Numerical solution of moving boundary problems in diffusion processes with attractive and repulsive interactions
Andrea Pietro Reverberi, Enrico Scalas, Francesco Vegliò · Journal of Physics A Mathematical and General · 2002
A moving boundary problem modelling a diffusion-limited reaction in the presence of a nonlinear diffusivity is studied in this paper. The equations are solved by means of a front-tracking method with proper regularizing techniques. Reliable results are obtained in the case of both attractive and repulsive interactions between the diffusing species. We investigate the effects of the two kinds of interaction and their relevant strength on the width of concentration profiles into the unreacted zone and the value of the unknown at the moving interface. The results are discussed in connection with Monte Carlo simulations of on-lattice models and with some experimental observations.