New Temperature Dependent Configurational Probability Diffusion Equation for Diluted FENE Polymer Fluids: Existence of Solution Results

Abstract

The theory for the non-isothermal rheology of polymer fluids proposed in Curtiss and Bird (Adv Polym Sci 125:1–101, 1996) used several approximations including the so-called linear gradient approximations for the temperature field and Brownian forces. While it had the significant advantage of dealing with linear equations, the approximations involved may have led to several non-physical predictions. This work is a continuation of Curtiss and Bird (1996) in that it obtains the corresponding non-linear configurational probability density equation in dimensionless form without the linear gradient approximations for the temperature field and Brownian forces. It does so for incompressible diluted polymer solutions with polymer molecules being modeled as FENE (Finitely Extensible Nonlinear Elastic) chains. Next we prove the existence of temperature dependent, positive variational solutions for the probability density equation of the FENE model.