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

A. M. Tartakovsky, P. De Anna, T. Le Borgne, A. Balter, D. Bolster

Research output: Contribution to journalArticle


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.

Original languageEnglish (US)
Article numberW02526
JournalWater Resources Research
Issue number2
StatePublished - 2012
Externally publishedYes

ASJC Scopus subject areas

  • Water Science and Technology

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