Net motion of acoustically levitating nano-particles: A theoretical analysis

A particle 2D-trapped in the nodal planed of a standing acoustic wave is prone to acoustic-phoretic motion as soon as its shape breaks polar or chiral symmetry. such a setup constitues an ideal system to study boundaryless 2D collective behavior with purely hydrodynamic long range interactions. \\ Recent studies [1] have indeed shown that quasi-spherical particles may undergo net propulsion, a feature partially understood theoretically in the particular case of infinite viscous boundary layers [2]. \\ We here extend the theoretical results of [2] to any boundary layer thickness, by that meeting typical experimental conditions. In addition, we propose an explanation for the net spinning of the trapped particles, as observed in experiments [1]. \\ \\ $[1]$ Wang, Castro, Hoyos, and Mallouk, ACS nano {\bf 6}(7) 2012 \\ $[2]$ Nadal and Lauga, Phys. Fluids {\bf 26}, 2014