ON THE CAPABILITIES OF THE DOUBLE-LAYER REPRESENTATION FOR STOKES FLOWS .1. ANALYTICAL SOLUTIONS

Boundary-integral equations of the second kind for Stokes flows known as the completed-double-layer (CDL) representations are promising form ulations for the solution of many-body problems in suspension mechanic s. It is therefore important to analyze their numerical properties for geometries where accurate numerical results are not readily obtained. In this paper, several analytical and semi-analytical results are der ived for the double-layer representation where particles are in close proximity to one another. In particular, the onset of spatial oscillat ion of the surface density is explored as a function of particle-parti cle separation. These oscillations are not spurious and pose a signifi cant challenge for discretization schemes.