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A Thermodynamical Description of Third Grade Fluid Mixtures

  • Matteo Gorgone ORCID logo EMAIL logo and Patrizia Rogolino
Published/Copyright: March 30, 2022

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, and on the symmetric part of the gradient of barycentric velocity. Compatibility with the 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.

Funding statement: This work is supported by the Gruppo Nazionale per la Fisica Matematica (GNFM) of the Istituto Nazionale di Alta Matematica “F. Severi.” M. G. acknowledges support through the “Progetto Giovani GNFM 2020.”

Acknowledgment

The authors thank the anonymous referees for the helpful comments leading to clarification of some aspects and improvement of the quality of the paper.

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Received: 2021-11-26
Revised: 2022-02-04
Accepted: 2022-02-18
Published Online: 2022-03-30
Published in Print: 2022-04-30

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