Effect of coupled radial and axial variability of viscosity on the peristaltic transport of Newtonian fluid

Many authors assume viscosity to be constant or a radius exponential function in Stokes’ equations in order to study the peristaltic motion of a Newtonian fluid through an axisymmetric conduit. In this paper, viscosity is assumed to be a function of both the radius and the axial coordinate. More precisely, it is dependent on the distance from the deformed membrane given the fact that the change in viscosity is caused by the secretions released from the membrane. The effect of this hypothesis on the peristaltic flow of a Newtonian fluid in axisymmetric conduit is investigated under the assumptions of long wavelength and low Reynolds number. The expressions for the pressure gradient and pressure rise per wavelength are obtained and the pumping characteristics and the phenomena of reflux and trapping are discussed. We present a detailed analysis of the effects of the variation of viscosity on the fluid motion, trapping and reflux limits. The study also shows that, in addition to the mean flow parameter and the wave amplitude, the viscosity parameter also affects the peristaltic flow. It has been noticed that the pressure rise, the friction force, the pumping region and the trapping limit are affected by the variation of the viscosity parameter but the reflux limit and free pumping are independent of it.