REACTIVE TRANSPORT THROUGH AN ARRAY OF CELLS WITH SEMI-PERMEABLE MEMBRANES

A problem of diffusion, convection, and nonlinear chemical reactions i n a periodic array of cells is studied. It is assumed that in the cell s there are porous bodies which are surrounded by semi-permeable membr anes, i.e., fluxes and concentrations are coupled nonlinearly at the i nterfaces between the cells and the surrounding fluid. We consider the limit when the number of cells tends to infinity and at the same time their size tends to zero while the volume fraction of the cells remai ns fixed. In the limit we get a nonlinearly coupled problem with two s cales, a global and a local one. We prove well-posedness of the micro- problems, uniqueness of the macro-problem, and convergence of the homo genization process. In order to determine the form of the limit equati ons we use the newly developed technique of two-scale convergence. Oth er methods being used are the theory of semilinear parabolic systems, maximum principles, compactness, monotonicity, and the energy method.