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

TL;DR

The paper examines objectivity and thermodynamic consistency for Korteweg-type fluids by comparing Dunn–Serrin's entropy-principle framework with a weakly nonlocal thermodynamics approach facilitated by the Liu procedure. It shows that both methods yield the same constitutive relations for Korteweg stresses, while differences in the ideal pressure tensors arise from symmetry constraints rather than fundamental failures of the theories. A spacetime, Galilean-covariant viewpoint clarifies why gradients are frame-independent and supports the objective use of constitutive variables, though a fully Galilean covariant Korteweg theory remains to be developed. The discussion connects these insights to diffuse interfaces, phase-field theory, and holographic properties, illustrating that both symmetric and asymmetric pressure forms can be thermodynamically admissible under appropriate constraints."

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.