Dissipative Two-Fluid Models

TL;DR

This paper derives and extends two-fluid mixture models from Hamilton's principle, including dissipative effects, and establishes an algebraic identity linking fundamental equations, ensuring hyperbolicity under certain conditions.

Contribution

It introduces a dissipative extension to two-fluid models derived from Hamilton's principle, connecting momentum, mass, energy, and entropy equations.

Findings

The system is hyperbolic for small relative phase velocities.

An algebraic identity linking key equations is established.

The model extends conservative two-fluid equations to include dissipation.

Abstract

From Hamilton's principle of stationary action, we derive governing equations of two-fluid mixtures and extend the model to the dissipative case without chemical reactions. For both conservative and dissipative cases, an algebraic identity connecting equations of momentum, mass, energy and entropy is obtained by extending the Gibbs identity in dynamics. The obtained system is hyperbolic for small relative velocity of the phases.