Particle motion near a deformable fluid interface

The present paper reports on one aspect of our recent studies of the hydrodynamic interactions of two deformable particles in a viscous fluid. This general hydrodynamics problem represents an initial step toward a fundamental invertigation of particle/ drop or droplet/droplet interactions in processes such as coalescence and flotation where both hydrodynamic and colloidal effects may be important. Here we consider only the limiting problem of translation of a rigid sphere with constant velocity normal to the plane of an initially flat interface. The Reynolds number is assumed to be vanishingly small; however, no restriction is imposed on the magnitude of the interface deformation.A primary focus of our research has been the qualitative dependence of the mode of interface deformation on the viscosity ratio, and on appropriate non-dimensional measures of interfacial tension and the density difference across the interface. In some instances, the deformation is relatively small and a so called “film drainage” configuration is attained as the particle passes across the plane of the undeformed interface. In other cases. however, the particle passes well into the domain of the second fluid while still surrounded by a layer of the first fluid that is connected to its original domain by a thin column (or “tail”) of fluid behind the sphere. In these latter cases, the rate of thinning of the tail is greate than the rate of thinning of the fluid layer around the particle; thus suggesting a second mode of particle “breakingthrough”, in addition to that associated with the film drainage configuration.