Permanent displacement and particle capture in vortical Stokes flow

Density-matched, force-free particles in Stokes flow are typically assumed to passively follow streamlines. When encountering a boundary, steric requirements forbidding penetration enforce deviations from the initial streamline, leading to well-defined changes in normal and tangential velocity components. We show that, if the geometry of the boundary or the geometry of the flow field break multiple symmetries, such deviations result in net displacement, and thus meaningful manipulation of particle transport, is possible. Internal vortical Stokes flows are well-suited for related applications, as the small displacement effects of wall encounters accumulate. In a class of symmetry-broken vortex and cavity flows, derived from Moffatt eddy solutions of the Stokes equations, significant displacements both away from and towards the wall become possible. In certain flows of this type, particles thus converge to predictable fixed points or limit-cycle trajectories. In others, they approach a wall or boundary ever more closely while contact remains impossible; in realistic situations, small-scale forces then lead to sticking in predictable positions. Exploiting such effects of particle displacement at zero Reynolds number together with those using finite particle inertia will lead to new protocols of particle manipulation generally and particle capture in filters specifically.