Dissipation-scale fluctuations and mixing transition in turbulent flows

A 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 the formation of scalar-enriched sheets of strongly fluctuating thickness eta(c). The molecular-level mixing is achieved by diffusion across these sheets (interfaces) separating the reactigants. Since the diffusion time scale is tau(d) proportional to eta(2)(c), knowledge of the probability density Q(eta(c), Re) is crucial for evaluation of mixing times and chemical reaction rates. According to Kolmogorov-Batchelor phenomenology, the stretching time tau(eddy) approximate to L/u(rms) = O(1) is independent of large-scale Reynolds number Re = u(rms) L/v and the diffusion time tau(d) approximate to tau(eddy)/ root Re << tau(eddy) is very small. Therefore, in previous studies, molecular diffusion was frequently neglected as being too fast to contribute substantially to the reaction rates. In this paper, taking into account strong intermittent fluctuations of the scalar dissipation scales, this conclusion is re-examined. We derive the probability density Q(eta(c), Re, Sc), calculate the mean scalar dissipation scale and predict transition in the reaction rate behaviour from R proportional to root Re (Re <= 10(3) - 10(4)) to the high-Re asymptotics R proportional to Re-0. These conclusions are compared with known experimental and numerical data.