振動床內顆粒運動之研究

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姓名

戴世璋(Shih-Chang Tai) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

振動床內顆粒運動之研究
(A study of the granular motion in a vibrated bed)

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摘要(中)

本論文探討二維及三維顆粒物質受到垂直振動時的運動狀態行為，本研究利用“凍結(jelled)”取樣的方法，在不使用昂貴的儀器操作下，有效計算三維振動顆粒床在不同振動條件下的顆粒分佈情形，並探討顆粒床自由表面的粒子運動行為和顆粒床內的流動轉換機制，藉由床體內粒子能量變化定義振動顆粒床的三種狀態行為:類固體狀態、過渡區和類液體狀態，當振動顆粒床的運動狀態從類固體狀態進入類液體狀態過程，顆粒床內的運動機制會由顆粒重組機制轉換為表面對流機制。在二維振動顆粒床方面，本研究討論不同振動參數對垂直顆粒床粒子運動的影響，發現振動速度越大、粒子佔有體積越小、顆粒層高度越低，會使得振動顆粒運動越劇烈，且在特別條件下，可以使得容器上壁能有效加強顆粒的運動。

摘要(英)

The dynamic behavior and the motion state of two-dimensional and three-dimensional granular materials subjected to external vibration were investigated. Sampling of a granular bed which had “jelled” at a steady state allowed for examination of the particle distributions inside the three-dimensional granular bed at different vibration conditions without involving expensive instruments. And the granular motion at the free surface of a vibrated bed and the transition of the flow regimes inside the bed could both be investigated. We studied the variation in the granular kinetic energy at the free surface of the three-dimensional vibrated bed under different vibration conditions. The variation in the energy defined the following motion states: solid-like state, transition region and liquid-like state. The movement mechanism inside the granular bed was transformed from particle reorganization to surface convection as the bed state transferred from a solid-like state to a liquid-like state. The influence of the vibration parameters on the granular motion of a two-dimensional vibrated granular bed was probed. It was found that the motion of the vibrated particles became stronger with the increase of dimensionless vibration velocity, the decrease of the solid fraction and the decrease of the dimensionless depth of the granular layer. Furthermore the upper-boundary of the container strengthened granular motion under some specific conditions.

關鍵字(中)

★ 振動速度
★ 類液體狀態
★ 過渡區
★ 類固體狀態
★ 粒子佔有體積
★ 顆粒層高度

關鍵字(英)

★ solid fraction
★ vibration velocity
★ liquid-like state
★ transition region
★ solid-like state
★ dimensionless depth of the granular layer

論文目次

摘要 I
Abstract II
誌謝 IV
Content VI
List of figures IX
Nomenclature XIV
Chapter 1 Introduction 1
1.1 Granular matter 1
1.2 Granular motion in a vibrated granular bed 3
1.2.1 Experimental studies 3
1.2.2 Numerical simulation and theoretical analysis 8
1.3 Phase transitions in the vibrated granular bed 10
1.4 Overview of this thesis 14
Chapter 2 Experimental Apparatus and Procedure 16
2.1 Vibrated granular bed system 16
2.2 Working particles and packing process 17
2.3 Image processing technology 19
Chapter 3 Movement Mechanisms during Solid-Like and Liquid-Like Motion States in a Vibrated Granular Bed 28
3.1 Results of movement mechanisms during different motion states 28
Chapter 4 Flow Regime during the Crystallization State and Convection State in a Vibrated Granular Bed 42
4.1 Results of four flow regimes 43
4.1.1 Slowly stabilizing crystallization state 47
4.1.2 Convection state 49
4.1.3 Fast stabilizing crystallization state 52
4.1.4 Unstable crystallization state 54
4.1.5 Relations between the flow regime and the motion mechanism 57
4.2 Results of time-average variations during stable motion varied with a/d 58
4.2.1 Transition from the slowly stabilizing crystallization state to the convection state 58
4.2.2 Transition from the convection state to the fast stabilizing crystallization state 59
4.2.3 Transition from the fast stabilizing crystallization state to the unstable crystallization state 60
4.2.4 Variation of parameters with the motion state and the motion mechanism 61
Chapter 5 Influences of the Vibration velocity, Solid Fraction and Dimensionless Depth of the Granular Layer on the Vibrated Granular Motion 78
5.1 Results of the vibrated granular motion 79
5.1.1 Variation of the granular motion given different conditions 80
5.1.2 Effect of changing the solid fraction on the granular motion 87
5.1.3 Effect of changing the dimensionless depth of the granular layer on the granular motion 91
Chapter 6 Conclusion 112
References 116
Appendix 129

