Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2007-06-29
Nonlinear Sciences
Chaotic Dynamics
Scientific paper
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.
No associations
LandOfFree
Dissipation Scale Fluctuations and Chemical Reaction Rates in Turbulent Flows does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Dissipation Scale Fluctuations and Chemical Reaction Rates in Turbulent Flows, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dissipation Scale Fluctuations and Chemical Reaction Rates in Turbulent Flows will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-682265