Dissipation Scale Fluctuations and Chemical Reaction Rates in Turbulent Flows

Small separation between reactants, not exceeding 10−8−10−7cm, is the necessary condition for various chemical reactions. It is shown that random advection and stretching by turbulence leads to formation of scalar-enriched sheets of strongly fluctuating thickness ηc. The molecular-level mixing is achieved by diffusion across these sheets (interfaces) separating the reactants. Since diffusion time scale is τd ∝ η c , the knowledge of probability density Q(ηc, Re) is crucial for evaluation of chemical reaction rates. In this paper we derive the probability density Q(ηc, Re, Sc) and predict a transition in the reaction rate behavior from R ∝ √ Re (Re ≤ 10) to the high-Re asymptotics R ∝ Re. The theory leads to an approximate universality of transitional Reynolds number Retr ≈ 10. It is also shown that if chemical reaction involves short-lived reactants, very strong anomalous fluctuations of the length-scale ηc may lead to non-negligibly small reaction rates.