Breaking Symmetry in Stokes Flows,
and Resulting Hydrodynamic Forces on Objects

Dr. Jacqueline Ashmore
Department of Applied Mathematics & Theoretical Physics Center
for Mathematical Sciences
University of Cambridge
United Kingdom

Date: Tuesday, March 8, 2005
Time: 4:00 p.m.
Place: Engineering II, Room 3361

ABSTRACT

The motion of a sphere through a viscous fluid close to a boundary is a fundamental problem which is relevant to many situations ranging from bearings to the behavior of colloidal suspensions. A heavy sphere moving adjacent to an inclined boundary leads to an interesting longstanding puzzle because the reversibility of Stokes equations and the local symmetry of the flow geometry indicate that no net hydrodynamic force normal to the boundary will arise. Hence, a heavy sphere is expected to make contact with the boundary, whereas experimental measurements indicate finite separation. I will discuss several possible ways in which the flow symmetry may be broken to provide a normal force on the sphere. Having identified which of these is significant in the experiments under consideration, I will present a quantitative model of the flow problem and a comparison between the theoretical predictions and experimental data. The motion of objects with other geometries will also be discussed.