On the flow of a fluid-particle mixture between two rotating cylinders, using the theory of interacting continua

International Journal of Non-Linear Mechanics

Volumn 35, Issue 6, 2000, Pages 1045-1058

  Massoudi, M ^a   Johnson, G ^b  

^a NATIONAL ENERGY TECHNOLOGY LABORATORY   (United States)

^b University of Pittsburgh   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; CYLINDERS (SHAPES); FLOW OF SOLIDS; GRANULAR MATERIALS; MATHEMATICAL MODELS; MULTIPHASE FLOW; NEWTONIAN LIQUIDS; ORDINARY DIFFERENTIAL EQUATIONS;

COUETTE FLOW; MIXTURE THEORY; NEWTONIAN FLUIDS;

CONTINUUM MECHANICS;

EID: 0034325836     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7462(99)00078-5     Document Type: Article

References (70)

1. G.B. Wallis, One-Dimensional Two-Phase Flows, McGraw-Hill, Inc., New York, 1969.
2. Anderson T.B., Jackson R. Fluid mechanical descriptions of fluidized beds, 1. Equations of motion. Ind. Engng. Chem. Fund. 6:1967;527.
3. Drew D.A., Segel L.A. Averaged equations for two-phase flows. Stud. Appl. Math. L:1971;205-231.
4. Drew D.A. Two phase flows: constitutive equations for lift and Brownian motion and some basic flows. Arch. Rational Mech. Anal. 62:1976;149-163.
5. G. Hestroni (Ed.), Handbook of Multiphase Systems, Hemisphere Publishing Corporation, New York, 1982.
6. R.E. Meyer (Ed.), Theory of Dispersed Multiphase Flow, Academic Press, New York, 1983.
7. G. Papanicolaou (Ed.), Advances in Multiphase Flow and Related Problems, SIAM, Philadelphia, 1986.
8. S.L. Soo, Particulates and Continuum, Hemisphere Publishing Corporation, New York, 1989.
9. S.L. Soo, Multiphase Fluid Dynamics, Science Press and Gower Technical, Brookfield, 1990.
10. R.D. Marcus, L.S. Leung, G.E. Klinzing, F. Rizk, Pneumatic Conveying of Solids, Chapman & Hall, London, 1990.
11. M. Kaviany, Principles of Heat Transfer in Porous Media, 2nd Edition, Springer, New York, 1995.
12. L.S. Fan, C. Zhu, Principles of Gas-Solid Flows, Cambridge University Press, New York, 1998.
13. Fick A. Über diffusion, Ann. Phys. 94:1855;56.
14. C. Truesdell, Sulle basi della termomeccanica, Rend Lincei, Ser. 8 22 (1957) 33-38 and 158-166.
15. Atkin R.J., Craine R.E. Continuum theories of mixtures: basic theory and historical development. Quart. J. Mech. Appl. Math. 29:1976;290.
16. Bedford A., Drumheller D.S. Recent advances: theories of immiscible and structured mixtures. Int. J. Engng. Sci. 21:1983;863.
17. R.M. Bowen, Theory of mixtures, in: A.C. Eringen (Ed.), Continuum Physics, Vol. 3, 1976, p. 1.
18. C. Truesdell, Rational Thermodynamics, 2nd Edition, Springer, Berlin, 1984.
19. M.M. El-Kaissy, The thermomechanics of multiphase systems with applications to fluidized continua, Ph.D. Thesis, Stanford University, 1975.
20. Homsy G.M., El-Kaissy M.M., Didwania A. Instability waves and the origin of bubbles in fluidized beds, part 2: comparison with theory. Int. J. Multiphase Flow. 6:1980;305-318.
21. Ahmadi G. On mechanics of saturated granular materials. Int. J. Non-Linear Mech. 15:1980;251.
22. Ahmadi G. A continuum theory for two phase media. Acta Mech. 44:1982;299.
23. S.L. Passman, J.W. Nunziato, Flow of a fluid-saturated granular material, in: A.P.S. Selvadurai (Ed.), Mechanics of Structured Continua, Part A, Elsevier, Amsterdam, 1981, pp. 343-353.
24. Passman S.L., Nunziato J.W., Bailey P.B., Reed K.W. Shearing motion of a fluid-saturated granular material. J. Rheol. 30:1986;167-192.
25. M. Massoudi, Application of mixture theory to fluidized beds, Ph.D. Thesis, University of Pittsburgh, Pittsburgh, PA, 1986.
26. Massoudi M. Stability analysis of fluidized beds. Int. J. Engng. Sci. 26:1988;765.
27. F. Dobran, Theory of Structured Multiphase Mixtures, Springer, New York, 1991.
28. K.R. Rajagopal, L. Tao, Mechanics of Mixtures, World Scientific Publishing, River Edge, NJ, 1995.
29. Murray J.D. On the mathematics of fluidization, part 1: fundamental equations and propagation. J. Fluid Mech. 21:1965;465.
30. K.R. Rajagopal, M. Massoudi, J.M. Ekmann, Mathematical modeling of fluid-solid mixtures, in: D. Dekee, P.N. Kaloni (Eds.), Recent Developments in Structured Continua II, Longman, New York, 1990, pp. 234-248.
31. Shi J.J.J., Rajagopal K.R., Wineman A.S. Applications of the theory of interacting continua to the diffusion of a fluid through a non-linear elastic media. Int. J. Engn. Sci. 19:1981;871-889.
32. Adkins J.E. Non-linear diffusion, 1. Diffusion and flow of mixture of fluids. Philos. Trans. Roy. Soc. London. A 255:1963;607.
33. Adkins J.E. Non-linear diffusion, 2. Constitutive equations for mixture of isotropic fluids. Philos. Trans. Roy. Soc. London. A 255:1963;635.
