Dissipation in peristaltic pumping of a compressible viscous fluid through a planar duct or a circular tube

Abstract

When a compressible viscous fluid is pumped through a linear channel by means of a running surface wave on the wall, energy is dissipated in the fluid. The rate of dissipation can be evaluated effectively from the work performed on the fluid by the wavy wall. Explicit expressions are derived for the rate of dissipation for a planar duct and a circular tube, valid to second order in the amplitude of the surface wave. In both cases the rate of dissipation shows a resonance as a function of frequency when the phase velocity of the surface wave equals the sound velocity of the fluid.