Peristaltic Transport in a Circular Cylindrical Pipe

Abstract

The flow of an incompressible viscous fluid through a circular pipe is studied for the case of an axisymmetric wave traveling along the wall when the initial motion is assumed to be a Hagen-Poiseuille flow. The solution is represented by a power series expansion to the second order of amplitude-to-radius ratio, ε2, which is assumed to be much less than unity. Two domains of the flow, with convective term not negligible compared to the viscous term, are of main concern. The first is the case of low Reynolds number (R = wave speed × radius/kinematic viscosity). The second is for small radius-to-wave-amplitude ratio (α = 2π radius/wavelength). Analytical calculations are carried out to the second order of R and α, respectively. The result obtained indicates that the series expansion in powers of α is applicable up to R-values of order 10.