HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

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

Abstract : 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.
Document type :
Journal articles
Complete list of metadata

Cited literature [35 references]  Display  Hide  Download

Contributor : Isabelle Dubigeon Connect in order to contact the contributor
Submitted on : Tuesday, March 5, 2013 - 1:39:53 PM
Last modification on : Wednesday, May 11, 2022 - 4:29:39 AM
Long-term archiving on: : Thursday, June 6, 2013 - 3:58:12 AM


Publisher files allowed on an open archive



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, American Geophysical Union, 2012, 48 (2), pp.W02526. ⟨10.1029/2011WR010720⟩. ⟨insu-00796966⟩



Record views


Files downloads