Constitutive Modelling of Korteweg Fluids Using Liu's Method

TL;DR

This paper develops a thermodynamically consistent constitutive model for Korteweg fluids using Liu's method, incorporating capillary effects and temperature-dependent parameters.

Contribution

It introduces a novel application of Liu's method to derive Korteweg stresses with thermodynamic consistency and cross-coupling effects.

Findings

Material parameter dependence on temperature aligns with kinetic theory.

Korteweg stresses derived from equilibrium conditions.

Generalized Gibbs' relation includes capillary effects.

Abstract

The paper studies constitutive modelling of Korteweg fluids. Thermodynamic consistency, i.e. compatibility with entropy balance law, is achieved using Liu's method of multipliers. Appropriate constitutive assumptions facilitated inclusion of the capillary effects in the specific entropy. Korteweg stresses are derived from the equilibrium conditions -- vanishing of the entropy production and its minimization in equilibrium. Material parameter in Korteweg stresses is allowed to depend on temperature, which turns out to be consistent with kinetic-theory results and leads to cross-coupling of mechanical and thermal effects. The generalized Gibbs' relation, which inherits the capillary effects, is derived as consequence, which is a peculiar feature of the Liu's method.