Viscous Flow through Porous Media. II. Approximate Three-Point Correlation Function

Lower bounds were derived earlier S. Prager, Phys. Fluids 4, 1447 (1961) for the resistance of a porous medium to the passage of a viscous fluid. The information required for the calculation of such bounds consists of certain two- and three-point correlations S and G. An approximate expression for G in terms of S is presented and used to calculate the resistance of a bed of widely spaced spheres. The result is about 5% above the resistance calculated using the correct G, which in turn is about 25% below the true value of the resistance. Improved lower bounds on the resistance are available, but have not yet been applied because of the complexity of the calculations involved.