The unsteady motion of a bubble or drop towards a liquid-liquid interface

The buoyancy-driven motion of bubbles or drops towards a liquid-liquid interface at small and moderate Reynolds numbers is studied. Solutions of the unsteady nonlinear mathematical problem are performed by means of a general finite-element technique of Lagrangian type. Data for the development of the interface shapes and the film thickness are presented, and comparisons with previous theories and experiments are performed, supporting the reliability of our results. Two interesting phenomena are observed: a transient concavity at the bottom of the particle and particle elongation in the direction of motion. The drainage of the film formed between the particle and the interface, and the tailing mode are studied. Occurrence of a transient surface wave at the liquid-liquid interface and a toroidal dimpling in the film zone are observed in the tailing mode.