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

AM Tartakovsky, P de Anna… - Water Resources …, 2012 - Wiley Online Library
Water Resources Research, 2012Wiley Online Library
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 Adet=
Bdet∼ t− 1. Contrary to this, experimental and numerical studies suggest that concentrations
decay significantly slower. Existing theory suggests at− 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 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 Adet = Bdett−1. Contrary to this, experimental and numerical studies suggest that concentrations decay significantly slower. Existing theory suggests a td/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 ∼td/4 behavior at characteristic transition time t*. We also derive analytical expressions for t* as a function of Damköhler number and the coefficient of variation of the initial concentration.
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