Some remarks on the objectivity and thermodynamic consistency of Korteweg-type fluids

TL;DR

This paper compares different approaches to modeling Korteweg-type fluids, showing they lead to consistent constitutive functions and clarifying the reasons for differences in pressure tensor symmetry.

Contribution

It demonstrates the equivalence of objectivity arguments in different thermodynamic frameworks for Korteweg fluids and explains the origin of pressure tensor differences.

Findings

Different objectivity approaches yield the same constitutive functions.

The pressure tensor differences arise from symmetry requirements.

The methodologies are thermodynamically consistent.

Abstract

In this note we compare the entropy principle and the objectivity arguments in the methodologies of Dunn and Serrin [1] and in the more recent weakly nonlocal thermodynamic analysis of Korteweg-type fluids in [2]. It is concluded that the different objectivity approaches lead to the same constitutive functions, and that the difference in the thermodynamically compatible pressure tensors of perfect Korteweg fluids is due to different symmetry requirements.