The effect of initial spatial correlations on late time kinetics of bimolecular irreversible reactions

Amir Paster, Diogo Bolster*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


We study anomalous kinetics associated with incomplete mixing for a bimolecular irreversible kinetic reaction where the underlying transport of reactants is governed by a fractional dispersion equation. As has been previously shown, we demonstrate that at late times incomplete mixing effects dominate and the decay of reactants follows a fundamentally different scaling comparing to the idealized well mixed case. We do so in a fully analytical manner using moment equations. In particular the novel aspect of this work is that we focus on the role that the initial correlation structure of the distribution of reactants plays on the late time scalings. We focus on short range and long (power law) range correlations and demonstrate how long range correlations can give rise to different late time scalings than one would expect purely from the underlying transport model. For the short range correlations the late time scalings deviate from the well mixed t-1 and scale like t-12α, where 1<α≤2 is the fractional dispersion exponent, in agreement with previous studies. For the long range correlation case it scales like t-β2α, where 0<β<1 is the power law correlation exponent.

Original languageEnglish
Pages (from-to)4654-4660
Number of pages7
JournalPhysica A: Statistical Mechanics and its Applications
Issue number20
StatePublished - 15 Oct 2012
Externally publishedYes


FundersFunder number
National Science FoundationEAR-1113704


    • Fractional dispersion
    • Incomplete mixing
    • Long range correlations
    • Reactions


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