Symmetric form for the hyperbolic-parabolic system of fourth-gradient fluid model

Abstract

The fourth-gradient model for fluids-associated with an extended molecular mean-field theory of capillarity-is considered. By producing fluctuations of density near the critical point like in computational molecular dynamics, the model is more realistic and richer than van der Waals' one and other models associated with a second order expansion. The aim of the paper is to prove-with a fourth-gradient internal energy already obtained by the mean field theory-that the quasi-linear system of conservation laws can be written in an Hermitian symmetric form implying the stability of constant solutions. The result extends the symmetric hyperbolicity property of governing-equations' systems when an equation of energy associated with high order deformation of a continuum medium is taken into account.

References in corpus (4)

• Variational Theory of Mixtures in Continuum Mechanics
• Hyperbolic Models of Homogeneous Two-Fluid Mixtures
• Hamilton's Principle and Rankine-Hugoniot Conditions for General Motions of Mixtures
• A variational principle for two-fluid models

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• The Hamilton principle for fluid binary mixtures with two temperatures
• Principle of virtual action in continuum mechanics
• The Least Action and the Metric of an Organized System
• Helicity in dispersive fluid mechanics