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 effect of steady and pulsatile flow in a symmetric wavy channel filled with an anisotropic porous medium. 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. δ≪1). Our primary objective is to investigate how the anisotropic permeability ratio influences flow reversal in 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, separation occurs near the crest region of the wavy wall, leading to the formation of recirculating zones where fluid becomes trapped. In contrast, for both pulsatile flow and the combined effects of steady and pulsatile flow, vortices form transiently at specific phases of the pulsation cycle. We explored the approximate flow reversal zone using Darcy’s approximation theory far from the wavy wall. The flow recirculation associated with steady flow offers critical insights into CO2 sequestration in deep saline aquifers. On the other hand, flow reversal at different time instances can optimize oxygen transfer in devices such as membrane oxygenators and promote convective mixing.