Dispersion in a slit with crossflow filtration through a porous wall.

This article focuses on generalizing Taylor dispersion theory to analyze solute transport in a slit–porous medium system subjected to crossflow filtration, where fluid flows tangentially along a slit and perpendicularly through a porous wall. The study develops a coupled mathematical model using unsteady-state advection–diffusion equations for both the slit and porous medium, linked by continuity conditions at their interface, and employs Reynolds decomposition and cross-sectional averaging to derive a reduced-order model describing effective axial velocity and dispersion coefficients. Results reveal a nonmonotonic relationship between the effective axial velocity and the Peclet number for crossflow, and identify two dispersion regimes characterized by distinct scaling laws for the nondimensional Taylor dispersion coefficient with respect to the Peclet numbers of the main flow and crossflow. The model recovers known results in the absence of crossflow and offers analytical expressions for solute concentrations and mass storage, providing insights applicable to industrial processes such as water treatment, chemical processing, and biotechnology where solute dispersion affects separation efficiency.