A thermodynamical description of third grade fluid mixtures

TL;DR

This paper provides a comprehensive thermodynamical framework for third grade fluid mixtures, incorporating gradient-dependent constitutive relations and ensuring compatibility with the second law of thermodynamics.

Contribution

It introduces a novel thermodynamic analysis for third grade fluid mixtures with gradient-dependent constitutive functions, ensuring second law compliance.

Findings

Explicit thermodynamic restrictions are derived.

A new form of entropy flux including non-local effects is obtained.

The analysis confirms the thermodynamic consistency of the model.

Abstract

A complete thermodynamical analysis for a non-reacting binary mixture exhibiting the features of a third grade fluid is analyzed. The constitutive functions are allowed to depend on the mass density of the mixture and the concentration of one of the constituents, together with their first and second order gradients, on the specific internal energy of the mixture with its first order gradient, as well as on the symmetric part of the gradient of barycentric velocity. Compatibility with second law of thermodynamics is investigated by applying the extended Liu procedure. An explicit solution of the set of thermodynamic restrictions is obtained by postulating a suitable form of the constitutive relations for the diffusional mass flux, the heat flux and the Cauchy stress tensor. Taking a first order expansion in the gradients of the specific entropy, the expression of the entropy flux is determined. It includes an additional contribution due to non-local effects.