Low Reynolds number motion of bubbles, drops and rigid spheres through fluid–fluid interfaces

Abstract

The low Reynolds number buoyancy-driven translation of a deformable drop towards and through a fluid–fluid interface is studied using boundary integral calculations and laboratory experiments. The Bond numbers characteristic of both the drop and the initially flat fluid–fluid interface are sufficiently large that the drop and interface become highly deformed, substantial volumes of fluid may be entrained across the interface, and breakup of both interfaces may occur. Specifically, drops passing from a higher- to lower-viscosity fluid are extended vertically as they pass through the interface. For sufficiently large drop Bond numbers, the drop may deform continuously, developing either an elongating tail or enlarging cavity at the back of the drop, analogous to the deformation characteristic of a single deformable drop in an unbounded fluid. The film of fluid between the drop and interface thins most rapidly for those cases that the drop enters a more viscous fluid or has a viscosity lower than the surrounding fluids. In the laboratory experiments, bubbles entering a less viscous fluid are extended vertically and may break into smaller bubbles. The column of fluid entrained by particles passing through the interface may also break into drops. Further experiments with many rigid particles indicate that the spatial distribution of particles may change as the particles pass through interfaces: particles tend to form clusters.