qualitatively in agreement with the limited experimental data available.

For bead-spring chains, the Rouse model, gives a result that is just a superposition of Hookean dumbbells, with a spectrum of relaxation times. Here again, however, non-Newtonian viscosity, normal stresses, and elongational viscosity are not described by the chain model.

For a dilute solution of elastic dumbbells in which there is a concentration gradient, the following constitutive equation is obtained [5a]:

(3.4)

This equation had been obtained earlier by El Kareh and Leal [12]. A summary of the effects of diffusion on the constitutive equation has been given by Beris and Mavrantzas [13].

In addition, the effect of temperature gradients on the stress tensor has been considered [5a], and the behavior of a charged Rouse chain in an electric field has also be considered [5a].

3b. Heat transport

First we discuss the relation between the thermal conductivity and the type of spring used in modeling polymer molecules as dumbbells. What we find is that the thermal conductivity is extremely sensitive to the nature of the springs. For example, if we compare Hookean dumbbells with Fraenkel dumbbells, we have:

Hooke:Fraenkel: (3.5; 3.6)