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Peristaltic pumping of viscous fluid in an elastic tube

Published online by Cambridge University Press:  24 February 2011

D. TAKAGI  and
N. J. BALMFORTH
D. TAKAGI
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
N. J. BALMFORTH*
Affiliation:
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, V6T 1Z2, Canada Department of Earth and Ocean Science, University of British Columbia, 6339 Stores Road, Vancouver, V6T 1Z4, Canada
*
†Email address for correspondence: njb@math.ubc.ca
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Abstract

A model is derived for long peristaltic waves propagating steadily down a fluid-filled, axisymmetric tube. The waves are driven by imposing a radial force of prescribed form on the tube. The resulting deformation of the tube wall is modelled using linear elasticity and the internal flow using the lubrication approximation. Numerical solutions for periodic wave trains and solitary waves are presented, along with asymptotic solutions at both small and large forcing amplitudes. Large-amplitude periodic waves are characterized by narrow blisters adjoining long occluded sections of the tube, whereas a solitary wave of strong contraction produces a long inflated bow wave that propels a large quantity of fluid. A measure of pumping efficacy is given by the ratio of the net fluid displacement to the power input, and is highest for a large-amplitude solitary wave.

JFM classification

Low-Reynolds-number flows: Lubrication theory Biological Fluid Dynamics: Peristaltic pumping Waves/Free-surface Flows: Solitary waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 672 , 10 April 2011 , pp. 196 - 218
Copyright
Copyright © Cambridge University Press 2011

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