Particle Manipulation in Viscous Streaming

The necessity of micromanipulation to separate, focus and transport discrete objects on a microscopic scale has emerged in recent years in areas from assisted fertilization to precision machining. This work explores the manipulation of microparticles suspended in viscous streaming flow. Streaming is a steady large-scale circulatory flow generated by the nonlinear interaction of the primary oscillatory motion. The first part of the study focuses on particle transport and trapping in the streaming flow generated by a single oscillating cylinder. The streaming flow is obtained by asymptotic expansion from previous work and the resulting velocity field is used to integrate the Maxey-Riley equation with the Saffman lift for the motion of an inertial spherical particle immersed in this flow. It is found that inertial particles spiral inward and become trapped inside one of the four streaming cells established by the cylinder oscillation, regardless of the particle size, density and flow Reynolds number. It is shown that the Faxen correction terms divert the particles from the fluid particle trajectories, and once diverted, the Saffman lift force is most responsible for effecting the inward motion and trapping. Results compare favorably with previous experiments.;We extend this study to various arrangements of oscillating probes. High fidelity computations are used to simulate the flow field to capture particle transport. It is shown that, by controlling the sequence of starting and stopping the oscillation of individual probes, inertial particles can be transported in a predictable manner between trapping points. In order to reduce the considerable expense of generating the flow field, we also explore the use of steady Stokes flow to serve as an approximate surrogate for the flow between probes. The boundary conditions for this flow are obtained by matching with the inner Stokes layer solution in the asymptotic expansion for small amplitude. Finally, the practical characteristics of transport by streaming are discussed.;Overall, this study reveals that viscous streaming is an effective mechanism with which to manipulate small particles. To the best of my knowledge, this work is the first to investigate inertial particle trapping and transport in viscous streaming theoretically and computationally.