參考文獻

Ahn, H., Brennen, C. E. and Sabersky, R. H., Measurements of velocity, velocity fluctuations, density and stresses in chute flows of granular materials. Journal of Applied Mechanics, 58 (1991) 792-803.
Alder, B. J. and Wainwright, T. E., Phase Transition in Elastic Disks, Phys. Rev., 127 (1962) 359-361.
Aranson,. I. S. et al., Electrostatically driven granular media: Phase transitions and coarsening, Phys. Rev. Lett., 84 (2000)3306-3309.
Aranson, I. S. B., Meerson, P. V. Sasorov and V. M. Vinokur, Phase separation and coarsening in electrostatically driven granular media, Phys. Rev. Lett., 88 (2002) 204301.
Argentina, M., Clerc, M. G. and Soto, R., van der Waals-like transition in fluidized granular matter, Phys. Rev. Lett., 89 (2002) 044301.
Asmar, B. N., Langston, P. A. and Matchett, A. J., A generalized mixing index in distinct element method simulation of vibrated particulate beds, Granul. Matter, 4 (2002) 129-138.
Baxter, G. W., Behringer, R. P., Fagert, T. and Johnson, G. A., Pattern formation in flowing sand, Phys. Rev. Lett., 62 (1989) 2825.
Baxter, G.W. and Olafsen, J.S., The temperature of a vibrated granular gas, Granular matter 9 (2007) 135-139.
Brennen, C. E., Ghosh, S., Wassgren, C. R., Vertical Oscillation of a Bed of Granular Material, J. of Appl. Mech., 63 (1996)156-161.
Brone, D. and Muzzio, F., Size-segregation in vibrated granular systems: A reversible process. Phys. Rev. E 56 (1997) 1059–1063.
Cafiero, R., Luding S. and Herrmann, H. J., Two-dimensional granular gas of inelastic spheres with multiplicative driving, Phys. Rev. Lett., 84 (2000) 6014-6017.
Campbell, C.S., Self-diffusion in granular shear flows, J. Fluid Mech. 348 (1997) 85–101.
Chapman, S. and Cowling, T. G., The Mathematical Theory of Non-Uniform Gases (Cambridge University Press, Cambridge (1970).
Carnahan, N. F. and Starling, K. E., Equations of State for Non-attracting Rigid Spheres, J. Chem. Phys., 51 (1969) 635-636.
Cartes, C., Clerc M. G., and Soto, R., van der Waals normal form for a one-dimensional hydrodynamic model, Phys. Rev. E., 70 (2004) 031302.
Cleary, P. W., Metcalfe, G. and Liffman K., How well do discrete element granular flow models capture the essentials of mixing processes? Appl. Math. Model., 22 (1998)995-1008.
Clément, E. and Rajchenbach, J., Fluidization of a bidimensional powder. Europhysics Letters, 16 (1991) 133-138.
Clément, E., Duran, J., Rajchenbach, J., Experimental study of heaping in a two-dimensional sandpile, Phys. Rev. Lett., 69 (1992) 1189-1192.
Clerc, M. G. et al., Liquid-solid-like transition in quasi-one-dimensional driven granular media, Nature physics, 4 (2008) 249-254.
Cordero, P., Ramirez, R. and Risso, D., Buoyancy driven convection and hysteresis in granular gases: numerical solution, Physica A, 327 (2003)82-87.
Cundall, P. K. and Strack, O. D. L., A discrete numerical model for granular assemblies, Géotechnique, 29 (1979) 47-65.
Daniels, K. E. and Behringer, R. P., Hysteresis and Competition between Disorder and Crystallization in Sheared and Vibrated Granular Flow, Phys. Rev. Lett., 94 (2005) 168001.
de. Gennes P. G., Granular matter: a tentative view, Phys Rev Lett., 71 (1999) S374-S382.
Douady, S., Fauve, S., Laroche, C., Subharmonic instabilities and defects in a granular layer under vertical vibrations, Europhys. Lett., 8 (1989) 621.
Drake, T. G., Granular flow: physical experiments and their implications for microstructural theories. Journal of Fluid Mechanics, 225 (1991)121-152.
