Flow of a dense particulate mixture using a modified form of the mixture theory

Particulate Science and Technology

Volumn 17, Issue 1-2, 1999, Pages 1-27

  Briggs, A ^a   Hwang, C C ^a   Massoudi, M ^b  

^a University of Pittsburgh   (United States)

^b NATIONAL ENERGY TECHNOLOGY LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BUOYANCY; DENSITY (SPECIFIC GRAVITY); FLOW OF SOLIDS; FLUIDIZED BEDS; NUMERICAL METHODS;

FLUID SOLID MIXTURE; MIXTURE THEORY; STRESS TENSOR;

MIXTURES;

DENSITY; FLOW KINETICS; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; PARTICULATE MATTER; PRIORITY JOURNAL; REVIEW;

EID: 0032871013     PISSN: 02726351     EISSN: 15480046     Source Type: Journal    
DOI: 10.1080/02726359908906803     Document Type: Article

References (49)

1. Adkins, J.E., “Non-Linear Diffusion, 1. Diffusion and Flow of o Mixture of Fluids”. Philosophical Transactions of the Royal Society of London, 255 A:607, 1963.
2. Adkins, J.E., “Non-Linear Diffusion, 2, Constitutive Eauations for a Mixture of Isotrooic Fluids”. Philosophical Transactions of the Royal Society of London, 255A:635, 1963
3. Ahmadi, G., “On Mechanics of Saturated Granular Materials”. International Journal of Non-Lineor Mechonics. 15:251, 1980.
4. Ahmadi, G., “A Continuum Theory for Two Phase Media”. Acta Mechanica, 44:299
5. Aoki, H., Kurosaki, Y, and Anzai, H, “Study on the Tubular Pinch EfTcct in Pipe Flow”. Bulletin of the Japanese Society Mechanical Engineering, 22:206-212, 1979.
6. Ascher, U., Christianson, J., and Russel, R.D., “Collocation Software for Boundary Value ODE’s”. ACM Transactions on Mathematical Software, 7(2):209-222, June 1981.
7. Atkin, R.J. and Crainc, R.E., “Continuee Theories of Mixtures” Basic Theory and Historical Development”. Quarterly Journal of Mechanics and Applied Mathematics, 29:290. 1976.
8. Batchelor, G.K., “Sedimentation in a Dilute Dispersion of Spheres. Journal of Fluids Mechanics, 52245-268, 1972.
9. Be ford, A., and DrumheUer, D.S., “Recent Advances: theories of Immiscible and Structured Mixtures”. International Journal of Engineering Science, 21:863, 1983.
10. Boyle, E.J., and Massoudi, M., “A Theory for Granular Materials Exhibiting Norma! Stress Effects Based on Enskong’s Dense Gas Theoty”. International Journal of Engineering Science, 28: 1261, 1990.
11. Bowen, R.M., “Theory of Mixtures”, Continuum Physics, Vol. 3: Academic Press, NY, 1976.
12. Briggs, A., Modifications of the Mixture theory to include Buoyancy Force. M.S. Thesis, University of Pittsburgh, 1995.
13. Drew, D.A., “Two Phase Flows:Constitutive Equations for Lift and Brownian Motion and some Basic Flows” Archive for Rational Mechanics and Analysis, 62:149-163, 1976.
14. Drew, D.A., “Mathematical Modeling of Two Phase Flow”. Annual Review of Fluid Mechanics, 15:261-291, 1983.
15. Goodman, M.A., and S.C. Cowin, “A Continuum Theory for Granular Materials”. Arch. Rational Mech. Anal., 44:249 (1972).
16. Green, A.E., and Naghdi, P.M., “On Basic Equations for Mixtures”. Quarterly Journal of Mechanics and Applied Mathematics, 22:427, 1969.
17. Hill, C.D., Bedford, A., and DrumheUer, D.S., “An Application of Mixture Theory to Particle Sedimentation”. Transactions of the ASME Journal of Applied Mechanics, 47:261-265, 1980.
18. Homsy, G.M., El-Kaissy, M.M., and Didwania, A., “Instability Waves and the Origin of Bubbles in Fluidi/ed Beds”, Part 2:Comparison With Theory”. International Journal of Multiphase Flow, 6:305-318, 1980.
19. Huang, C.R., “A Mathematical Model of Sedimentation Analysis Applied to Human Whole Blood”. Biorheology, 8:157-163, 1971.
20. Hutter, K. and K.R. Rajagopal, “On flows of granular materials”, Comtinuum Mech. Thermodyn, 6: 81-139 (1994).
21. Jakson, R., “Hydrodynamic Stability of Fluid-Particle Systems”. In Fluidization, Edited by J. F. Davidson, R. Clift, and D. Harrsion. Academic Press, 1985.
