STOKES-FLOW CAUSED BY THE MOTION OF A RIGID SPHERE CLOSE TO A VISCOUSINTERFACE

The subject of this work is the creeping motion of liquid caused by st eady translation and rotation of a solid sphere close to an interface between two fluid phases. The case of vanishingly small Reynolds and c apillary numbers is considered. We account for the intrinsic viscous p roperties of the liquid boundary, characterised by dilatational and sh ear surface viscosities, in the frame of the Boussinesq-Scriven model. Numerical computations are presented for the velocity and pressure di stributions throughout the flow domain. The drag force and the torque exerted on the particle are obtained by means of analytical integratio n of the stresses over the spherical surface. At small distances of se paration between the rigid sphere and the wall, the role of the surfac e viscosity becomes quite substantial: the drag and the toque can be s everal times bigger than those which correspond to motion in an unboun ded fluid. For steady rotation the flow around the solid particle is r estrained in a relatively narrow region, whereas with translation the velocity field extends to large distances. Consequently, the rotating sphere should be closer in order to start 'feeling' the wall. Our resu lts are relevant for systems which contain surfactant laden interfaces . We showed that even with low molecular weight surfactants such inter faces can behave much like solid ones. This is particularly true for f luid boundaries covered by proteins, as they turn out to be completely immobilised. (C) 1998 Elsevier Science Ltd. All rights reserved.