Stokeslets-meshfree computations and theory for flow in a collapsible microchannel

Abstract

We present both a theoretical model and Stokeslets-meshfree computations to study the induced flow motions and transport in a 2D microchannel with moving multiple prescribed dynamic collapses (contractions) along the upper wall. The channel is assumed to have a length that is much greater than its width, i.e., \({(\delta = W/L \ll1)}\) . The wall contractions are set to move with or without time (phase) lags with respect to each other. The theoretical analysis presented is based on the quasi-steady state approximations and the lubrication theory at the low Reynolds number flow regime. The meshfree numerical method is based on the method of fundamental solutions MFS, which uses a set of singularized force elements called Stokeslets to induce the flow motions. The flow field developments and structures induced by these wall contractions are given at various time snapshots during the collapsing cycle. The effect of the wall contractions amplitudes and the phase lags between individual contractions on the flow variables and on the time-averaged net flow over a complete cycle of contractions motions is studied. The present study is motivated by pumping mechanisms observed in insects, physiological systems that use multiple contractions to transport fluid, and the emerging novel microfluidic devices that mimic these systems.