本文運用實驗的方式探討顆粒體在垂直振動床內，不同的液體含量、表面張力和黏度對其動態行為的影響。研究主題包括不同的液體條件下對振動顆粒床體的迴流運動、整體粒子溫度、顆粒體擾動速度分佈及粒子自我擴散運動的探討。
　　本文首先以實驗的方法，定性探討附著性顆粒振動床的迴流運動現象，實驗結果與相關文獻的實驗結果比較，頗為符合；進一步以定量的觀點分析顆粒間液體含量、表面張力、黏度與粒子溫度的關係，同時計算迴流中心質量流率的大小。接著，以實驗的方法討論顆粒體擾動速度分佈及顆粒體振動床的自我擴散運動，粒子自我擴散運動乃是經由粒子間持續碰撞運動的變動速度所產生。在實驗方面，應用影像處理技術及粒子追蹤的方法，可準確量測並計算出追蹤粒子的位置與速度大小，藉由追蹤粒子的擴散位移與時間的關係可計算出粒子的自我擴散係數。此外，振動床體平均變動速度、粒子溫度的大小與自我擴散係數，由於受到垂直振動外力的影響，呈現非等向性分佈，在垂直方向分量大於水平方向分量，相關的研究在本文中均有深入的探討。
關於含有液體的顆粒體，文中以不同液體黏度、表面張力和液體添加量的ㄧ百二十組實驗做為分析對象，來探討顆粒體間液橋力對顆粒體動態行為的影響。當顆粒體受垂直振動力的作用時，床體能量會因為某些因素的的影響而消散，包括粒子間的摩擦阻力與非完全彈性碰撞、黏性液橋力的黏滯阻力與毛細結合力等。由實驗結果顯示，在固定振動條件下，能量的消散主要來自於液體液橋力的黏滯阻力，毛細力的影響較不明顯，能量消散的大小並隨著粒子間液體多寡的增加而增加。

This thesis examines the dynamic behaviors of granular materials subjected to external vertical vibration. The cohesive materials are considered in this thesis. Two-dimensional experiment method is used to study the flow behaviors when we added different liquid content, different viscous liquids and liquids of different surface tension.
The flow behaviors of convection cells of cohesive materials under vertical vibration are first investigated by experiment method. The results are consistent with the former experimental results. The convection flow rate and the granular temperatures are studied with different liquid content, different viscous liquids and liquids of different surface tension . The influences of flow parameters on self-diffusion in the vibrated granular bed are studied by simulation and experiment. Employing the image processing technology and particle tracking method, the local displacements and velocities of particles are measured. The self-diffusion coefficients are determined from the history of particle’s diffusive displacements. The flow behaviors of convection cell are strongly related to the self-diffusion of particles induced by the energy input from the vertical external vibration. The velocity fluctuations, granular temperature and self-diffusions are anisotropic with greatest components in the vertical direction. The self-diffusion coefficients and the granular temperature are discussed carefully.
One hundred twenty types of liquids with different liquid content, different viscous liquids and liquids of different surface tension are used in this thesis. The effect of liquid bridge force with particle dynamic behavior are studied in this paper. The energy dissipations during vertical vibration are generated from the friction and inelasticity between particles, viscous resistance and liquid bridge bond rupture due to the liquid bridge. For cohesive granular materials, the energy dissipation is mainly associated with the viscous force, the interparticle friction and the inelasticity of collision, rather than with the capillary force of liquid bridge. The results of experiment reveals that the energy dissipation caused by viscous force are larger than capillary force. The energy dissipation increases monotonously with the increase of the dimensionless interstitial liquid volume, and the dissipation are strongly influenced by the properties of viscous liquids.

1.Campbell, C. S., 1990, “Rapid Granular Flows,” Annu. Rev. Fluid Mech.,Vol. 22, pp. 57-92.
2. Reynolds, Osborne, 1887, “Experiments Showing Dilutency, A Property
of Granular Materials Possibly Connected with Gravitation,” Proc. Roy.
Inst. Great Brit., Vol. 11, pp. 354.
3. Campbell, C. S. and Brennen, C. E., 1985a, “Computer Simulation of
Granular Shear Flows,” J. Fluid Mech., Vol. 151, pp. 167－188.
4. Walton, O. R. and Braun, R.L., 1986b, “Stress Calculations for
Assemblies of Inelastic Spheres in Uniform Shear,” Acta
Mechanica,Vol. 63. pp. 73－86.
