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

Alexandre Tartakovsky (1) , Pietro de Anna (2) , Tanguy Le Borgne (3) , A. Balter (1) , Diogo Bolster (4)

1 PNNL - Pacific Northwest National Laboratory
2 Transferts d'eau et de matière dans les milieux hétérogènes complexes
3 GR - Géosciences Rennes
4 CEEES - Department of Civil and Environmental Engineering and Earth Science [Notre Dame]

The effect of spatial concentration fluctuations on the reaction of two solutes, A þ B* C, is considered. In the absence of fluctuations, the concentration of solutes decays as Adet ¼ Bdet 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 Damköhler number and the coefficient of variation of the initial concentration.

Domains: Earth Sciences

Alexandre Tartakovsky, Pietro de Anna, Tanguy Le Borgne, A. Balter, Diogo Bolster. Effect of spatial concentration fluctuations on effective kinetics in diffusion-reaction systems. Water Resources Research, 2012, 48 (2), pp.W02526. ⟨10.1029/2011WR010720⟩. ⟨insu-00796966⟩