Effects of topographical wall patterns on flow through porous media

The present study addresses the flow characteristics of a viscous, incompressible, steady, and Newtonian fluid flow through the undulating microchannel with a porous medium. The flow is governed by the Darcy-Brinkman model with no-slip boundary conditions at walls. The objective of this study is to develop theoretical and computational models for flow parameters that are independent of the permeability of the medium and to extend the scope of previous studies. The lubrication theory is used to determine key flow parameters, such as flow rate, velocity, and wall shear stress, in complex-shaped microchannels. To overcome the limitations of lubrication and boundary perturbation methods, the spectral method is applied to a sinusoidal microchannel. We observe that flow parameters are significantly affected by dimensionless quantities such as pattern amplitude, wavelength, and permeability ( κ ). The spectral model indicates non-linear flow rate behavior when the permeability is very high ( κ ≫ 1 ) and accurately captures the transition behavior of flow rate in the Darcian flow regime for various wavelengths, unlike other theories. Conversely, for small and large wavelengths with low permeability ( κ ≪ 1 ) at the Stokes flow limit, the flow rate behavior is monotonic. The spectral model demonstrates greater reliability compared to classical lubrication theory, extended lubrication theory, and boundary perturbation methods, especially for large values of the dependent variables. Predictions from the spectral approach closely align with numerical results over a broad range of parameters. A detailed analysis of the influence of various parameters on flow quantities is presented.