Small acoustically forced symmetric bodies in viscous fluids

Abstract

The total force exerted on a small rigid body by an acoustic field in a viscous fluid is addressed analytically in the limit where the typical size of the particle is smaller than both the viscous diffusion length scale and the acoustic wavelength. In this low-frequency limit, such a force can be calculated provided the effect of the acoustic steady streaming is negligible. Using the Eulerian linear expansion of Lagrangian hydrodynamic quantities (velocity and pressure), the force on a small solid sphere free to move in an acoustic field is first calculated in the case of progressive and standing waves, and it is compared to past results. The proposed method is then extended to the case of more complex shapes with three planes of symmetry. For a symmetric body oriented with one of its axis along the wave direction, the acoustic force exerted by a progressive wave is affected by the particle shape at leading order. In contrast, for a standing wave (with the same orientation), the force experienced by the particle at leading order is the same as the one experienced by a sphere of same volume and density.