時，則是呈現顆粒直徑越大，剪應變率越小，特徵長度較大的情形，並且有較大的安息角角度及較小的流動層厚度。最後我們透過一無因次參數可以發現，核心侵蝕率與相位領先率對無因次參數分別是呈現不同數學模型的關係。

In this study, we report on experiments performed to investigate the core dynamic and the transport properties in a rotating drum with liquids of different viscosities and different particle sizes. In all of the slurry experiments, the drum was completely filled with the interstitial liquid. Several experiments were performed with mixtures of water and glycerin in a range of viscosities.
The experimental results indicate that both of the viscosity of the interstitial fluid and the particle size has a significant effect on the creeping flow in the slurry granular flow. When the particle size is the same, the increase in the liquid viscosity causes the erosion and precession to increase, while all the transport properties seem to decrease. However, the effect of particle size on the core dynamic and the transport properties are more complicated. A dimensionless variable is used to obtain the empirical formula. We found that the correlation between the dimensionless variable, erosion rate, and precession rate as an exponential function and a linear function respectively.

1. H.J. Herrmann, “Physics of granular media,” Chaos, Solitons and Fractals, Vol.6, pp.203-212, 1995.
2. 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,” Chemical Engineering Science, Vol.57, pp.4053-4065, 2002.
3. R.A. Bagnold, “Experiments on a gravity-free dispersion of large solid spheres in a newtonian fluid under shear,” Proceeding Royal Society of London, series A, Vol.225, pp. 49-63, 1954.
4. S. Ogawa., “Multi-temperature theory of granular materials,” In Proceedings of US-Japan Seminar on Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Materials, pp.208-217, 1978.
5. P. Bak, C. Tang and K. Wiesenfeld “Self-organized criticality: an explanation of 1 / f noise,” Physical Review Letters, Vol.59, pp.381-384, 1987.
6. H. Ahn, C.E. Brennen, and R.H. Sabersky, “Measurements of velocity fluctuation, density, and stressesin chute flows of granular materials,” Journal of Applied Mechanics, Vol. 58, pp. 792-803, 1991.
7. S.S. Hsiau and M.L. Hunt, “Shear-induced particle diffusion and logitndinal velocity fluctuations in a granular-flow mixing layer,” Journal of Fluid Mechanics, Vol. 251, pp. 299-313 , 1993.
8. V.V.R. Natarajan, M.L. Hunt, and E.D. Taylor, “Local measurements of velocity fluctuations and diffusion coefficients for a granular material flow,” Journal of Fluid Mechanics, Vol. 304, pp. 1-25, 1995.
9. X.Y. Liu, E. Specht, and J. Mellmann, “Experimental study of the lower and upper angles of repose of granular materials in rotating drums,” Powder Technology, Vol. 154, pp. 125-131, 2005.
10. N.A. Pohlman, B.L. Severson, J.M. Ottino, and R.M. Lueptow, “Surface roughness effects in granular matter: influence on angle of repose and the absence of segregation,” Physical Review E, Vol. 73, pp. 031304, 2006.
11. G. Felix, V. Falk, and U. D’Ortona, “Segregation of dry granular material in rotating drum: experimental study of the flowing zone thickness,” Powder Technology, Vol. 128, pp. 314-319, 2002.
12. H. Henein, J.K. Brimacomble, and A.P. Watkinson, “Experimental study of transverse bed motion in rotary kilns,” Metallurgical and Materials Transactions B, Vol. 14, pp. 191-205, 1983.
13. J. Rajchenbach, “Flow in powders: from discrete avalanches to continuous regime,” Physical Review Letters., Vol. 65, pp. 2221-2224, 1990.
14. J. Mellmann, “The transverse motion of solids in rotating cylinders-forms of motion and transition behavior,” Powder Technology, 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,” Chemical Engineering Science, 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 Technology, 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,” International Journal of 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,” Physical Review E, Vol. 64, pp. 1-13, 2001.
19. N. Jain, J.M. Ottino, and R.M. Lueptow, “An experimental study of the flowing granular layer in a rotating tumbler,” Physics of Fluids, Vol. 14, pp. 572-582, 2002.
20. T.S. Komatsu, S. Inagaki, N. Nakagawa, and S. Nasuno, “Creep motion in a granular pile exhibiting steady surface flow,” Physical Review Letters, Vol. 86, pp. 1757-1760, 2001.
21. J.J. McCarthy, T. Shinbrot, G. Metcalfe, J.E. Wolf, and J.M. Ottino, “Mixing of granular materials in slowly rotated containers,” AIChE Journal, Vol. 42, No. 12, pp. 3351-3363, 1996.
22. B.A. Socie, P. Umbanhowar, R.M. Lueptow, N. Jain, and J.M. Ottino, “Creeping motion in granular flow,” Physical Review E, Vol. 71, 031304, 2005.
23. T. Arndt, A. Brucks, J.M. Ottino, and R.M. Lueptow, “Creeping granular motion under variable gravity levels,” Physical Review E, Vol. 74, 2006.
24. S.J. Fiedor and J. M. Ottino, “Dynamic of axial segregation and coarsening of dry granular materials and slurries in circular and square tubes,” Physical Review Letters, Vol. 91, pp. 244301, 2003.
25. N. Jain, J.M. Ottino, and R.M. Lueptow, “Effect of interstitial fluid on a granular flowing layer,” Journal of Fluid Mechanics., Vol. 508, pp. 23-44, 2004.
26. T. Finger and R. Stannarius, “Influences of the interstitial liquid on segregation patterns of granular slurries in a rotating drum,” Physical Review E, Vol. 75, pp. 031308, 2007.
27. N. Jain, J.M. Ottino, and R.M. Lueptow, “Regimes of segregation and mixing in combined size and density granular systems: an experimental study,” Granular Matter, Vol.7, pp. 69-81, 2005.
28. A.A. Boateng and P.V. Barr, “Granular flow behaviour in the transverse plane of a partially filled rotating cylinder,” Journal of Fluid Mechanics, Vol. 330, pp. 233-249, 1997.
29. J.R. Ferron and D.K. Singh, “Rotary Kiln Transport Processes,” AIChE Journal, Vol. 37, pp. 747-758, 1991.
30. 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 Technology, Vol. 106, pp. 183-191, 1999.
31. G.J. Finnie, N.P. Kruyt, M. Ye, C. Zeilstra and, J.A.M. Kuipers, “Longitudinal and transverse mixing in rotary kilns: a discrete element method approach,” Chemical Engineering Science, Vol. 60, pp. 4083-4091, 2005.
32. H. Leslie, E.D. William, and S. S. Leonard, “Experimental study of bedrock erosion by granular flows,” Journal of Geophysical Research, Vol. 113, pp. F02001, 2008.
33. C. Jean-Francois and R. Patrick, “Characteristic lengths in granular piles exhibiting steady surface flows,” Geomechanics from Micro to Macro. pp. 141- 146, 2015.
34. S.C. du Pont, P. Gondret, B. Perrin, and M. Rabaud, “Granular Avalanches in Fluids,” Physical Review Letters, Vol. 90, pp. 044301, 2003.
35. J. Crassous, J.F Metayer, P. Richard, and C. Laroche, “Experimental study of a creeping granular at very low velocity,” Statistical Mechanics: Theory and Experiment, pp. 03009, 2008.