Journal of Fluid Mechanics

Journal of Fluid Mechanics (1977), 83:2:249-272 Cambridge University Press
Copyright © 1977 Cambridge University Press

Computational and experimental investigations of two-dimensional nonlinear peristaltic flows

Thomas D.  Brown a1 and Tin-Kan  Hung a2
a1 Department of Orthopaedic Surgery, University of Pittsburgh, Pennsylvania 15261
a2 Departments of Civil Engineering and Neurosurgery, University of Pittsburgh, Pennsylvania 15261

Article author query
brown td   [Google Scholar] 
hung t   [Google Scholar] 


An implicit finite-difference technique employing orthogonal curvilinear co-ordinates is used to solve the Navier–Stokes equations for peristaltic flows in which both the wall-wave curvature and the Reynolds number are finite (§2). The numerical solutions agree closely with experimental flow visualizations. The kinematic characteristics of both extensible and inextensible walls (§3) are found to have a distinct influence on the flow processes only near the wall. Without vorticity, peristaltic flow observed from a reference frame moving with the wave will be equivalent to steady potential flow through a stationary wavy channel of similar geometry (§4). Solutions for steady viscous flow (§5) are obtained from simulation of unsteady flow processes beginning from an initial condition of potential peristaltic flow. For nonlinear flows due to a single peristaltic wave of dilatation, the highest stresses and energy exchange rates (§6) occur along the wall and in two instantaneous stagnation regions in the bolus core. A series of computations for periodic wave trains reveals that increasing the Reynolds number from 2[cdot B: small middle dot]3 to 251 yields a modest augmentation in the ratio of flow rate to Reynolds number but induces a much greater increase in the shear stress (§7.1). The transport effectiveness is markedly reduced for pumping against a mild adverse pressure drop (§7.2). Increasing the wave amplitude will lead to the development of travelling vortices within the core region of the peristaltic flow (§7.3).

(Published Online April 12 2006)
(Received February 3 1977)