No net motion for oscillating near-spheres at low Reynolds numbers

We investigate the flow around an oscillating nearly-spherical particle at low, yet non-vanishing, Reynolds numbers, and the potential resulting locomotion. We analytically demonstrate that no net motion can arise up to order one in Re and order one in the asphericity parameter, regardless of the particle's shape. Therefore, geometry-induced acoustic streaming propulsion, if any, must arise at higher order.