Homogenization Approach to the Dispersion Theory for Reactive Transport through Porous Media
Grégoire Allaire, Andro Mikelić, Andrey Lvovich Piatnitski · SIAM Journal on Mathematical Analysis · 2010
We study the homogenization problem for a convection-diffusion equation in a periodic porous medium in the presence of a chemical reaction on the pores' surface. Mathematically this model is described in terms of a solution to a system of convection-diffusion equations in the medium and ordinary differential equation defined on the pores' surface. These equations are coupled through the boundary condition for the convection-diffusion problem. Under an appropriate choice of scaling factors (large Péclet and Damköhler numbers), we obtain the homogenized problem in a moving frame whose effective velocity does actually depend on the chemical reaction.