5. Campbell, C. S. and Gong, A., 1986, “The Stress Tensor in a Two-
Dimensional Granular Shear Flow,” J. Fluid Mech., Vol. 164. pp. 107－ 125.
6. Campbell, C. S., 1989, “The Stress Tensor for Simple Shear Flow of a
Granular Material,” J. Fluid Mech.,Vol. 203. pp. 449－473.
7. Savage, S. B. and Jeffrey, D. J., 1981, “The Stress Tensor in a Granular
Flow at High Shear Rates,” J. Fluid Mech., Vol. 110, pp. 255－272.
8. Jenkins, J. T. and Savage, S. B., 1983, “A Theory for the Rapid Flow of
Identical, Smooth, Nearly Elastic, Particles,” J. Fluid Mech., Vol. 130,
pp. 187－202
9. Lun, C. K. K., Savage, S. B., Jeffrey, D. J. and Chepurniy, N., 1984,
“Kinetic Theories for Granular Flow:Inelastic Particles in Couette
Flow and Slightly Inelastic Particles in a General Flowfield,” J. Fluid
Mech., Vol. 140, pp. 223－256.
10. Savage, S. B. and Mckeown, S., 1983, “Shear Stress Developed during
Rapid Shear of Dense Concentrations of Large Spherical Particles
between Concentric Cylinders,” J. Fluid Mech., Vol. 127,
pp. 453－ 472.
11. Savage S. B. and Sayed, M., 1984, “Stresses Developed by Dry
Cohesionless Granular Materials Sheared in an Annular Shear Cell,” J.
Fluid Mech., Vol. 142, pp. 391－430.
12. Hanes, D. M. and Inman, D. L., 1985, “Observations of Rapid Flowing
Granular--Fluid Flow,” J. Fluid Mech., Vol. 150, pp. 357－380.
13. Wang, D. G. and Campbell, C. S., 1992, “Reynolds Analogy for a
Shearing Granular Msterials,” J. Fluid Mech., Vol. 244, pp. 527－546.
14. Ahn, H., Brennen, C. E. and Sabersky, R. H., 1991, “Measurements of
Velocity Fluctuation, Density, and Stressesin Chute Flows of Granular
Materials,” J. Appl. Mech., Vol. 58, pp. 792－803.
15. Hsiau, S. S. and Hunt, M. L., 1993a, “Shear-Induced Particle Diffusion
and Logitndinal Velocity Fluctuations in a Granular-Flow Mixing
Layer,” J. Fluid Mech., Vol. 251, pp. 299－313.
16. Natarajan, V. V. R., Hunt, M. L. and Taylor, E. D., 1995, “Local
Measurements of Velocity Fluctuations and Diffusion Coefficients for A
Granular Material Flow,” J. Fluid Mech., Vol. 304, pp. 1－25.
17. Savage, S. B., 1992, “Disorder, Diffusion and Structure Formation in
Granular Flows,” in Disorder and Granular Media, D. Bideau, ed.,
Elsevier Science Publishers, Amsterdam, pp. 225-285.
18. Hsiau, S. S. and Hunt, M. L., 1993b, “Kinetic Theory Analysis of Flow-
Induced Particle Diffusion and Thermal Conduction in Granular S. S.
19. Kennard, E. H., 1938, “Kinetic Theory of Gases,” McGraw-Hill.
20. Hwang, C. L. and Hogg, R., 1980, “Diffusive Mixing in Flowing Powder
Calculations for Shearing Assemblies of Inelastic, Frictional disks,” J.
Rheol.,Vol. 30. pp. 949－980.
21. Bridgwater, J.,1980, “Self-Diffusion Coefficients in Deforming Powders,
” Powder Technol., Vol. 25, pp. 129－131.
22. Buggusch, H. and Loffelmann, G., 1989, “Theoretical and Experimental
Investigations into Local Granulate Mixing Mechanisms,” Chem. Engng.
Process, Vol. 26, pp. 193－200.
23. Johanson, K., Rabinovicha, Y., Moudgilb, B., Breeceb, K., Taylor, H.,
2003, “Relationship between particle scale capillary forces and bulk
unconfined yield strength,” Powder Technol., Vol. 138, pp. 13-17.
24. Wassgren, C. R, Brennen, C. E, and Hunt, M. L., 1996,“Vertical
vibration of a deep beds of granular material in a contiainer,”J. Appl.
