The stress tensor in colloidal suspensions

Abstract

This paper presents a new derivation of an expression for the average stress tensor in colloidal suspensions of interacting particles, based on methods from statistical mechanics. In conventional methods all contributions to the stress tensor are added one by one to compose the final result, and each contribution requires a separate justification. Especially hard sphere interaction potentials between the colloidal particles in combination with Brownian motion present conceptual difficulties. The method presented here is advantageous in two ways. First, the hard sphere interaction potential is treated the same as any other potential, yielding direct hard sphere contributions in a very simple way and second, all contributions to the stress tensor are present from the start, eliminating the need of superposition of contributions to the stress tensor. Thus familiar contributions to the stress tensor are recovered, which for hard spheres coincide with the well-known results of Batchelor [G.K. Batchelor, J. Fluid Mech. 83, 97 (1977)], and less obvious, those of Brady [J.F. Brady, J. Chem. Phys. 99, 567 (1993)], obtained with different methods. Furthermore, a calculation is presented that produces the direct hard sphere contribution for arbitrary densities within the framework of the conventional theories of the stress tensor. The two methods of calculating the same direct hard sphere contribution are clarifying when discussing the interpretation of the hard sphere property of the colloidal particles as Brownian motion in a restricted configuration space, or as a normal short range repulsive pair potential.