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 ∼ 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 ∼t -1 to ∼t -d/4 behavior at characteristic transition time t. We also derive analytical expressions for t* as a function of Damkhler number and the coefficient of variation of the initial concentration.
ASJC Scopus subject areas
- Water Science and Technology