Peristaltic transport of multilayered power-law fluids with distinct viscosities: a mathematical model for intestinal flows

This paper is concerned with the theoretical study of two-dimensional peristaltic flow of power-law fluids in three layers with different viscosities. The analysis is carried out under low Reynolds number and long wavelength approximations. The shapes of the interfaces are described by a system of non-linear algebraic equations which are solved numerically as streamlines. It is found that the non-uniformity in the intermediate and peripheral layers diminishes when the viscosity of the intermediate layer is increased and that of the outermost layer is kept unaltered for both the pseudo-plastic and dilatant fluids. Similar are the observations when the viscosity of the outermost layer is increased and that of the intermediate layer is kept fixed. The flow rate increases with the viscosities of the peripheral and the intermediate layers but the viscosity of the outermost layer is more effective. However, the knowledge of the effect of the viscosity of the intermediate layer facilitates us to achieve the required flow rate without disturbing the outermost layer. An increase in the flow behaviour index too favours larger flow rates. The trapping limits increase with the viscosity of the intermediate layer but decrease with the viscosity of the outermost layer and the flow behaviour index. Thus, a medicinal intervention that creates a more viscous intermediate layer and reduces pseudo plasticity may reduce constipation.