A new class of Finitely Extensible Nonlinear Elastic FENE-P model obtained with a thermodynamical approach and the use of compressible natural configurations. Part I: Isothermal deformations

Abstract

In a recent contribution to the fundamental understanding of polymer fluid dynamics, Khambhampati and Rajagopal (2021) established a connection between the natural configuration theory of Rajagopal and Srinivasa (2000) and the FENE-P model of Bird et al. (1987 [6]). In this paper we capitalize on the result in Khambhampati and Rajagopal (2021) and present a new class of FENE-P models using a more general Helmholtz potential within the conceptual framework of evolving natural configurations. To show its qualitative behavior, we exemplify with a classical Couette flow between infinite parallel plates. The model is capable of reproducing key features experimentally observed such as stress relaxation and the overshoot of the shear stress at the beginning of typical shear stress growth experiments. Comparison against the FENE-P type model obtained in Khambhampati and Rajagopal (2021) is used for comparison.