MODELING AND HOMOGENIZING A PROBLEM OF ABSORPTION/DESORPTION IN POROUS MEDIA
Andro Mikelić, Mario Primicerio · Mathematical Models and Methods in Applied Sciences · 2006
We consider a convection–diffusion problem in a porous medium saturated by a solution of a chemical substance A in water. A nonlinear non-equilibrium kinetics of absorption/desorption of A on the porous matrix is assumed. We assume that the chemical substance can be transported by ionic exchange through the walls of an array of parallel tubes in which the solution flows at a prescribed velocity. The well-posedness of the problem is proved under different boundary conditions. If the array of tubes is periodic, we homogenize the problem and prove that there exists a unique solution to the homogenized problem, in which the terms of interaction due to chemical exchange through the walls of the tubes are cast in the differential equation.