Hyperbolic Models of Homogeneous Two-Fluid Mixtures

TL;DR

This paper develops hyperbolic models for homogeneous two-fluid mixtures using Hamilton's principle, deriving governing equations and jump conditions, and proving hyperbolicity under certain flow assumptions.

Contribution

It introduces a novel Hamiltonian-based approach to model two-fluid mixtures, deriving new governing equations and jump conditions with hyperbolicity analysis.

Findings

Derived governing equations and Rankine-Hugoniot conditions for two-fluid mixtures.

Proved hyperbolicity of the system for small relative velocities.

Established a Hamiltonian framework for modeling miscible fluid mixtures.

Abstract

One derives the governing equations and the Rankine - Hugoniot conditions for a mixture of two miscible fluids using an extended form of Hamilton's principle of least action. The Lagrangian is constructed as the difference between the kinetic energy and a potential depending on the relative velocity of components. To obtain the governing equations and the jump conditions one uses two reference frames related with the Lagrangian coordinates of each component. Under some hypotheses on flow properties one proves the hyperbolicity of the governing system for small relative velocity of phases.