Stress tensor for arbitrary flows of dilute solutions of rodlike macromolecules

Abstract

An equation for the stress tensor in terms of the rate of strain tensor is obtained for a dilute suspension of rigid macromolecules with Brownian motion. The result is given as a series of memory integrals up through terms of third order; the kernel functions contain two constants: the number density and time constant for the macromolecules. In obtaining this series, the distribution function for arbitrary unsteady homogeneous flows is developed up through terms of second order. It is shown that one need consider only irrotational flow in determining the kernel functions for the memory integral expansion. Relations between the kernel functions and the coefficients in the retarded motion expansion are also given. In addition it is shown how the Eulerian components of the rate-of-deformation tensor are related to the fixed components by using the theory of matrizants.