Peristaltic pumping of viscous fluid in an elastic tube

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.