Analytical study on the flow of immiscible fluids through a curved pipe

In this paper, the flow of two immiscible fluids through a curved pipe induced due to a pressure gradient in axial direction is studied. The fluid in core region is assumed to be highly viscous than that of the peripheral region as such types of flows are observed in real life (viz. blood flow through arteries). Equations governing the flow are considered without ignoring any curvature ratio terms and are solved analytically by considering the perturbation series. The continuity of velocities and shear stresses at the fluid-fluid interface is taken into account along with no-slip, symmetric and regularity conditions, while solving the two-fluid flow problem under consideration. The effect of various fluid parameters such as curvature ratio, Reynolds number, viscosity ratio and density ratio on the axial velocity is studied through 2-dimensional graphs and contour plots.