Mech.,Vol.63, pp.712-719.
25. Hunt, M. L., Hsiau, S. S. and Hong, K. T., 1994, “Particle Mixing and
Volumetric Expansion in a Vibrated Granular Bed,” J. Fluids Engi.,
Vol. 116, pp. 785－791.
26. Hsiau, S. S. and Pan, S. J., 1998,“Motion state transitions in a vibrated
granular bed,”Powder Technol., Vol. 96, pp.219-226.
27. Hsiau and Yu, H. Y., 1997, “Segregation phenomena in a shaker,” Powder Technol., 93, pp. 83-88.
28. Barker, G. C. and Mehta, A., 1993, “Size Segregation Mechanisms,”
Nature, Vol. 364, pp. 486－487.
29. Bachman, D., 1940, Verfahrenstechnik Z .D.I . Beiheft, No. 2, pg. 43.
(cited by Thomas et al., 1989.)
30. Suzuki, K., Hosaka, H., Yamazaki, R. and Jimbo, G., 1980, “Drying
Characteristics of Particles in a Constant Drying Rate Period in
Vibro-Fluidized Bed,” J. Chem. Engi., Japan, Vol. 13, pp.117-122.
31. Yu, S. H., Ma, B. J. and Weng, Y. Q., 1992, “Drying Performance and
Heat Transfer in a Vibrated Fluidized Beds,” Drying 92, A. S. Mujumdar,
ed., Elsevier Science Publishers, Amsterdam, pp. 731-740.
32. Pakowski, Z., Mujumdar, A. S. and Strumillo, C., 1984, “Theory and
Application of Vibrated Beds and Vibrated Fluid Beds for Drying
Processes,” Advances in Drying, Vol. 3, A. S. Mujumdar, ed.,
Hemisphere Publishing, pp. 245-306.
33. Chlenov, V. A. and Mikhailov,N.V., 1965,“Some properties of a vibrating
fluidized bed,”J. of Eng. Phys., Vol. 9, pp. 137-139.
34. Evesque, p. and Rajchenbach, J., 1989, “Instability in a sand heap,”Phys.
Rev. Lett., Vol. 69, No. 1, pp. 44-46.
35. Hsiau, S. S., Wu, M. H. and Chen, C. H., 1998, “Arching phenomena in
a vibrated granular bed,”Powder Technol., Vol. 99, pp. 185-193
36. 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.
37. Cooke, W., Warr, S., Huntley, J. M. and Ball, R. C., 1996, “Particle size
segregation in a two-dimensional bed undergoing vertical
vibration,”Phys. Rev. E., Vol. 53, pp. 2812-2822.
38. Vanel, Loic, Rosato, A. D., and Dave, R. D., 1997,“Rise-time regimes of
a large sphere in vibrated bulk solids,”Phy. Rev. Lett., Vol. 78, pp.
1255-1258.
39. Fraysse, N., Thome, H., and Petit, L., 1999, “Humidity effects on the
stability of a sandpile,” Europe. Phys. J. B, Vol. 11, pp. 615-619.
40. Howell, D. W., Aronson, Igor. S. And Crabtree, G. W., 2001, “Dynamics
of electrostatically driven granular media: Effects of humidity,” Phys.
Rev. E., Vol. 63, 050301(R).
41. Albert, R., Albert, I., Hombaker, D., Schiffer, P. and Barabasi, A. L.,
1997, “Maximum angle of stability in wet and dry spherical granular
media,” Phys. Rev. E. Vol.56, pp. 6271(R)－6274(R).
42. Rennie, P. R., Chen, X. D., Hargreaves, C.,Mackereth, A. R., 1999, “A
study of the cohesion of dairy powders, ” J. Food. Engng., Vol. 39, pp.
277-284.
43. Hsiau, S. S. and Yang, S. C., 2003, “Numerical simulation of
self-diffusion and mixing in a vibrated granular bed with the cohesive
effect oh liquid bridges,” Chem. Engng Sci., Vol. 58, pp. 339-351.
44. Nase, S.T., Vargas, W.L., Abatan, A.A., McCarthy, J.J., 2001, “Discrete
characterization tools for cohesive granular material,” Powder Technol.,
Vol. 116, pp. 214-223.
45. Jain, K., and McCarthy, J.J., 2002, “Discrete characterization of cohesion
in gas-solid flows,” Proceedings of IMECE2002, IMECE2002-32491.
