Buoyancy-driven viscous interaction of a rising drop with a smaller trailing drop

An axisymmetric boundary-integral method was developed and used to study the interaction of two deformable drops (or bubbles) rising (or settling) due to gravity in a viscous medium under conditions of small Reynolds number. The focus is on cases where the smaller drop trails behind the larger drop. When the Bond number is small, interfacial tension keeps the drops nearly spherical, and they separate with time. At higher Bond numbers, however, deformation is significant and the trailing drop is stretched due to the flow created by the leading drop; it may form one or more necks and break when one of these pinches off. The leading drop is flattened due to the flow created by the trailing drop; it may form a depression on its underside which evolves into a plume that rises through its center. Moreover, at sufficiently high Bond numbers, the larger leading drop does not leave the trailing drop behind, but instead may entrain and engulf it within the depression or plume. Systematic results for the parameter ranges which demarcate impending breakup and coalescence are presented.