Effect of spatial concentration fluctuations on effective kinetics in diffusion-reaction systems

The effect of spatial concentration fluctuations on the reaction of two solutes, A + B -> C, is considered. In the absence of fluctuations, the concentration of solutes decays as A(det) = B-det similar to t(-1). Contrary to this, experimental and numerical studies suggest that concentrations decay significantly slower. Existing theory suggests a t(-d/4) scaling in the asymptotic regime (d is the dimensionality of the problem). Here we study the effect of fluctuations using the classical diffusion-reaction equation with random initial conditions. Initial concentrations of the reactants are treated as correlated random fields. We use the method of moment equations to solve the resulting stochastic diffusion-reaction equation and obtain a solution for the average concentrations that deviates from similar to t(-1) to similar to t(-d/4) behavior at characteristic transition time t*. We also derive analytical expressions for t* as a function of Damkohler number and the coefficient of variation of the initial concentration.