Shape change, engulfment, and breakup of partially engulfed compound drops undergoing thermocapillary migration

Compound drops comprise two or more immiscible phases, one of which entirely or partially engulfs the others. In this work we consider the thermocapillary-induced motion of partially engulfed compound drops, composed of two phases, in an immiscible fluid. If the capillary number is negligibly small, Ca << 1, the partially engulfed compound drop is composed of three spherical surface segments, intersecting at contact angles that are determined by the three interfacial tensions associated with the three fluid phases that make up the compound drop and the ambient medium. Corrections to the shapes of the undeformable case at Ca = 0 are expected to be of the order Ca. However, as the drop propagates through the nonisothermal fluid, the temperature at the three-phase contact line and, hence, the contact angles, may considerably change, resulting in a dramatic change of the compound drop shape. Moreover, the changes in the interfacial tensions may be so significant that the partially engulfed configuration may become impossible and either two immiscible parts of the compound drop separate or one of them becomes completely engulfed by the other.