Nonlinear and curvature effects on peristaltic flow of a viscous fluid in an asymmetric channel

Abstract

The flow of an incompressible viscous fluid driven by the travelling waves along the boundaries of an asymmetric channel is studied when inertia and streamline curvature effects are not negligible. The channel asymmetry is produced by choosing the wave train on the walls to have different amplitudes and phases. An asymptotic solution is obtained to second order in δ, a ratio of channel width to the wavelength, giving the curvature effects. A domain transformation is used to transform the channel of variable cross section to a uniform cross section, and this facilitates in easy way of finding closed form solutions at higher orders. The relation connecting the pressure gradient and time rate of flux is a cubic leading to non-uniqueness of flux. A uniqueness criterion is derived which restricts the parameters to get a unique flux for a prescribed pressure gradient. The effects of inertia and curvature on pumping, trapping and shear stress are discussed for symmetric and asymmetric channels and compared with the existing results in the literature. Even under a favorable pressure gradient the possibility of fluid flow in a direction opposite to the direction of the waves propagating on the walls is detected as in the case of some non–Newtonian fluids. It is noticed that the effects of Reynolds number and asymmetry may play an important role in producing mixing. Another interesting observation is that the shear stress distribution on the walls vanishes at some points and this will not indicate any flow separation.