Dissipation Scale Fluctuations and Chemical Reaction Rates in Turbulent Flows

TL;DR

This paper develops a probabilistic model for scalar sheet thickness in turbulent flows, predicting how reaction rates transition with Reynolds number and highlighting the impact of fluctuations on chemical reactions.

Contribution

It derives the probability density for scalar sheet thickness in turbulence and predicts a transition in reaction rate behavior at a critical Reynolds number.

Findings

Reaction rate scales as rom or low Re to Re^0 at high Re

Universal transition Reynolds number around 10^4

Strong fluctuations can significantly reduce reaction rates

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.