Kinetic theory and rheology of dilute solutions of flexible macromolecules. I. Steady state behavior

For a dilute solution of macromolecules idealized as elastic dumbbells with Brownian motion, expressions are obtained giving the stress tensor in terms of rate-of-strain tensors for an arbitrary, steady, homogeneous flow. The rheological equations of state are fit into a retarded motion expansion. For dumbbells with arbitrary, nonlinear, elastic connectors, the result is given up through terms of second-order. Stress tensor equations for two specific models, Hookean dumbbells and finitely extendible non-linear elastic (FENE) dumbbells, are given up through terms of third order.