Peristaltic Transport

Abstract

Peristaltic pumping (viscous fluid flow induced by a sinusoidal traveling wave motion of the walls of a tube) at moderate amplitudes of motion is analyzed in the two-dimensional case. The nonlinear convective acceleration is considered and the nonslip condition is applied on the wavy wall (rather than on the mean position) in order to account for the mean flow induced by the wall motion. In the case in which there is no other cause of flow, the mean flow induced by the peristaltic motion of the wall is proportional to the square of the amplitude ratio (wave amplitude/half width of channel). The velocity profile depends on the mean pressure gradient. In this paper only those cases in which the pressure gradient will produce a flow of the same order of magnitude as that induced by the peristaltic motion are considered. If the pressure gradient is positive and equal to a certain critical value, then the velocity is zero on the center line. Pumping against a positive pressure gradient greater than the critical value would induce a backward flow (reflux) in the core region of the stream. There will be no reflux if the pressure gradient is smaller than the critical value. The velocity profile and the value of the critical pressure gradient are presented in this paper.