34. Goodman M.A., Cowin S.C. Two problems in gravity flow of granular materials. J. Fluid Mech. 45:1971;321.
35. Goodman M.A., Cowin S.C. A continuum theory for granular materials. Arch. Rational Mech. Anal. 44:1972;249.
36. Cowin S.C. Constitutive relations that imply a generalized mohr-coulomb criterion. Acta Mech. 20:1974;41.
37. Savage S.B. Gravity flow of cohesionless granular materials in chutes and channels. J. Fluid Mech. 92:1979;53-96.
38. Savage S.B. The mechanics of rapid granular flows. Adv. Appl. Mech. 24:1984;289.
39. K.R. Rajagopal, M. Massoudi, A method for measuring the material moduli of granular materials: flow in an orthogonal rheometer, Topical Report, U.S. Dept. of Energy DOE/PETC/TR-90/3, 1990.
40. Savage S.B., Sayed M. Stresses developed by dry cohesionless granular materials sheared in an annular shear cell. J. Fluid Mech. 142:1984;391-430.
41. Hanes D.M., Inman D.L. Observations of rapidly flowing granular-fluid materials. J. Fluid Mech. 150:1985;357.
42. Walton O.R., Braun R.L. Stress calculations for assemblies of inelastic spheres in uniform shear. Acta Mech. 63:1986;73-86.
43. Walton O.R., Braun R.L. Viscosity, granular-temperature, and stress calculations for shearing assemblies of inelastic, frictional disks. J. Rheol. 30:1986;949-980.
44. E.J. Boyle, M. Massoudi, A theory for granular materials exhibiting normal stress effects based on Enskog's dense gas theory, Int. J. Engng. Sci. 28 (1990) 1261-1275.
45. Bagnold R.A. Experiments on a gravity free dispersion of large spheres in a Newtonian fluid under shear. Proc. Roy. Soc. London. A 225:1954;49.
46. Anderson K.G., Jackson R. A comparison of the solutions of some proposed equations of motion of granular materials for fully developed flow down inclined planes. J. Fluid Mech. 242:1992;145.
47. Tardos G.I. A fluid mechanistic approach to slow, frictional flow of powders. Powder Technol. 92:1997;61.
48. Jyotsna R., Kesava Rao K. A frictional-kinetic model for the flow of granular materials through a wedge-shaped hopper. J. Fluid Mech. 346:1997;239.
49. Savage S. Analyses of slow high-concentration flows of granular materials. J. Fluid Mech. 377:1998;1.
50. Hutter K., Rajagopal K.R. On flow of granular materials. Continuum Mech. Thermodyn. 6:1994;81.
51. R.M. Nedderman, Statics and Kinematics of Granular Materials, Cambridge University Press, Cambridge, 1992.
52. A. Mehta (Ed.), Granular Matter: An Interdisciplinary Approach, Springer, New York, 1994.
53. Green A.E., Naghdi P.M. On basic equations for mixtures. Quart. J. Mech. Appl. Math. 22:1969;427.
54. G. Johnson, M. Massoudi, K.R. Rajagopal, A review of interaction mechanisms in fluid-solid flows, Topical Report, U.S. Dept. of Energy, DOE/PETC/TR-90/9, 1990.
55. Müller I. A thermodynamic theory of mixtures of fluids. Arch. Rational Mech. Anal. 28:1968;1-39.
56. Saffman P.G. The lift on a small sphere in slow shear flow. J. Fluid Mech. 22:1965;385-400.
57. Saffman P.G. Corrigendum. J. Fluid Mech. 31:1968;624.
58. McTigue D.F., Givler R.C., Nunziato J.W. Rheological effects of nonuniform particle distributions in dilute suspensions. J. Rheol. 30:1986;1053-1076.
59. Johnson G., Massoudi M., Rajagopal K.R. Flow of a fluid-solid mixture between flat plates. Chem. Engng. Sci. 46:1991;1713-1723.
60. G. Johnson, M. Massoudi, K.R. Rajagopal, Flow of a fluid infused with solid particles through a pipe, Int. J. Engng. Sci. 29 (1991) 649-661.
61. A. Briggs, C.C. Hwang, M. Massoudi, Flow of a dense particulate mixture using a modified form of the mixture theory, Particulate Sci. Technol. 17 (1999) 1-27.
62. M. Massoudi, K.R. Rajagopal, T.X. Phuoc, On the fully developed flow of a dense particulate mixture in a pipe, Powder Technol. 164 (1999) 258-268.
63. Batchelor G.K. Sedimentation in a dilute dispersion of spheres. J. Fluid Mech. 52:1972;245-268.
64. Drew D.A. Mathematical modeling of two phase flow. Ann. Rev. Fluid Mech. 15:1983;261-291.
65. Beevers C.E., Craine R.E. On the determination of response functions for a binary mixture of incompressible Newtonian fluids. Int. J. Engng. Sci. 20:1982;737.
66. Zheng X.M., Hill J.M. Boundary effects for Couette flow of granular materials; Dynamic modelling. Appl. Math. Modelling. 20:1996;82.
67. Ascher U., Christianson J., Russel R.D. Collocation software for boundary value ODE's. ACM Trans. Math. Software. 7(2):1981;209-222.
68. Johnson G., Massoudi M., Rajagopal K.R. Couette flow of a fluid with entrained solid particles. Recent Adv. Mech. Structured Continua, ASME. AMD-117:1991;97.
69. Repetti R.V., Leonard E.F. Segre'-Silberberg annulus formation: a possible explanation. Nature. 194:1964;1346-1348.
70. H. Schlichting, Boundary-Layer Theory, McGraw-Hill, New York, 1979.