SLOW MOTIONS OF A SOLID SPHERICAL-PARTICLE CLOSE TO A VISCOUS INTERFACE

In order to investigate the hydrodynamic interaction between an interf ace and a spherical particle and its dependence on the type of interfa ce, it is essential to compute the drag and torque exerted on the sphe re in the vicinity of the interface. In this paper, the problem of all slow elementary motions (relative translation and rotation) and stati onary movement of a spherical particle next to a solid, viscous or fre e interface is considered. For low capillary numbers and different val ues of surface dilatational and shear viscosities in a curvilinear co- ordinate system of revolution with bicylindrical co-ordinates in merid ian planes, the problem reduces from three to two dimensions. The mode l equations and boundary conditions, which contain second-order deriva tives of the velocities, transform to an equivalent well-defined syste m of second-order partial differential equations which is solved numer ically for medium and small values of the dimensionless distance to th e interface. Very good agreement with the asymptotic equation for a tr anslating sphere close to a solid interface could be achieved. The num erical results reveal in all cases the strong influence of the surface viscosity on the motion of the solid sphere. For small distances from the interface, the drag and torque coefficients change significantly depending on the surface viscosity.