On the characterization of constitutive equations for third grade viscous Korteweg fluids

TL;DR

This paper characterizes the constitutive equations for third grade viscous Korteweg fluids using an extended Liu procedure, revealing additional entropy flux terms and constraints to broaden phase boundary admissibility.

Contribution

It introduces a detailed algorithm applying the extended Liu procedure to explicitly solve entropy constraints for non-local constitutive relations in complex fluids.

Findings

Recovered an extra entropy flux term in the model.

Identified constraints to allow more general phase boundaries at equilibrium.

Characterized material functions for third grade viscous Korteweg fluids.

Abstract

We consider a model of a third grade viscous Korteweg--type fluid in three space dimensions, and apply the extended Liu procedure in order to explicitly solve the constraints imposed by the entropy principle on the non--local constitutive relations. We detail the algorithm we use, and are able to characterize the material functions involved in the constitutive equations. In a natural way, the application of the extended Liu procedure allows us to recover an extra term in the entropy flux, preserving all the features of third grade viscous Korteweg--type fluids. Moreover, a further constraint, in order to avoid that at equilibrium only very special phase boundaries are admissible, is investigated.