Microscopic Study of the Properties of the Reaction Front in an A + B → C Reaction-Diffusion Process

A cellular automata model of the reaction-diffusion process A + B → C studied by Galfi and Racz is proposed. Numerical simulations on a two-dimensional system show that the reaction rate obeys a scaling form R(x,t) = t-β F(xt-α), in the long-time regime. The exponent α which characterizes the width of the reaction region is found to be 0.186 ± 0.005, in disagreement with the mean-field value of 1/6 obtained by Galfi and Racz. Moreover, the amplitude of the reaction rate of our automata model is also significantly different from its mean-field approximation. These discrepancies show the relevant role played by the microscopic fluctuations in this nonequilibrium phenomenon.