Bubble-turbulence interaction in binary fluids

Multiphase flows represent a central issue in many natural, biological and industrial fields. For instance, liquid jets vaporization, petroleum refining and boiling, emulsions in pharmaceutical applications, are all characterized by a disperse phase, such as solid particles or liquid bubbles, which evolve in a Newtonian carrier fluid. Features such as the global evaporation rates of liquid fuels in air or the homogeneity of the emulsions are controlled by the finest interaction details occurring between the two phases. In this paper we study the rising motion of a bubble induced by buoyancy in a viscous fluid. Usually this issue is tackled by tracking the bubble interface by means of sharp interface methods. However this approach requires "ad hoc" techniques to describe changes in the topological features of the deforming interface and to enforce the mass preservation. Here the problem is addressed by using a different philosophy based on a diffuse interface method, that allows a straightforward analysis of complex phenomena such as bubbles coalescence and break up without any numerical expedient. The model we adopt, funded on a solid thermodynamical and physical base, relies on the Cahn-Hilliard equation for the disperse phase, see Cahn & Hilliard (1958) and Elliott & Songmu (1986).