Duran, J., Mazozi, T., Clément, E. and Rajchenbach, J., Size segregation in a two-dimensional sandpile: convection and arching effect, Phys. Rev. E., 50 (1994) 5138-5141.
Ehrichs, E.E., Jaeger, H.M., Karczmar, G.S., Knight, J.B., Kuperman, V.Y. and Nagel, S.R., Granular convection observed by magnetic resonance imaging, Science, 267 (1995) 1632-1634.
Elperin, T. and Golshtein, E., Effects of convection and friction on size segregation in vibrated granular beds, Physica A, 247 (1997) 67-78.
Eshuis, P., van der Weele, K., van der Meer, D., Bos, R. and Lohse, D., Phase diagram of vertically shaken granular matter, Phys. Fluids, 19 (2007) 123301.
Evesque, P. and Rajchenbach, J., Instability in a Sand Heap, Phys. Rev. Lett. 62 (1989) 44-46.
Faraday, M, On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces, Philos. Trans. R. Soc. London, 121 (1831) 299
Fauve, J., Douady, S., Laroche, C., Collective behaviors of granular masses under vertical vibrations, J. Phys., 50 (1989) 699.
Fiscina, J., Ohligschläger, M. and Mücklich, F., W-Cu Graded Alloys Produced by Size Segregation of Agglomerates Induced by Vertical Vibration at High Frequencies, Journal of Materials Science Letters, 22 (2003) 1455-1457.
Fiscina, J., Ilic, D.J. and Mücklic, F., Applying the Brazil-nut approach to manufacture W-Cu-graded materials, Granular Matter, 6 (2004) 207-213.
Fiscina, J. and Caceres, M., Fermi-Like Behavior of Weakly Vibrated Granular Matter, Physical Review Letters, 95 (2005) 108003-1—108003-4.
Gallas, J. A. C., Herrmann, H. J. and Sokolowski, S., Convection Cells in Vibrating Granullar Media, Phys. Rev. Lett., 69 (1992) 1371-1374.
Gennes, P. G. de, Reflections on the mechanics of granular matter, Physica A., 261 (1998) 267-293.
Goldman, D.I., Shattuck, M.D., Moon, S.J., Swift, J.B. and Swinney, H.L., Lattice dynamics and melting of a nonequilibrium pattern, Phys. Rev. Lett., 90 (2003) 104302.
Gotoh, K., Masuda, H. and Higashitani, K., Powder Technology Handbook, Marcel Dekker, New York (1997).
Grebenkov, D. S., Ciamarra, Nicodemi, M. Pica, Coniglio, M., A., Flow, ordering, and jamming of sheared granular suspensions, Phys. Rev. Lett., 100 (2008)078001.
Gyenis, J., Assessment of mixing mechanism on the basis of concentration pattern, Chem. Eng. Process., 38 (1999) 665–674.
Herrman H. J., Hovi J.P. and Luding S, Physics of Dry Granular Media (Kluwer, Dordrecht, The Netherlands) (1998)
Hsiau, S. S. and Hunt, M. L., Kinetic theory analysis of flow-induced particle diffusion and thermal conduction in granular material flows, Trans. ASME C: J. Heat Transf., 155 (1993) 541–548.
Hsiau, S. S. and Shieh, Y. H., Fluctuations and self-diffusion of sheared granular material flows, Journal of Rheology., 43 (1999) 1049-1066.
Hsiau, S. S. and Hunt, M. L., Shear-induced particle diffusion and longitudinal velocity fluctuations in a granular-flow mixing layer. Journal of Fluid Mechanics, 251 (1993) 299-313.
Hsiau, S.S. and Yu, H.Y., Segregation phenomena in a shaker, Powder Technol. 93 (1997) 83–88.
Hsiau, S. S. and Jang, H. W., Measurements of velocity fluctuations of granular materials in a shear cell. Experiments in Thermal and Fluid Science, 17 (1998) 202-209.
Hsiau, S. S. and Chen, C. H., Granular convection cells in a vertical shaker, Powder Tech., 111 (2000) 210-217.
