Abstract
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 language | English (US) |
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Pages (from-to) | 199-207 |
Number of pages | 9 |
Journal | Physics of Fluids A |
Volume | 1 |
Issue number | 2 |
DOIs | |
State | Published - 1989 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Engineering(all)