Long-wave peristaltic transport of a compressible viscous fluid in a finite pipe subject to a time-dependent pressure drop

Axisymmetric viscous flow in a long pipe, driven by the pulsating pressure gradient and the wall deformation, is investigated. This kind of a flow is relevant to the peristaltic transport of blood due to the heart pumping along with the synchronic expansion/constriction of the vessel. Following the spirit of the lubrication theory, a reduced system of equations is derived. An obtained explicit solution demonstrates crucial role of peristalsis on the total fluid flux through the pipe. In order to account for the inertia effect, a model based on an averaging of the momentum equation using an a priori parabolic flow pattern across the pipe, is also derived.