Hsiau, S.S. and Yang, W.L., Stresses and transport phenomena in sheared granular flows with different wall conditions, Phys. Fluids, 14 (2002) 612–621.
Hsiau, S.S., Wang, P.C. and Tai, C.H., Convection cells and segregation in a vibrated granular bed, AIChE J., 48 (2002) 1430–1438.
Hsiau, S.S. and Huang, T.C., Motion Mechanism in a Vibration Bed under Weakly Vibrating Conditions, Proceedings of 29th National Conference on Theoretical and Applied Mechanics, Hsinchu (2005) B007-1—B007-8.
Hsiau, S.S. and Tai, S.C., Motion Mechanism in a Weakly Vibrating Bed. Proceedings of 23th National Conference of Chinese Society of Mechanical Engineers, Tainan (2006) 379-383.
Hunt, M.L., Hsiau, S.S. and Hong, K.T., Particlemixing and volumetric expansion in a vibrated granular bed, ASME J. Fluids Eng., 116 (1994) 785–791.
Ilic, D.J., Self formed Cu-W functionally graded material created via powder segregation, thesis (2007).
Jaeger, H. M. and Nagel, S. R., For a review of the physics of granular media see, for example, Science, 255 (1992) 1523
Jaeger, H.M. and Nagel, S.R., Granular solids, liquids, and gases, Rev. Mod. Phys., 68 (1996) 1259-1273.
Jullien, R. and Meakin, P., Three-dimensional model for particle-size segregation by shaking, Phys. Rev. Lett., 69 (1992) 640–643.
Kadanoff L. P., Theoretical Ideas Inspired by the Flow of Granular Materials, Rev Mod Phys, 71 (1999) 435-444.
Kim, K. and Pak, H. K., Coarsening Dynamics of Striped Patterns in Thin Granular Layers under Vertical Vibration, Phys. Rev. Lett., 88 (2002) 204303.
Kim, K., Moon, J.K., Park, J.J., Kim, H.K. and Pak, H.K., Jamming transition in a highly dense granular system under vertical vibration, Phys. Rev. E, 72 (2005) 011302.
Knight, J. B., Jaeger, H. M. and Nagel, S. R., Vibrated-induced size separation in granular media: the convection connection, Phys. Rev. Lett., 70 (1993) 3728-3731.
Knight, J.B., Frandrich, C.G., Lau, C.N., Jaeger, H.M.and Nagel, S.R., Density relaxation in vibrated granular materials, Phys. Rev. E, 51 (1995) 3957–3963.
Knight, J.B., Ehrichs, E.E., Kuperman, V.Y., Flint, J.K., Jaeger, H.M. and Nagel, S.R., Experimental study of granular convection, Physical Review E, 54 (1996) 5726-5738.
Knight, J.B., External boundaries and internal shear bands in granular convection, Physical Review E, 55 (1997) 6016-6023.
Kolb, E., Cviklinski, J., Lanuza, J., Claudin, P. and Cle´ment, E., Reorganization of a dense granular assembly: The unjamming response function, Phys. Rev. E., 69 (2004) 031306.
Kolb, E., Goldenberg, C., Inagaki, S., and Cle´ment, E., Reorganization of a two-dimensional disordered granular medium due to a small local cyclic perturbation, J. Stat. Mech., 7 (2006) P07017.
Kosterlitz, J. M. and Thouless, D. J., Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C., 6 (1973) 1181-1203.
Kudrolli, A., Size separation in vibrated Granul. Matter, Rep. Prog. Phys. 67 (2004) 209–247.
Lan, Y. and Rosato, A.D., Macroscopic behavior of vibrating beds of smooth inelastic spheres, Phys. Fluids, 7 (1995) 1818-1831.
Lan, Y. and Rosato, A.D., Convection related phenomena in granular dynamics simulations of vibrated beds, Physical Fluids, 9 (1997) 3615-3624.
Laroche, C., Douady, S. and Fauve, S., Convective flow of granular masses under vertical vibrations, J. Phys. France., 50 (1989) 699-706.
Liu, C-h. and Nagel, S. R., Sound in sand, Phys. Rev. Lett., 68 (1992) 2301-2304.
Lindemann, F. A., The Calculation of Molecular Vibration Frequencies, Phys. Z., 11 (1910) 609.
