Frictional coefficients of multisubunit structures. I. Theory

Abstract

The theory of Kirkwood for the translational frictional coefficients of structures composed of subunits has been generalized in two ways in order to consider aggregates of nonidentical subunits. One of these generalizations fails when the sizes of subunits are too disparate; the other, derived from a surface shell distribution of frictional elements, is effective over the whole range of relative sizes. It is shown that, in the limit of a continuous surface distribution, a shell model reproduces Stoke's law for a sphere. Comparison is made between the frictional coefficients of spheres, ellipsoids, and rods modeled by finite numbers of subunits and by continuous shells of frictional elements, and those calculated from other theories. Agreement is generally good, though the shell model for prolate ellipsoids of revolution deviates by a few per cent from the Perrin value.