Mechanisms driving the acoustic propulsion of nanoparticles

A particle possessing shape or density asymmetries trapped in an acoustic standing wave can undergo propulsion due to a steady streaming flow generated by the particle. Remarkably, a reversal occurs in the propulsion direction at a critical value of dimensionless frequency (scaled by the viscous diffusion time), which varies depending on the shape and/or density asymmetries of the particle. We investigate the origin of this reversal in propulsion by studying a canonical problem of the streaming flow around a sphere that undergoes oscillatory rotations, which is suspended in an unbounded fluid exhibiting rectilinear oscillations (which may be phase-shifted relative to the sphere rotations). An analytical expression of the flow field is derived in the limit of the infinitesimal amplitude of both the applied oscillatory flow and the particle's rotational oscillations. We find that two distinct bifurcations occur as a function of frequency. At the first bifurcation, a stagnation point forms in the interior of the flow which then splits into a saddle node and a vortex centre as the dimensionless frequency increases. A reversal happens at the second bifurcation when the stagnation point approaches infinity and then flips from the equator to the poles. Furthermore, we show that the streaming flow in the far field coincides with that of a Stokeslet whose magnitude is the net force exerted on the particle.