On the characterization of constitutive equations 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.

arXiv comment25 pages. arXiv admin note: text overlap with arXiv:2108.03237

References in corpus (3)

• Lie remarkable partial differential equations characterized by Lie algebras of point symmetries
• Weakly nonlocal thermodynamics of binary mixtures of Korteweg fluids with two velocities and two temperatures
• Continua with non-local constitutive laws: exploitation of entropy inequality

Cited by in corpus (3)

• Thermodynamical analysis and constitutive equations for a mixture of viscous Korteweg fluids
• A thermodynamical description of third grade fluid mixtures
• Two-dimensional equilibrium configurations in Korteweg fluids