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 $\mathcal{R}\propto \sqrt{Re}$ ($Re\le 10^4$) to the high-Re asymptotics $\mathcal{R}\propto R{e}^0$. The theory leads to an approximate universality of transitional Reynolds number $R{e}_{tr}\approx 10^4$. 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.

References in corpus (3)

• Asymptotic Exponents from Low-Reynolds-Number Flows
• Sub-Kolmogorov-Scale Fluctuations in Fluid Turbulence
• Geometry of intensive scalar dissipation events in turbulence

Cited by in corpus (2)

• Lagrangian views on turbulent mixing of passive scalars
• Quantum Carleman linearisation efficiency in nonlinear fluid dynamics