Dispersion of Solute in a Fluid Layer Sandwiched Between Two Anisotropic Porous Layers

ABSTRACT The study investigates solute dispersion and mass transport phenomena in a composite channel partially filled with a fluid layer with a variable viscosity, sandwiched between two anisotropic porous layers. The motivation for this work comes from the study conducted by Ling, Tartakovsky, and Battiato, who investigated the dispersion phenomena in a fluid layer with a constant viscosity confined between two isotropic porous layers. We obtain an analytical expression for the dispersion coefficient within the fluid layer in connection with the channel matrix properties such as anisotropic permeability ratio, angle, stress jump coefficient, and viscosity ratio. We have compared the one‐dimensional upscaled model accuracy with the two‐dimensional numerical solution. We present the asymptotic behavior of the dispersion coefficient of the fluid layer for the corresponding clear flow and pure Darcy situations. We see that the dispersion coefficient for the coupled channel matrix situation when the porous nature of the matrix prevails is always less than that of the clear flow situation, that is, when the porous matrix is highly permeable (equivalent to a homogeneous fluid layer). The impact of the anisotropic properties of the porous medium, stress jump coefficient, and viscosity ratio is more prominent on the dispersion coefficient in the convective zone. This model provides valuable insights into the solute transport process within blood arteries, where factors such as the variable viscosity of blood and the anisotropic properties of the endothelium glycocalyx play a crucial role in solute movement.