22. Johnson, G., Massoudi, M., and Rajagopal, K.R., “A Review of Interaction Mechanisms in Fluid-Solid Flows”. Technical Report, U.S. Dept. Of Energy Report, DOE/PETC/TR-90/9, 1990.
23. Johnson, G., Massoudi, M., and Rajagopal, K.R., “Flow of a Fluid-Solid Mixture Between Flat Plates,” Chem. Engng. Sei., 46:1713, 1991.
24. Johnson, G., Massoudi, M., and Rajagopal, K.R., “Flow of a Fluid Infused with Solid Particles through a Pipe”. Int. J. Engng. Sei., 29:649,1991.
25. Johnson, G., “Application of Continuum theories to Flows of Fluid-Solid Mixtures” PhD Thesis, University of Pittsburgh, PA 1991
26. Katsubc, N., and M.M. Carroll, “The Modified Mixture Theory for Fluid-Filled Porous Materials:Thcory”. ASME J. Applied Mechanics, 87-APM-7, 1987.
27. Katsubc, N., and M.M. Carroll, “The Modified Mixture Theory for Fluid-Filled Porous Materials:Applications”. ASMFSJ. Applied Mechanics, 87-APM-8,1987.
28. Massoudi, M., “Application of Mixture Theory to Fluidized Beds”. PhD Thesis, University of Pittsburgh, PA, 1986.
29. Maxey, M.R., and J.J. Riley, “Equation of Motion for a Small Rigid Particle in Nonuniform Flow”, Phys. Fluids, 26:883, 1983.
30. Muller, I., “A Thermodynamic Theory of Mixtures of Fluids”. Archive for Rational Mechanics and Analysis, 28:1-39, 1968.
31. Ounis, H., ond G. Ahmadi, “Motions of Small Rigid Spheres in Simulated Random Velocity Fluid”. ASCEJ. Engng. Mech., 115:2107,1989.
32. Panton, R.L., Incompressible Flow. IViley-Inlersciencc Publ., 1984.
33. Passman, S.L., Nunziato, J.W. Bailey, P.B., and Reed, K.W., “Shearing Motion of a Fluid-Saturated Granular Material”. Journal of Rheology, 30:167-192, 1986.
34. Patankar, S.V. Numerical Heat Transfer and Fluid Flow. Hemisphere Publ. Corp., Washington, DC, 1980.
35. Rajagopal, K.R., and Massoudi, M., “A Method for Measuring the Material Moduli of Granular Materials:Flow in an Orthogonal Rheometer”. Technical Report, U.S. Dept. Of Energy. DOE/PETC/TR-90n, 1990
36. Rajagopal, K.R., M, Massoudi, and A, S. Wincman. “Flow of Granular Materials Between Rotating Disks,” Mech. Research Comm., 6:629, 1994.
37. Rajagopal, K.R., Massoudi, M., and Ekmann, J.M., “Mathematical Modeling of Fluid-solid Mixtures”. Recent Developments in Structured Continua Il.Longman, pp. 236–248, 1990
38. Rajagopal, K.R., and L. Tao, Mechanics of Mixtures. World Scientific Publishing Co., Ltd. Nw Jersey, 1995
39. RcpcUi, R.V., and Leonard, E.F., “Scgrc-Silbcrbcrg Annulus Formation:A Possible Explanation”. Nature, 194:1346-1348, 1961.
40. Rizk, M.A., and S.E. Elghobashi, “The Motion of a Spherical Particle Suspended in a Turbulent Flow Near a Plane Wall”. Phys. Fluids, 28:806, 1985.
41. Savage, S.B., “Gravity Flow of Cohcnsionlcss Granular Materials in Chutes and Channels”. J Fluid Mech., 9253, 1979
42. Segre, G., and A. Silberberg, “Behavior of Macroscopic Rigid Spheres in Poiseuille Flow”. Pan 2, J. Fuid Mech., 14: 115, 1962.
43. Segre, G., and A. Silberberg, “Behavior of macroscopic Rigid Spheres in Poiseuille Flow”. Pan 2, J. Fuid Mech., 14: 136, 1962.
44. Soo, S.L., Fluid Dynamics of Multiphase Systems. Blaisdcll Publishing, 1967.
45. Spcckharl, F.H., and Green, W.L., “A guide to Using CSMP-Thc Continuous Systems Modeling Program”. Prentice Hall, Englewood Cliffs, NJ, 1976.
46. Tchcn, C.M., “Mean Value and Correlation Problems Connected with the Motion of Small Particles Suspended in a Turbulent Fluid”. Martinus Nijhoff, the Hague. 1947.
47. Tmcsdcll, C., Rational Thermodynamics. Springer-Verlag, 2nd edition, 1984.
48. Trucsdcll, C. and W. Noll. The Non-Linear Field Theories of Mechanics. Scond Edition. Springer-Verlag, Heidelberg, 1992.
49. Whelan, J.A., Huang, C.R., and Copley, A.L., “Concentration Profiles in Erthrocyte Sedimentation in Human Whole Blood”. Biorheoiogy, 7:205-212, 1971.