Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-18T18:51:40.607Z Has data issue: false hasContentIssue false
  • English
  • Français

Slow flow through stationary random beds and suspensions of spheres

Published online by Cambridge University Press:  29 March 2006

T. S. Lundgren
Get access Rights & Permissions [Opens in a new window]

Abstract

Stokes flow through a random, moderately dense bed of spheres is treated by a generalization of Brinkman's (1947) method, which is applicable to both stationary beds and suspensions. For stationary beds, Darcy's law with a permeability result similar to Brinkman's is derived. For suspensions an effective viscosity μ/(1–2·60ψ) is found, where ψ is the volume fraction of spheres. Also, an expression for the settling velocity is derived.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 51 , Issue 2 , 25 January 1972 , pp. 273 - 299
Copyright
© 1972 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Beran, M. J. 1968 Statistical Continuum Theories. Interscience.
Brinkman, H. C. 1947 A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. A 1, 27.Google Scholar
Budiansky, B. 1965 On the elastic moduli of some heterogeneous materials. J. Mech. Phys. Solids, 13, 223.Google Scholar
Cheng, P. Y. & Schachman, H. K. 1955 Verification of the validity of the Einstein viscosity law and Stokes law of sedimentation. J. Polym. Sci. 16, 19.Google Scholar
Davidson, J. F. & Harrison, D. 1963 Fluidized Particles. Cambridge University Press.
Einstein, A. 1906 Ann. Phys. 19, 289. (Trans. in 1956 Theory of Brownian Movement, Dover.)
Einstein, A. 1911 Ann. Phys. 34, 591. (Trans. in 1956 Theory of Brownian Movement, Dover.)
Ford, T. F. 1960 Viscosity-concentration and fluidity-concentration relations for suspensions of spherical particles in Newtonian liquids. J. Phys. Chem. 64, 1168.Google Scholar
Happel, J. 1957 Viscosity of suspensions of uniform spheres. J. Appl. Phys. 28, 1288.Google Scholar
Happel, J. & Brenner, H. 1965 Low Reynolds number hydrodynamics. Prentice-Hall.
Happel, J. & Epstein, N. 1954 Cubical assemblages of uniform spheres. Ind. Eng. Chem. 46, 1187.Google Scholar
Hashin, Z. 1970 Contributions to Mechanics (ed. Abir), p. 347. Pergamon.
Hess, W. R. 1920. Beitrag zur Theorie der Viskositat heterogener Systeme. Kolloid Z. 27, 1.Google Scholar
Kynch, G. J. 1959 Sedimentation and effective viscosity. Nature, 184, 1311.Google Scholar
Landau, L. D. & Lifshitz, F. M. 1959 Fluid Mechanics. Addison-Wesley.
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics. McGraw-Hill.
Richardson, J. F. & Zaki, W. N. 1954 Sedimentation and fluidization. Trans. Inst. Chem. Engrs. 32, 35.Google Scholar
Saffman, P. G. 1971 On the boundary condition at the surface of a porous medium. Studies in Appl. Math. 50, 93.Google Scholar
Spielman, L. & Goren, S. L. 1968 Model for predicting pressure drop and filtration efficiency in fibrous media. Environ. Sci. & Technol. 2, 279.Google Scholar
Tam, C. K. W. 1969 The drag on a cloud of spherical particles in low Reynolds number flow. J. Fluid Mech. 38, 537.Google Scholar
Vand, V. 1948 Viscosity of solutions and suspensions. J. Phys. Chem. 52, 300.Google Scholar
Williams, P. S. 1953 Flow of concentrated suspensions. J. Appl. Chem. 3, 120.Google Scholar