A new class of thermodynamically admissible non-Newtonian fluids obtained with the use of compressible natural configurations and their relation to the Finitely Extensible Nonlinear Elastic FENE-P models of kinetical theory

Abstract

Based on the previously published work of Gomez-Constante and Palade (see Introduction Section), we study the effect of temperature changes on the elastic limit of a polymer fluid. First, we prove that any Helmholtz potential depending on the invariants of deformation and of the temperature produces the same constitutive equations that would be obtained using the corresponding Helmholtz potential without any temperature dependence on the strain limit. Next, by establishing an Ad-Hoc relation between the strain limit and the temperature and incorporating it into the Helmholtz potential, we derive a constitutive equation based on the model previously derived by Khambhampati and Rajagopal. As a byproduct of temperature-dependent Helmholtz potential, we obtain the internal energy potential as a function of temperature and the invariants of deformation. Next, we show a comparison between the model here obtained and the model of similar nature of Khambhampati and Rajagopal and establish how the First Law of Thermodynamics behaves in the two cases. We find that the classical approach to internal energy has some limitations that are overcome with the proposed model. Finally, a comparative presentation of the models predictions for Couette, large amplitude oscillatory shear (LAOS) and large amplitude rectangular shear (LARS) flows - with the later case being here studied for the first time - is done and discussed. For small enough strains the linear viscoelastic behavior is obtained. Moreover, we study and analyze the heat dissipation during the LAOS and LARS flows, an important aspect only seldom studied.