Optimal allocation of boundary singularities for stokes flows about pairs of particles

Abstract

Abstract Methods of allocation of singularities for the Method of Fundamental Solutions are proposed, implemented and applied to a Stokes flow about pairs of particles. New local normal and combined Stokeslets allocation methods are proposed to solve Stokes flows using a moderate number of singularities. In the proposed methods the singularities are located at surfaces inside the particles but dissimilar to the particles׳ shapes. Optimization of location of Stokeslets is performed for peanut-shaped and barrel-shaped particles. Convergence of numerical solution as a function of numbers of Stokeslets is evaluated and show substantial reduction in the needed number of Stokeslets compared to the prior methods in which Stokeslets are located at surfaces created similar to the particle shape. Using proposed methods of allocation of Stokeslets, patterns of pressure and velocity vector field near particles are obtained and discussed. The Stokes force exerted by a Stokes flow on the pair of particles is computed at different stages of their collective behavior including separate location of particles in proximity to each other, merging of particles, and re-orientation of cluster along the flow. These results help to determine the least stable location of particles׳ pair for the purpose of their separation off the flow.