Second Kind Integral Equation Formulation of Stokes’ Flows Past a Particle of Arbitrary Shape

The problem of determining the slow viscous flow of an unbounded fluid past a single solid particle is formulated exactly as a system of linear Fredholm integral equations of the second kind for a distribution of Stresslets over the particle surface plus a pair of singularities (Stokeslet and Rotlet) located in the interior of the particle, singularities which give rise to a force and torque with magnitude depending linearly upon the unknown density of the surface Stresslets. It is shown that this integral equation possesses a unique continuous solution when the particle boundary is a Lyapunov surface and the velocity data on the boundary surface is continuous.