Lun, C. K. K., Savage, S. B., Jeffrey, D. J. adn Chepurniy, N., Kinetic theories for granular flow: inelastic particle in couette Flow and slightly inelastic particles in a flow field. Journal of Fluid Mechanics, 140 (1984) 233-256.
Luding, S., Cle´ment, E., Blumen, A. and Rajchenbach, J., Onset of convection in molecular dynamics simulations of grain, J. Duran, Phys. Rev. E., 50 (1994) R1762-R1765.
Melby, P. et al., The dynamics of thin vibrated granular layers, J. Phys. Condens. Matter, 17 (2005)S2689-S2704.
Midi, G. D. R., On dense granular flows, E. Phys. J. E., 14 (2004)367-371.
Mitus, A. C., Weber, H. and Marx, D., Local structure analysis of the hard-disk fluid near melting, Phys. Rev. E., 55 (1997) 6855-6859.
Melo, F., Umbanhowar, P.B. and Swinney, H.L., Transition to parametric wave patterns in a vertically oscillated granular layer, Phys. Rev. Lett., 72 (1994) 172.
Melo, F., Umbanhowar, P.B. and Swinney, H.L., Hexagon, Kinks, and Disorder in Oscillated Granular Layers, Phys. Rev. Lett., 75 (1995) 3838-3842.
Moucka, F. and Nezbeda, I., Detection and Characterization of Structural Changes in the Hard-Disk Fluid under Freezing and Melting Conditions, Phys. Rev. Lett., 94 (2005) 040601.
Natarajan, V.V.R., Hunt, M.L. and Taylor, E.D., Local measurements of velocity fluctuations and diffusion coefficients for a granular material flow, The Journal of Fluid Mechanics, 304 (1995) 1-25.
Olafsen, J. S. and Urbach, J. S., Two-Dimensional Melting Far from Equilibrium in a Granular Monolayer, Phys. Rev. Lett., 95 (2005) 098002.
Ogawa, S., Multi-temperature theory of granular materials. In Proceedings of US-Japan Seminar on Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Materials, Tokyo, Japan, (1978) 208-217.
Olafsen, J. S. and Urbach, J. S.. Clustering, Order, and Collapse in a Driven Granular Monolayer, Phys. Rev. Lett., 81 (1998) 4369-4372.
Pak, H. K. and Behringer, R. P., Surface waves in vertically vibrated granular materials, Phys. Rev. Lett., 71 (1993) 1832-1835.
Pak, H. K., Van Doorn, E., and Behringer, R. P., Effects of Ambient Gases on Granular Materials under Vertical Vibration, Phys. Rev. Lett., 74 (1995) 4643-4646.
Pinto, S. F., Couto, M. S., Atman, A. P. G., Alves, S. G., Bernardes, A. T., de Resende, H. F. V. and Souza, E. C., Granular fingers on jammed systems: new fluidlike patterns arising in grain-grain invasion experiments, Phys. Rev. Lett., 99 (2007) 068001.
Pöschel, T. and Herrmann, H. J., Size segregation and convection. Europhys. Lett., 29 (1995) 123-128.
Prados, A., Javier Brey, J.and S´anchez-Rey, B., Hysteresis in vibrated granular media, Physica A, 284 (2000) 277-296.
Prevost, A., Melby, P., Egolf, D. A. and Urbach, J. S., Non-equilibrium two-phase coexistence in a confined granular layer, Phys. Rev. E., 70 (2004) 050301(R).
Reynolds, O., On the Dilatancy of Media Composed of Rigid Particles in Contact, With experimental illustrations, Phil. Mag., 20 (1885) 469-481.
Reynolds, O., Experiments Showing Dilatancy, A Property of Granular Materials Possibly Connected with Gravitation, Proc. Roy. Inst. Of Gr. Britain., 11 (1886) 354-363.
Reis, P. M., Ingale, R. A. and Shattuck, M. D., Crystallization of a Quasi-Two-Dimensional Granular Fluid, Phys. Rev. Lett., 96 (2006) 258001.
Rhodes, M. J., Wang, X. S., Nguyen, M., Stewart, P. and Liffman K., Study of mixing in gas-fluidized beds using a DEM model, Chem. Eng. Sci., 56 (2001) 2859-2866.
