Sedimentation of a solid particle immersed in a fluid film

International audienceThis paper examines the slow viscous settling migration of a solid particle immersed in a viscous fluid film confined by two plane and parallel solid wall and free surface. The approach rests on the use of suitable boundary-integral equations on the surface of the particle and the analytical calculation of a new Green tensor that complies with all the boundary conditions satisfied by the liquid flow on the plane boundaries. The numerical implementation resorts to standard boundary elements on the particle's surface and provides at a reasonable cpu time cost the motion of the particle and, if necessary, the velocity field in the liquid film. The migration of a sphere is found to deeply depend on its location, the gravity field and the fluid film thickness. Depending on these parameters the sphere may either translate faster, slower or at the same speed than in absence of boundaries. This latter case arises at a critical location of the sphere for a gravity field parallel to the boundaries. Copyright © 2006 Tech Science Press