Particle Transport in Quasistatic Stokes Flow

Abstract

Abstract Particle transport associated with quasistatic second-order streaming flow in wavy-walled channels is theoretically investigated. Small amplitude tangential oscillations of both walls drive steady second-order streaming, while superposed, large-amplitude oscillations of one wall produce the time-dependent, quasisteady flows of interest. Short-time transport is characterized by collective particle motion in the direction of large-scale boundary displacement and by filamentary motion in the opposite direction, both consistent with transport in traveling waves [E. Moses and V. Steinburg, Phys. Rev. Lett. 60, 2030 (1988)]. Long time or asymptotic transport is characterized by particle agglomeration toward, or repulsion from, moving elliptic points. Under certain conditions, collective, periodic motion on the periphery of central cells also occurs. These characteristics correspond respectively to attraction or repulsion to or from period-1 elliptic points and attraction toward limit cycles on the Poincare map.