Rectified Motion of Microparticles: Generalizing Streaming and Radiation Forces

It is well known that a wide variety of oscillating flows gives rise to steady streaming, i.e., rectified motion of fluid elements. Small spherical particles introduced into such a flow have been shown to experience an additional lift force that ultimately leads to particle trajectories that differ systematically from the fluid element pathlines. We demonstrate a systematic derivation of this differential particle motion on the steady streaming time scale, so that time-averaged particle trajectories can be directly predicted without computation on the fast, oscillatory time scale. The resulting dynamics can be interpreted as a generalization of streaming flow, while the closed-form lift force provides a generalization of the secondary radiation force, to which it reduces in appropriate limiting cases. These very general results are validated by comparison with experiments in the context of bubble streaming, but apply to a large class of other flows as well.