Peristaltic Pumping by a Lateral Bending Wave

Abstract

A form of fluid transport induced by an arbitrary traveling wave in the walls of a two-dimensional channel filled with a viscous incompressible fluid is investigated. This can be considered as a more general case of peristaltic transport, the latter transport phenomena being classically restricted to a wave motion which produces a progressive wave of area contraction or expansion. A perturbation solution is found satisfying the complete Navier-Stokes equations for the case of small amplitude ratio (wave amplitude/channel half width). All other parameters are left arbitrary. Two particular types of boundary waves are investigated. First, a sinusoidal wave of identical phase is imposed on each wall (in-phase motion), and secondly, an in-phase and a π out-of-phase contraction wave are imposed simultaneously. For the case of in-phase motion, a peristaltic induced mean flow is found to be proportional to the amplitude ratio squared. However, for the second case, the mean flow is found to depend linearly on amplitude ratio when an imposed pressure gradient exists, producing a peristaltic assist. Thus we see that for the superposition of two waves, the transport mechanism can increase from a second-order to a first-order effect.