Multi-scale analysis of solute transport in hydrodynamic fluid flows through a porous channel with anisotropic permeability and boundary absorption

The present study investigates the transverse concentration distribution of a passive contaminant in an incompressible viscous fluid. The parallel plate device is filled with an anisotropic porous medium with boundary absorption at both the plates. Das et al. (Phys Fluids 36(2):023610, 2024) have considered a similar configuration in an oscillatory Couette flow and analyzed the solute dispersion based on the method of moments and finite difference discretization. They have suggested a control mechanism based on the anisotropic parameters on the growth of mean concentration. In the current study, we consider a combined Couette–Poiseuille device and develop an analytical solution using the small aspect ratio of the channel, \(\epsilon \) $ϵ$ . Further, we employ a multi-scale homogenization technique to derive the dispersion coefficient, mean concentration, and transverse concentration up to the third order, i.e. \(O(\epsilon ^3)\) $O({ϵ}^3)$ . The study examines the effects of Darcy number, relative viscosity, and anisotropy parameters on the velocity profile, dispersion coefficient, as well as mean and transverse concentration distributions. The dispersion coefficient in an anisotropic medium increases to \(76\%\) $76\%$ , and significantly enhances the solute dispersion over isotropic conditions. The transverse concentration variation of anisotropic medium changes by up to \(80\%\) $80\%$ compared to isotropic conditions. Boundary absorption causes persistent transverse non-uniformity in concentration variation, shifting the peak downstream. When the absorption is off at one of the walls, overlapping occurs at the center. The peak transverse variation changes from a bimodal to a unimodal distribution. These findings enhance the understanding of solute dispersion in enhanced oil recovery, particularly in anisotropic porous rock structures.