Dissipation Scale Fluctuations and Chemical Reaction Rates in Turbulent Flows

Abstract

Small separation between reactants, not exceeding $10^{-8}-10^{-7}cm$, 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 {\it strongly fluctuating thickness} $\eta_{c}$. The molecular-level mixing is achieved by diffusion across these sheets (interfaces) separating the reactants. Since diffusion time scale is $\tau_{d}\propto \eta_{c}^{2}$, the knowledge of probability density $Q(\eta_{c},Re)$ is crucial for evaluation of chemical reaction rates. In this paper we derive the probability density $Q(\eta_{c},Re,Sc)$ and predict a transition in the reaction rate behavior from ${\cal R}\propto \sqrt{Re}$ ($Re\leq 10^{4}$) to the high-Re asymptotics ${\cal R}\propto Re^{0}$. The theory leads to an approximate universality of transitional Reynolds number $Re_{tr}\approx 10^{4}$. It is also shown that if chemical reaction involves short-lived reactants, very strong anomalous fluctuations of the length-scale $\eta_{c}$ may lead to non-negligibly small reaction rates.