Peristaltic Transport

Résumé du livre

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. It is shown that the non-linear convective acceleration must be considered and that the non-slip condition must be 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 course 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 centerline. 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. (Author).