approximate procedure for estimating the pair distribution function. This is discussed in the Curtiss-Bird paper in J. Chem. Phys. (1999) dealing with diffusion.

3. SOME RESULTS FOR POLYMERIC FLUIDS

Next we will discuss some of the phenomena that we have been able to describe with the phase-space kinetic theory. From these results it is also possible to focus on problems that need to be solved as well as experiments that are needed.

3a. Momentum transport

The main driving force for studying kinetic theory of polymers was the need to develop a rational basis for developing constitutive equations for solving fluid dynamics problems for polymer solutions and undiluted polymers (i.e., polymer melts). The first textbook devoted to this topic was that of Bird, Curtiss, Armstrong & Hassager. Earlier research monographs were those of Kirkwood [7] and Yamakawa [8]. An introduction to the theories based on the "tube" models may be found in the treatise of Doi and Edwards [9]; the tube models are not discussed in the present article. None of these references discuss the problems of heat and mass transport or the coupling of these with momentum transport.

The simplest model considered for the connection between polymer structure and rheology was the elastic (Hookean) dumbbell. For a dilute solution of such dumbbells, it was shown [10] many years ago that a convected Maxwell equation for the polymer contribution to the "extra stress tensor" is the appropriate constitutive equation; that is,

where(3.1)