A consistent thermodynamical model of incompressible media as limit case of quasi-thermal-incompressible materials

TL;DR

This paper develops a thermodynamically consistent model for incompressible media as a limit case of quasi-thermal-incompressible materials, establishing conditions for stability and approximations for fluids and solids.

Contribution

It introduces a thermodynamically consistent framework for modeling incompressible media as a limit of quasi-thermal-incompressible materials, including stability conditions.

Findings

Pressure cannot exceed a very large critical value

Compressibility factor must be greater than a very small lower limit

Model applies to both fluids and thermoelastic solids

Abstract

In this paper we consider the conditions on quasi-thermal-incompressible so that they satisfy all the principles of thermodynamics, including the stability condition associated with the concavity of the chemical potential. We analyze the approximations under which a quasi-thermal-incompressible medium can be considered as incompressible. We find that the pressure cannot exceed a very large critical value and that the compressibility factor must be greater than a lower limit that is very small. The analysis is first done for the case of fluids and then extended to the case of thermoelastic solids.