Deformation of a partially engulfed compound drop slowly moving in an immiscible viscous fluid

Abstract

Compound drops are comprised of two or more immiscible phases, one of which entirely or partially engulfs the others. In this work, we consider a partially engulfed compound drop comprised of two immiscible incompressible fluids, dispersed in an isothermal liquid, and that moved under the action of gravity and buoyancy. The contact angles between the three phases are determined by three interfacial tensions associated with the different fluids comprising the compound drop. The surfaces deform as the drop moves through the ambient fluid. If the capillary number is small (Ca⪡1), corrections to the shapes of the undeformable case (Ca=0) are constructed, making use of a perturbation technique. We report on stationary drops’ deformation for a variety of the physical parameters involved, such as volume ratio and surface tension of each interface, which determine the unperturbed configuration and the distribution of density between the two phases of the drop. Several examples of various transient behaviors of hi...