A THEORETICAL-STUDY OF VISCOUS EFFECTS IN PERISTALTIC PUMPING

Intuition and previous results suggest that a peristaltic wave tends t o drive the mean flow in the direction of wave propagation. New theore tical results indicate that, when the viscosity of the transported flu id is shear-dependent, the direction of mean flow can oppose the direc tion of wave propagation even in the presence of a zero or favourable mean pressure gradient. The theory is based on an analysis of lubricat ion-type flow through an infinitely long, axisymmetric tube subjected to a periodic train of transverse waves. Sample calculations for a she ar-thinning fluid illustrate that, for a given waveform, the sense of the mean flow can depend on the theology of the fluid, and that the me an flow rate need not increase monotonically with wave speed and occlu sion. We also show that, in the absence of a mean pressure gradient, p ositive mean flow is assured only for Newtonian fluids; any deviation from Newtonian behaviour allows one to find at least one non-trivial w aveform for which the mean flow rate is zero or negative. Introduction of a class of waves dominated by long, straight sections facilitates the proof of this result and provides a simple tool for understanding Viscous effects in peristaltic pumping.