本論文以旋轉鼓為實驗對象，研究在旋轉鼓中的流動層下方的潛變流區域，在高填充率下可以發現核心的產生，隨著時間的增加核心會不斷地縮小，被稱為侵蝕現象，且核心的轉速相較於旋轉鼓轉速稍快，稱為相位領先。本研究欲透過實驗了解顆粒表面粗糙度對於潛變流的影響，利用混合碳化矽與玻璃珠，透過球磨機製造出表面較粗糙的玻璃珠，與表面光滑的4 mm玻璃珠進行不同表面粗糙度對於旋轉鼓中潛變流之影響分析，分別在五個不同填充率下使用光滑顆粒與粗糙顆粒進行實驗，利用攝影機進行長時間的影像紀錄，利用高速攝影機拍攝影像透過PIV進行速度場分析，核心分析的結果顯示，顆粒表面粗糙度對於核心侵蝕和相位領先有存在著相關性，填充率越大，侵蝕越快，且粗糙顆粒有較大的侵蝕率；填充率越大，相位領先率越快，且光滑顆粒有較大的相位領先率。本文利用速度場分析出相關參數且利用數學模型對其現象進行討論，透過剪應變率、流動層厚度、特徵長度，剪應變率隨著填充率越大而越小，且粗糙顆粒有較小的剪應變率，特徵長度隨著填充率越大而越大，且粗糙顆粒有較大的特徵長度。剪應變率將主導相位領先的過程，而特徵長度將主導核心縮小的趨勢，改變顆粒粗糙度將會影響剪應變率及特徵長度，進而改變潛變流中的運動行為，包含核心的侵蝕和相位領先，最後本文將透過數學模型的預測比較理論的核心之相位領先和侵蝕和實驗結果，結果顯示實驗與理論趨勢相同。

This thesis is aimed to the effect of particles surface roughness on granular flow in a quasi-two dimensional rotating drum. The dynamic behavior of creeping flow under the flowing layer is discussed. The core is found in the center of rotating drum as fill ratio lager than 50%. The size of the core in the center of the rotating drum decreases as the drum rotating number increasing. This is so-call core erosion. The rotating speed of the core is larger than the rotating speed of the drum. This is so-call core precession.
Two different surface roughness of glass particles with 4mm diameter are used in the experiment. The rougher particles are roughened by a ball mill equipment with silicon carbide grit. The experiments are performed in five different fill rates in a 50 cm diameter rotating drum. A model from the literature based on the two regions of velocity profile is adopted to investigate the core dynamic. Depend on this model, the experimental results show that the characteristic length yR0R and the shear rate in the flowing layer both are dependent on the particles surface roughness. The characteristic length is larger for the rough surface of particle and larger at high fill rate. The shear rates are smaller for the rough surface of particle and smaller at high fill rate. The shear rates dominate the core precession and the characteristic length dominates the core erosion. Therefore, dynamic behavior of the core in the rotating drum is also different with different surface roughness of particles and different fill ratio. Core precession rate is smaller for the rough surface of particles and larger at high fill ratio. The core erosion rate is larger for the rough surface of particles and larger at high fill ratio.
Although there exists discrepancies between core dynamic model predictions and experimental measurement for the values of core precession rate and core erosion rate. The tendencies of the results from model prediction are in agreements with the experimental data for core precession and erosion.

[1] Fuerstenau, D. W., Lutch, J. J. and De, A., “The effect of ball size on the energy efficiency of hybrid high-pressure roll mill/ball mill grinding,” Powder Technology, Vol. 105, No. 1-3, pp. 199-204, 1999.
[2] Belyakov, A., Sakai, Y., Hara, T., Kimura, Y. and Tsuzaki, K., “Effect of dispersed particles on microstructure evolved in iron under mechanical milling followed by consolidating rolling,” Metallurgical and Materials Transactions A, Vol. 32, No.7, pp. 1769-1776, 2001.
[3] Yasmin, A., Abot, J. L. and Daniel, I. M., “Processing of clay/epoxy nanocomposites by shear mixing,” Scripta Materialia, Vol. 49, No. 1, pp. 81-86, 2003.
[4] Parker, D. J., Dijkstra, A. E., Martin, T. W. and Seville, J. P. K., “Positron emission particle tracking studies of spherical particle motion in rotating drums,” Chemical Engineering Science, Vol. 52, No. 13, pp. 2011-2022, 1997.
[5] Mellmann, J., “The transverse motion of solids in rotating cylinders - forms of motion and transition behavior,” Powder Technology, Vol. 118, No. 3, pp. 251-270, 2001.
[6] Fan, X. H., Li, J., Chen, X. L., Wang, Y. and Gan, M., “Temperature Field Simulation Model for Rotary Kiln of Iron Ore Oxidized Pellet,” Journal of Iron and Steel Research International, Vol. 20, No. 4, pp. 16-19, 2013.
[7] Shi, Y. C., Specht, E., Herz, F., Knabbe, J. and Sprinz, U., “Experimental investigation of the axial discharging velocity of particles from rotary kilns,” Granular Matter, Vol. 13, No. 4, pp. 465-473, 2011.
