The influence of a peripheral layer of different viscosity on peristaltic pumping with Newtonian fluids

Abstract

The analysis by Shapiro et al. (1969) of a two-dimensional peristaltic pump at small Reynolds number and with long wavelengths is extended to include a Newtonian peripheral layer adjacent to the wall to simulate the effect of a coating in physiological flows. An earlier analysis by Shukla et al. (1980) violates mass conservation because of an incorrect deduction of the interface shape. We present a detailed analysis of the effect of the peripheral layer on the fluid motions, the pumping characteristics, and the phenomena of reflux and trapping. For prescribed wall motion, a peripheral layer more viscous than the inner fluid improves pumping performance, while a less-viscous outer layer degrades performance. Even a very thin peripheral layer may substantially reduce pumping if the viscosity in this layer is very low relative to the inner region. The effects of the peripheral layer on reflux and trapping depend on the conditions which are held fixed while making the comparison. However, the general trend with decreasing peripheral-layer viscosity is towards an overall decrease in trapping, a decrease in reflux with fixed total volume flow rate, but an increase in reflux with fixed pressure head.