46. Kohonen, M. M., Geromichalos, D., Scheel, M., Schierb, C.,
Herminghausb, S., 2004, ”On capillary bridges in wet granular
materials,” Phys. A., Vol. 339, pp. 7-15.
47. Yang, S. C. and Hsiau, S. S. , 2001, “The simulation of powders with
liquid bridges in a 2D vibrated bed,” Chem. Eng. Sci. 56. 6837-6849.
48. Ennis, B. J., Tardos, J. Li, G. I., Pfeffer, R., “The influence of viscosity
on the strength of an axially strained pendular liquid bridge,” Chem. Eng. Sci. 45 (1990) 3071-3088.
49. Adams, M. J., Thormton, C., Lian, G., “First International Particle
Technology Forum,” 1994, Aggllomerate Coalescence, Vol.1, August
17-19, Denver, USA, pp. 220-224.
50. Mason, T.G., Levine, A. J., Ertas, D., Halsey,T.C., Phys. Rev. E 60 (1999) R5044.
51. Fisher, R. A., 1926, “On the Capillary Forces in an Ideal Soil,” J. Agric.
Sci., Vol. 16, pp. 492-505.
52. Lian, G., Thornton, C., Adams, M. J., ”Microscopic simulation of
oblique collisions of ‘wet’agglomerates,” in: R.P. Behringer,
J. T. Jenkins(Eds.), Powders and Grains 97, Balkema, Rotterdam, 1997,
pp.223-226.
53. Lian, G., Thornton, C., Adams, M. J., “Discrete particle simulation of
agglomerate impact coalescence,” Chem. Eng. Sci. 53 (1998)
3381-3391.
54. Mikami, T., Kamiya, H., Horio, M. “Numerical simulation of cohesive
powder behavior in a fluidized bed,” Chem. Eng. Sci. 53 (1998)
1927-1940.
55. Lian, G., Thornton, C., Adams, M. J., “A theoretical study of the liquid
bridge forces between two rigid spherical bodies,” Interface Science,
161.
56. Goldman, A.J., Cox, R. G., and Brenner, H., 1967, “Slow viscous motion of a sphere parallel to a plan wall I. Motion through a quiescent fluid,” Chem Eng. Sci. 22, pp.637-651.
57. McCarthy, J. J., 2003, “Micro-modeling of cohesive mixing processes,”
Powder Technol., Vol. 138, pp. 63-67.
58. Li, H., McCarthy, J.J., 2005, “Cohesive paticle mixing and segregation
under shear,”Powder Technol., Vol. 164, pp. 58-64.
59. Li, H., McCarthy, J.J., 2005, “Phase diagrams for cohesive particle
mixing and segregation,” Phys. Rev., E 71, 021305.
60. Bagnold, R. A., 1954, “Experiments on a gravity-free dispersion of large
solid spheres in a Newtonian fluid under shear,”Mathematical and
Physical Sciences., Vol. 225, No. 1160, pp.49-63.
61. Hsiau, S. S. and Hunt, M. L., 1993, “Shear-Induced Particle Diffusion
and Logitndinal Velocity Fluctuations in a Granular-Flow Mixing
Layer,” J. Fluid Mech., Vol. 251, pp. 299-313.
62. Savage, S. B. and Dai, R., 1993, “Studies of Shear Flows. Wall
slipVelocity, ‘Layering’ and Self-Diffusion,” Mech. Materials, Vol. 16,
pp. 225-238.
63. Einstein, A., 1956, “Investigations on the Theory of the Brownian
Movement,” (ed. R. Furth) Dover Publications Inc.
64. Hsiau, S. S. and Hunt, M. L., 1993b, “Kinetic Theory Analysis of Flow-
Induced Particle Diffusion and Thermal Conduction in Granular S. S.
Hsiau and H. Y. Yu, Segregation phenomena in a shaker, Powder
Technol., 93, pp. 83-88, 1997.
65. Willett, C. D., Adams, M. J. and Johnson, S. A., 2000, “Capillary Bridge between Two Spherical Bodies,” Langmuir, 16, pp. 9396-9405.
66. Iveson, S. M., Beathe, J. A., Page, Neil W., 2002, “The dynamic
strength of partially saturated powder compacts: the effect of liquid
properties,” Powder Technol. Vol. 127, pp. 149-161.