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Recent experiments showed that standing acoustic waves could be exploited toinduce self-propulsion of rigid metallic particles in the directionperpendicular to the acoustic wave. We propose in this paper a physicalmechanism for these observations based on the interplay between inertial forcesin the fluid and the geometrical asymmetry of the particle shape. We consideran axisymmetric rigid near-sphere oscillating in a quiescent fluid along adirection perpendicular to its symmetry axis. The kinematics of oscillationscan be either prescribed or can result dynamically from the presence of anexternal oscillating velocity field. Steady streaming in the fluid, theinertial rectification of the time-periodic oscillating flow, generates steadystresses on the particle which, in general, do not average to zero, resultingin a finite propulsion speed along the axis of the symmetry of the particle andperpendicular to the oscillation direction. Our derivation of the propulsionspeed is obtained at leading order in the Reynolds number and the deviation ofthe shape from that of a sphere. The results of our model are consistent withthe experimental measurements, and more generally explains how time periodicforcing from an acoustic field can be harnessed to generate autonomous motion.

Asymmetric steady streaming as a mechanism for acoustic propulsion of rigid bodies