Rosato, A.D., Strandburg, K.J., Prinz, F. and Swendsen, R., Why the Brazil nuts are on top: size segregation of particulate matter by shaking, Phys. Rev. Lett., 58 (1987) 1038– 1040.
Rosato, A.D., Blackmore, D.L., Zhang, N. and Lan, Y., A perspective on vibration-induced size segregation of granular materials, Chemical Engineering Science, 57 (2002) 265-275.
Savage, S.B. and Dai, R., Study of shear flows—Wall slip velocities, ‘layering’ and self-diffusion, Mech. Mater., 16 (1993) 225–238.
Savage, S. B., Streaming motions in a bed of vibrationally fluidized dry granular material, J. Fluid Mech., 194 (1988) 457-478.
Saija, F., Prestipino, S. and Giaquinta, P. V., Evaluation of phenomenological one-phase criteria for the melting and freezing of softly repulsive particles, J. Chem. Phys., 124 (2006) 244504.
Schmidt, M. and Löwen, H., Phase diagram of hard spheres confined between two parallel plates, Phys. Rev. E 55 (1997) 7228–7241.
Seshadri R. and Westervelt, R. M., Statistical mechanics of magnetic bubble arrays. II. Observations of two-dimensional melting, Phys. Rev. B., 46 (1992) 5150-5161.
Shinbrot, T., Competition between randomizing impacts and inelastic collisions in granular pattern formation, Nature, 389 (1997) 574-576.
Taguchi, Y.H., New origin of convective motion: elastically induced convection in granular materials, Phys. Rev. Lett., 69 (1992) 1367-1370.
Tai, C.H. and Hsiau, S.S., Dynamic behaviors of powders in a vibrated bed, Powder Technol., 139 (2004) 221–232.
Tsuji, Y., Kawaguchi, T. and Tanaka, T., Discrete particle simulation of two-dimensional fluidized bed, Powder Technol., 77 (1993) 79.
Tsuji, Y., Multi-scale modeling of dense phase gas-particle flow, Chem. Eng. Sci., 62 (2007) 3410.
Umbanhowar, P. B., Melo, F., and Swinney, H. L., Localized excitations in a vertically vibrated granular layer, Nature, 382 (1996) 793-796.
Vanel, L., Rosato, A. D., and Dave, R. N., Rise-Time Regimes of a Large Sphere in Vibrated Bulk Solids, Phy. Rev. Lett., 78 (1997) 1255--1258.
Walton, O. R. and Braun, R. L., Stress calculations for assemblies of inelastic spheres in uniform shear. Acta Mechanica, 63 (1986) 73-86.
Warr, S., Huntley, J.M., Jacques, G.T., Fluidization of a two-dimensional granular system: experimental study and scaling behavior, Phys. Rev. E, 52 (1995) 5583.
Wassgren, C.R., Brennen, C.E. and Hunt, M.L., Vertical vibration of a bed of granular material in a container, J. Appl. Mech., 63 (1996) 712.
Weele van der, J. P., Meer van der, R. M., Versluis, M. and Lohse, D., Hysteretic clustering in granular gas, Europhysics letters, 53 (2001) 328-334.
Williams, J. C., The Segregation of Particulate Materials – a Review, Powder Tech., 15(1976) 245-251
Wildman, R. D. Huntley, J. M., Novel method for measurement of granular temperature distributions in two-dimensional vibro-fluidised beds, Powder Technol., 113 (2000) 14-22.
Workshop on Physics of Granular Matter, Scuola Normale Superiore, Pisa, Italy, October 22-24, (1998).
Yang, S.C. and Hsiau, S.S., Simulation study of the convection cells in a vibrated granular bed. Chemical Engineering Science, 55 (2000) 3627-3637.
Zeilstra, C., Hoef, M. and Kuipers, J.A.M., Simulation study of air-induced segregation of equal-sized bronze and glass particles, Physical Review E, 74 (2006) 010302.
Zik, O. and Stavans, J., Self-diffusion in granular flows, Europhys. Lett., 16 (1991) 255–258.

指導教授

蕭述三(Shu-San Hsiau)

審核日期

2009-8-4

推文