Analytical Studies of Diffusion by the Dissociative Mechanism in the Case of a Foreign Atom Source

The analytical treatment of dissociative diffusion by using the matched perturbation method given in the literature deals with a virtually infinite foreign-atom source producing a constant^concentration at the boundary. In this paper, a new mathematical model is developed for analysing the dissociative diffusion of the solute atoms in the case of finite-source conditions. The mathematical model combines the reaction-diffusion equations which govern solute atom diffusion by the dissociative mechanism and the boundary condition expressing the fact that the rate at which solute leaves the source is always equal to that at which it enters the sheet over the surface x=0. Solutions obtained by applying the matched perturbation method and their comparison with those of the numerical study are also presented in this paper.