Processes in which a chemical species diffused into a thin homogeneous film that contained fixed sites at which the species could reversibly bind were considered. A situation was addressed in which interaction between the diffusing species and sites was described by the Langmuir isotherm. The differential equations that described this non-linear diffusion reaction problem were studied. It was found that the problem could be divided into 6 cases. Approximate analytical solutions for the concentration profiles in each case were given as a function of time for both adsorption and desorption.

P.N.Bartlett, J.W.Gardner: Philosophical Transactions of the Royal Society A, 1996, 354, 35-57