Viscous oscillatory flow past particles, governed by the unsteady Stokes equation, is considered. The problem is addressed in its general form for arbitrary flows and particle shapes using the boundary-integral method. It is shown that the leading-order correction to the force exerted on a particle in unsteady flow may be inferred directly from the drag in steady translational motion. For axisymmetric flow, a numerical procedure for solving the boundary-integral equation is developed, and is applied to study streaming oscillatory flow past spheroids, dumbbells, and biconcave disks. The effect of the particle geometry on the structure of the flow is studied by comparing the streamline pattern associated with these particles to that for the sphere. The results reveal the existence of travelling stagnation points on the surface of non-spherical particles, and the formation of unsteady viscous eddies in the interior of the flow. These eddies grow during the decelerating flow period, and shrink during the accelerating flow period. For particles with concave boundaries, unsteady free eddies may originate from an expansion of wall eddies that reside within the concave regions.
Non-singular boundary integral methods for fluid mechanics applications