Reversible A <-> B reaction - diffusion process with initially mixed   reactants: boundary layer function approach
  The reversible A <-> B reaction-diffusion process, when species A and B are initially mixed and diffuse with different diffusion coefficients, is investigated using the boundary layer function method. It is assumed that the ratio of the characteristic time of the reaction to the characteristic time of diffusion is taken as a small parameter of the task. It was shown that diffusion-reaction process can be considered as a quasi-equilibrium process. Despite this fact the contribution of the reaction in changes of the species concentration is comparable with the diffusion contributions. Moreover the ratios of the reaction and diffusion contributions are independent of time and coordinate. The dependence of the reaction rate on the initial species distribution is analyzed. It was firstly obtained that the number of the reaction zones is determined by the initial conditions and changes with time. The asymptotic long-time behaviour of the reaction rate also dependents on the initial distribution. 
M. Sinder, V. Sokolovsky, J. Pelleg