The creeping motion of a sphere normal to a deformable fluid-fluid interface has been studied using numerical and experimental techniques. A numerical method based on the distribution of point force singularities at fluid surfaces, the boundary integral method, has been applied to sphere motion in the presence of an interface subject to the constraint of either constant velocity normal to the interface, or constant non-hydrodynamic body force normal to the plane of the undeformed interface. Cases for several values of the viscosity ratio, density difference, and interfacial tension between the two fluids are considered. Calculations reveal two distinct modes of interface deformation: a film drainage mode in which fluid drains away in front of the sphere leaving an ever thinning film, and a tailing mode where the sphere passes several radii beyond the plane of the initially undeformed interface, while remaining encapsulated by the original surrounding fluid which is connected with its main body by a thin thread-like tail behind the sphere. We consider the influence of the viscosity ratio, density difference, interfacial tension and starting position of the sphere in determining which of these two modes of deformation will occur.
Experiments were performed for a rigid sphere translating normal to a deformable fluid-fluid interface with large capillary number. The motion of fluid at the interface in both the axial and radial directions was recorded as was the total force on the sphere. The experimental results were compared to boundary integral calculations of the interface position and force on the sphere, employing both a fully mobile and completely immobile model for interfacial dynamics. These comparisons indicate significant reduction in the interface mobility for the experimental system.
In order to increase our understanding of the actual breakthrough process, a third model for interfacial dynamics was developed. The latest model includes the disjoining pressure in the normal stress jump boundary condition. Preliminary calculations indicate that dispersion forces can result in a change in the calculated mode of breakthrough, converting tailing cases to the film drainage mode. Further, for the range of parameters studied here, the effect of dispersion forces was relatively small until the sudden onset of motion of the interface toward the sphere caused breakthough.
