TRACTION SINGULARITIES ON SHARP CORNERS AND EDGES IN STOKES FLOWS

An integral identity developed by Brenner (1964) is used in the ''reve rsed'' context to derive a fixed point iterative scheme for the surfac e tractions on a rigid particle of arbitrary shape submerged in Stokes flows. The iterative approach facilitates the solution of very large systems of equations and thus the employment of high resolution discre tization schemes. The utility of the approach is demonstrated by illus trative computations of the tractions on regular polyhedra, with speci al emphasis on the results near the edges and corners where (integrabl e) singular behavior is expected to provide a stringent test for the n umerical method. Excellent agreement between our numerical estimates f or the exponent of these singularities with the analytical result (loc al 2-D analysis) were obtained. The emphasis in this work is on valida tion of the approach, but references to applications, such as fluidic self-assembly of semiconductor microstructures, are provided.