Homogeneous-heterogeneous pore-scale reactive transport with fractional time derivative

This study presents a pore-scale model of a complex homogeneous-heterogeneous reaction. It is based on the Stokes equations, convection-diffusion-reaction equations, and Robin boundary conditions. The fluid is considered non-Newtonian, and the Carreau model of viscosity is employed. A heterogeneous reaction is defined by the Langmuir isotherm, whereas a homogeneous reaction is described by cubic autocatalysis over the entire pore space. The Crank-Nicholson scheme is used for time discretization. Newton’s iterative method is implemented to solve a non-linear problem for reactive mass transport and Picard iterations for non-Newtonian fluid flow. The problem is considered in a one-way coupling where fluid flow influences the species transport, but there is no backward influence of the species concentration on the fluid flow. The dimensionless form of equations was used throughout the entire numerical analysis. The influence of the fractional time derivative on the reacting processes is investigated.
This work was supported by the Russian Science Foundation (No. 23-71-30013).