On ideal and real two-fluid mixtures of dispersed type: bubbly and droplet flow.*

Starting from Hamilton's principle, we derive an ideal two-phase fluid model in Lagrangian form. With this description, insight toward understanding the ill-posedness of such two-phase flow models is obtained. Issues related to non-hyperbolicity, stability, and existence of strong solutions are also revisited. Adding the effect of viscosity to each fluid, we study the behavior of (linear) sound waves in this type of media (real multi-fluid). This classical physics question is a continuation of the wave studies of Kirchhoff (1868) and Stokes (1845) in a (mono)fluid. We give attenuation and dispersion formulae due to viscous effect in real two-fluid mixtures of dispersed type.