CLOSE APPROACH AND DEFORMATION OF 2 VISCOUS DROPS DUE TO GRAVITY AND VANDERWAALS FORCES

The rate of approach and deformation of two small drops of different sizes in buoyancy-driven axi-symmetric motion is analyzed within the asymptotic limit of small capillary number, in which deformation becomes important only when the minimum separation between the drops is much smaller than either radius. Then, the drops translate with nearly equal velocities, and the small relative motion as the larger drop slowly catches up with the smaller drop can be described by an analysis which assumes a lubrication regime in the thin gap between them. When this lubrication squeeze flow in the gap exerts a sufficient tangential stress on the drop interfaces to drive an internal flow within the drops, then the coupling between these flows is analyzed by a boundary integral formulation. Numerical calculations are used to track the evolution of the shapes of the drops from a relatively undeformed state until the gap takes the form of a dimple and a long-time quasi-steady pattern is established. As the drop separation decreases, attractive van der Waals forces come into play and bring about the rupture of the fluid film between the drops. The rupture time is predicted, and a demarcation is observed between "nose rupture" for drops with small deformations and "rim rupture" for drops with large deformations and dimples. © 1991 Academic Press, Inc. All rights reserved.