New bounds on the permeability of a random array of spheres

J. D. Beasley, S. Torquato

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7 Scopus citations


The recently derived variational principle of Rubinstein and Torquato (J. Fluid Mech., in press) is applied to obtain new rigorous two- and three-point upper bounds on the fluid permeability k for slow viscous flow around a random array of identical spheres which may penetrate one another in varying degrees. The n-point bounds involve up to n-point correlation function information. Both bounds are simplified and computed for the special case of mutually impenetrable spheres for a wide range of sphere volume fractions. The three-point bound is sharp and provides significant improvement over the two-point bound, especially at high sphere volume fractions (low porosities). It is the sharpest upper bound on k for a random array of impenetrable spheres developed to date and begins to approach the Kozeny-Carman empirical relation at low porosities.

Original languageEnglish (US)
Pages (from-to)199-207
Number of pages9
JournalPhysics of Fluids A
Issue number2
StatePublished - 1989
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Engineering


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