Resistance to Potential Flow through a Cubical Array of Spheres

Abstract

Precise conductivity measurements on models sectioned out from a cubic lattice of spheres in a continuous medium indicate that the effective conductance of such a system deviates from the values predicted by Lord Rayleigh's analytic solution of this potential distribution problem. Deviations become particularly significant when the spheres approach close packing, and when the conductance of spheres is much greater than that of the continuum. By use of a different function for potential, and by consideration of higher terms in the series expression for the potential in the continuous phase, Rayleigh's results are modified, yielding an analytical expression that represents effective conductance satisfactorily in the concentration region approaching close packing.