[8] Rosato, A.,Strandburg, K. J., Prinz, F. and Swendsen, R. H. “Why the Brazil nuts are on top: size segregation of particulate matter by shaking,” Physical Review Letters, Vol. 58, pp. 1038-1040, 1987.
[9] Gray, J. M. N. T., and Hutter, K., “Pattern formation in granular avalanches,” Continuum Mechanics and Thermodynamics, Vol. 9, No. 6, pp. 341-345, 1997.
[10] Zuriguel, I., Peixinho, J. and Mullin, T., “Segregation pattern competition in a thin rotating drum,” Physical Review E, Vol. 79, 051303, 2009.
[11] Khakhar, D. V., McCarthy, J. J. and Ottino, J. M., “Radial segregation of granular mixtures in rotating cylinders,” Physics of Fluids, Vol. 9, No. 12, pp. 3600-3614, 1997.
[12] Khakhar, D. V., Orpe, A. V., and Hajra, S.K., “Segregation of granular materials in rotating cylinders,” Physica A, Vol. 318, pp. 192-136, 2003.
[13] Henein, H., Brimacomble, J. K. and Watkinson, A.P., “Experimental study of transverse bed motion in rotary kilns,” Metallurgical Transactions B, Vol. 14, pp. 191-205, 1983.
[14] Rajchenbach, J., “Flow in powders: from discrete avalanches to continuous regime,” Physical Review Letters, Vol. 65, pp. 2221-2224, 1990.
[15] Hill, K. M. and Kakalios, J., “Reversible Axial Segregation of Rotating Granular Media,” Physical Review E, Vol. 52, No.4, pp.4393-4400, 1995.
[16] Jain, N., Ottino, J. M. and Lueptow, R. M., “An experimental study of the flowing granular layer in a rotating tumbler,” Physics of Fluids, Vol. 14, No. 2, pp. 572-582, 2002.
[17] Orpe, A. V. and Khakhar, D. V., “Scaling relations for granular flow in quasi-two-dimensional rotating cylinders,” Physical Review E, Vol. 64, pp. 1-13, 2001.
[18] Socie, B. A., Umbanhowar, P., Lueptow, R. M., Jain, N. and Ottino, J. M., “Creeping motion in granular flow,” Physical Review E, Vol. 71, No. 3, 031304, 2005.
[19] Komatsu, T. S., Inagaki, S., Nakagawa, N. and Nasuno, S., “Creep motion in a granular pile exhibiting steady surface flow,” Physical Review Letters, Vol. 86, No. 9, pp. 1757-1760, 2001.
[20] Bonamy, D., Daviaud, F. and Laurent, L., “Experimental study of granular surface flows via a fast camera: A continuous description,” Physics of Fluids, Vol. 14, No.5, pp. 1666-1673, 2002.
[21] du Pont, S. C., Fischer, R., Gondret, P., Perrin, B. and Rabaud, M., “Instantaneous velocity profiles during granular avalanches,” Physical Review Letters, Vol. 94, No. 4, 048003, 2005.
[22] Mueth, D. M., Debregeas, G. F., Karczmar, G. S., Eng, P. J., Nagel, S. R. and Jaeger, H. M., “Signatures of granular microstructure in dense shear flows,” Nature, Vol. 406, No. 6794, pp. 385-389, 2000.
[23] Crassous, J., Metayer, J.F., Richard, P. and Laroche, C., “Experimental study of a creeping granular flow at very low velocity,” Journal of Statistical Mechanics-Theory and Experiment, P03009, 2008.
[24] Gray, J. M. N. T., “Granular flow in partially filled slowly rotating drums,” Journal of Fluid Mechanics, Vol. 441, pp. 1-29, 2001.
[25] Metcalfe, G., Graham, L., Zhou, J. and Liffman, K., “Measurement of particle motions within tumbling granular flows,” Chaos, Vol. 9, No. 3, pp. 581-593, 1999.
[26] McCarthy, J. J., Shinbrot, T., Metcalfe, G., Wolf, J. E. and Ottino, J. M., “Mixing of granular materials in slowly rotated containers,” Aiche Journal, Vol. 42, No. 12, pp. 3351-3363, 1996.
[27] Arndt, T., Brucks, A., Ottino, J. M. and Lueptow, R. M., “Creeping granular motion under variable gravity levels,” Physical Review E, Vol. 74, No. 3, 2006.
[28] Lai, P. Y., Jia, L. C. and Chan, C. K., “Friction induced segregation of a granular binary mixture in a rotating drum,” Physical Review Letters, Vol. 79, No. 25, pp. 4994-4997, 1997.
[29] Zhou, Y. C., Xu, B. H., Yu, A. B. and Zulli, P., “An experimental and numerical study of the angle of repose of coarse spheres,” Power Technology, Vol.125, No. 1, pp. 45-54, 2002.
[30] Srebro, Y. and Levine, D., “Role of friction in compaction and segregation of granular materials,” Physical Review E, Vol. 68, No. 6, 061301, 2003.
