An investigation into the combined effect of steady and pulsatile flow within a wavy channel filled with an anisotropic porous medium

Abstract

We provide an analytical solution to examine the impact of steady and pulsatile flow in a symmetric wavy channel filled with an anisotropic porous medium. The flow inside the wavy channel with a porous substrate is governed by the Darcy-Brinkman equation. We used the perturbation approach to ascertain the solution to the problem, assuming that the ratio between the channel width and the wavelength is very small (i.e., $\delta^2 \ll 1$). We solved the problem up to $O(\delta^2)$ by assuming $\lambda^2 \delta^2 \ll 1$, where $\lambda$ is the ratio of anisotropic permeability. Our primary objective is to investigate how the anisotropic permeability ratio influences flow reversal near the crest and trough of a wavy wall under both steady flow conditions and when a pulsatile component is superimposed on the steady flow. In the case of steady flow, flow separation occurs near the crest region of the wavy wall, leading to the formation of recirculating zones where fluid becomes trapped. In contrast, for pulsatile flow as well as combined effects of steady and pulsatile flow, vortices form transiently at certain phases of the pulsation cycle. Subsequently, these vortices bulge into the mainstream, resulting in a complete backflow. We explored the approximate flow reversal zone using Darcy's approximation theory far from the wavy wall. The flow recirculation associated with steady flow is critical for mass transport and enhances convective mixing. On the other hand, flow reversal at different time instances can optimize oxygen transfer in devices such as membrane oxygenators.