The creeping motion of a rigid sphere in the presence of a deformable fluid/fluid interface has been considered using theoretical, experimental and numerical techniques. Solutions for small perturbations in shape, for an initially flat interface, are obtained to calculate the additional forces and torques on a sphere rotating and translating both normal to and parallel with a slightly deformed interface. The interfacial shape as well as the forces and torques are calculated as a function of sphere position and interfacial deformation parameters, viscosity ratio, capillary number, and ratio of Bond number to capillary number. The interface deformation was found to yield no correction to the torque or parallel force on the sphere for any combination of sphere motion. The interface deformation did yield a force directed away from the interface for all sphere motions which generate a deformation for the interface.
A new direct force measurement experimental apparatus is used to study the normal motion of a rigid sphere approaching a deformable interface under conditions of constant interfacial deformation parameters. The sphere was lowered at a constant velocity and the force on the body was measured as a function of the interface shape and values of the deformation parameters.
Study of the translation of a nonrotating sphere parallel with a fluid/fluid interface, experiencing finite amplitude deformations, utilizes a numerical collocation technique. The forces and torques on the body are calculated as a function of body displacement from the interface and the interface deformation parameter (ratio of Bond number to capillary number). The interface shapes are determined and the forces and torques on the sphere are calculated.
