Inertial particle trapping in viscous streaming

Abstract

The motion of an inertial particle in a viscous streaming flow of Reynolds number order 10 is investigated theoretically and numerically. The streaming flow created by a circular cylinder undergoing rectilinear oscillation with small amplitude 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 Faxén 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. The speed of this trapping increases with increasing particle size, decreasing particle density, and increasing oscillation Reynolds number. The effects of Reynolds number on the streaming cell topology and the boundaries of particle attraction are also explored. It is found that particles initially outside the streaming cell are repelled by the flow rather than trapped.