Short and long wave peristaltic flow: Modeling and mathematical analysis

In this paper, we present a mathematical model for the peristaltic flow of a Newtonian fluid in an axisymmetric channel with small aspect ratio. In particular, we study the effects of the wave length of the wall oscillation distinguishing between long wave length (same order of the vessel's length) and short wave length (same order of the vessel's radius). We prove that the oscillation produces flow even in the absence of a pressure gradient in case of long wave. In case of short wave length, peristalsis does not affect the flow. We also prove that, in both cases, the tube resistance increases as the oscillation amplitude increases.