On the resolvability of the dynamics of one fluid flow via a testing fluid in a two-fluids flow model

TL;DR

This paper justifies a simplified two-fluids flow model as an asymptotic limit of a more complex isentropic fluid interaction system, enabling the resolution of one fluid's density from the other’s data.

Contribution

It provides a rigorous derivation and justification of a simplified two-fluids flow model from a more detailed interaction model, clarifying the conditions under which the simplification holds.

Findings

The simplified model is valid as an asymptotic limit for large symmetric drag forces.

Equations for each fluid component with interaction terms are explicitly identified.

The model allows resolving the density of one fluid based on the other’s density and velocity.

Abstract

In this work, by considering an isentropic fluid-fluid interaction model with a large symmetric drag force, a commonly used simplified two-fluids flow model is justified as the asymptotic limit. Equations for each fluid component with an interaction term are identified in addition to the simplified two-fluids flow model, which can be used to resolve the density of one fluid specie based on information on density and the velocity of the other fluid specie, i.e., the testing flow.