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

## TL;DR

This paper analytically proves that oscillating near-spherical particles at low Reynolds numbers cannot achieve net motion up to first order in Reynolds number and shape asymmetry, implying higher-order effects are necessary for propulsion.

## Contribution

The study provides a rigorous analytical demonstration that no net locomotion occurs at low Reynolds numbers for oscillating near-spheres, clarifying the conditions for propulsion mechanisms.

## Key findings

- No net motion up to first order in Re and shape asymmetry.
- Higher-order effects are required for propulsion.
- Shape does not induce net movement at low Re.

## Abstract

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.