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

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 the density and the velocity of the other fluid specie, i.e., the testing flow.