Shapes of a rising miscible droplet

Abstract

We model the buoyancy-driven motion of a liquid droplet in an ambient liquid, assuming that the liquids are miscible. The classical representation of miscible liquids as a single-phase fluid with impurity (neglecting surface tension effects) cannot describe all experimental observations of moving droplets in a miscible environment, in particular, the tendency of droplets to pull to a spherical shape. In the framework of the classical approach, we show that the motion of a miscible droplet results in its instant dispersion (except for a very slow rise). We also model the motion of a miscible droplet in the framework of the phase-field approach, taking into account surface tension forces. We vary the value of the surface tension coefficient within a very wide range, modeling a droplet that rises preserving a spherical shape, or a droplet which dynamically becomes indistinguishable from the droplet with an interface endowed with no surface tension. We also show that by employing the concept of dynamic surface tension, one may reproduce the motion of a droplet that pulls into a sphere in the initial period of its evolution and that disintegrates similar to a droplet with zero surface tension at the later stages.