[31] Pohlman, N. A., Severson, B. L., Ottino, J. M. and Lueptow, R. M., “Surface roughness effects in granular matter: Influence on angle of repose and the absence of segregation,” Physical Review E, Vol. 73, No. 3, 031304, 2006.
[32] Jain, N., Ottino, J.M. and Lueptow, R.M., “Regimes of segregation and mixing in combined size and density granular systems: an experimental study,” Granular Matter E, Vol. 7, No. 2-3, pp. 69-81, 2005.
[33] Sheng, L. T., Kuo, C. Y., Tai, Y. C. and Hsiau, S. S., “Indirect measurements of streamwise solid fraction variations of granular flows accelerating down a smooth rectangular chute,” Experiments in Fluids, Vol. 51, No. 5, pp 1329-1342, 2011.
[34] Pudasaini, S. P., Hutter, K., Hsiau, S. S., Tai, S. C., Wang, Y., and Katzenbach, R., “Rapid flow of dry granular materials down inclined chutes impinging on rigid walls,” Physics of Fluids, Vol. 19, No. 5, 053302, 2007.
[35] Pudasaini, S. P., Hsiau, S. S., Wang, Y. Q., Hutter, K., “Velocity measurements in dry granular avalanches using particle image velocimetry technique and comparison with theoretical predictions,” Physics of Fluids, Vol. 17, No. 9, 093301, 2005.
[36] Van Puyvelde, D. R., Young, B. R., Wilson, M. A. and Schmidt, S. J., “Experimental determination of transverse mixing kinetics in a rolling drum by image analysis,” Powder Technology, Vol. 106, No. 3, pp. 183-191, 1999.
[37] Finnie, G. J., Kruyt, N. P., Ye, M., Zeilstra, C. and Kuipers, J. A. M., “Longitudinal and transverse mixing in rotary kilns: A discrete element method approach,” Chemical Engineering Science, Vol. 60, No. 15, pp. 4083-4091, 2005.
[38] Orpe, A. V. and Khakhar, D. V., “Rheology of surface granular flows,” Journal Of Fluid Mechanics, Vol. 571, pp. 1-32, 2007.
[39] Liu, X. Y., Specht, E., Gonzalez, O. G. and Walzel, P., “Analytical solution for the rolling-mode granular motion in rotary kilns,” Chemical Engineering and Processing, Vol. 45, No. 6, pp. 515-521, 2006.
[40] Boateng, A. A., “Boundary layer modeling of granular flow in the transverse plane of a partially filled rotating cylinder,” International Journal of Multiphase Flow, Vol. 24, No. 3, pp. 499-521, 1998.
[41] Boateng, A. A. abd Barr, P. V., “Granular flow behaviour in the transverse plane of a partially filled rotating cylinder,” Journal of Fluid Mechanics, Vol. 330, pp. 233-249, 1997.
[42] Mellmann, J., Specht, E. and Liu, X. Y., “Prediction of rolling bed motion in rotating cylinders,” Aiche Journal, Vol. 50, No. 11, pp. 2783-2793, 2004.
[43] Schwedes, J. and Schulze, D., “Measurement of Flow Properties of Bulk Solids,” Powder Technology, Vol. 61, No. 1, pp. 59-68. 1990.
[44] Liao, C. C., Hsiau, S. S. and Wu, C. S., “Experimental study on the effect of surface roughness of the intruder on the Brazil nut problem in a vertically vibrated bed,” Physical Review E, Vol. 86, No. 6, 061316, 2012.
[45] Ferron, J. R. and Singh, D. K., “Rotary Kiln Transport Processes,” Aiche Journal, Vol. 37, No. 5, pp. 747-758,1991.
[46] Ding, Y. L., Forster, R. N., Seville, J. P. K. and Parker, D. J., “Scaling relationships for rotating drums,” Chemical Engineering Science, Vol. 56, No. 12, pp. 3737-3750, 2001.
[47] Schmaehling, J., Hamprecht, F. A. and Hoffmann, D. M. P., “A three-dimensional measure of surface roughness based on mathematical morphology,” International Journal of Machine Tools and Manufacture, Vol. 46, No. 14, pp. 1764-1769, 2006.
[48] Janus, J., Fauxpoint, G., Arntz, Y., Pelletier, H. and Etienne, O., “Surface roughness and morphology of three nanocomposites after two different polishing treatments by a multitechnique approach,” Dental Materials, Vol. 26, No. 5, pp. 416-425, 2010.
[49] Paik, P. and Kar, K. K., “Surface roughness and morphology of polypropylene nanospheres: effects of particles size,” Surface Engineering, Vol. 24, No. 5, pp. 341-349, 2008.
[50] Qu, J. and Shih, A., “Analytical surface roughness parameters of a theoretical profile consisting of elliptical arcs,” Machining Science and Technology, Vol. 7, No. 2, pp 281-294, 2003.
[51] Kunzler, T. P., Drobek, T., Sprecher, C. M., Schuler, M. and Spencer, N. D., “Fabrication of material-independent morphology gradients for high-throughput applications,” Applied Surface Science, Vol. 253, No. 4, pp. 2148-2153, 2006.