Peristaltic flow of a multilayered power-law fluid through a cylindrical tube

Abstract

This paper is an analytical study of the flow of a power-law fluid through a cylindrical tube in the presence of a peripheral layer of another power-law fluid with different viscosity. It serves as a model for the study of flow of chyme through small intestines. The interface which is a streamline in the flow pattern has been determined as a solution of an algebraic equation obtained from the function by imposing the condition for the mass conservation within the core fluid. The relation between the flow-rate and the pressure difference for one wavelength has been determined. Moreover, the trapping and the reflux limits as well as the efficiency of pumping have also been determined. It is found that unlike Newtonian flows in cylindrical vessels, the power-law fluid flow does not experience reflux throughout the domain. The computational results indicate that the flow-rate decreases with the decrease in the value of the flow behaviour index or in the viscosity of the outer layer. In physiological flows, it is found that the viscosity of the peripheral layer is often less than that of the core layer. In that case, a thinner peripheral layer is responsible for a greater flow-rate. The cylindrical flow-rate is higher than that in the two-dimensional case under identical conditions.