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Peristaltic transport due to finite amplitude bending and contraction waves

This analysis demonstrates theoretically that a lateral bending wave propagating along the walls of a two-dimensional channel filled with a viscous incompressible fluid will induce a mean flow. In addition to this ‘pure’ bending wave, another possible condition is investigated: that of the superposition of an area contraction wave propagating with the same speed as the lateral bending wave. This second condition, called complex wave motion, takes into account the slight occlusion which occurs naturally at the amplitude peaks when a finite amplitude bending wave propagates along the walls of a container. A perturbation solution is found which satisfies Navier—Stokes equations for the case in which wave amplitude/wavelength is ‘small’. However the wave amplitude is finite, in the sense that it is of the same order as the channel width. Under these conditions, the occlusion at the amplitude peaks is allowed to be of the same order as the channel width. For the case of a pure bending wave the motion induced by the peristaltis is found to be of second order in the perturbation parameter, whereas in the more realistic case a first-order pumping effect is obtained.