  This paper studies an infinitely fast bimolecular chemical reaction in a
two-dimensional bi-periodic Navier-Stokes flow. The reactants in stoichiometric
quantities are initially segregated by infinite gradients. The focus is placed
on the initial stage of the reaction characterized by a well-defined one
dimensional material contact line between the reactants. Particular attention
is given to the effect of the diffusion of the reactants. This study is an
idealized framework for isentropic mixing in the lower stratosphere and is
motivated by the need to better understand the effect of resolutionon
stratospheric chemistry in Climate-Chemistry Models.
  Adopting a Lagrangian stretching theory approach, we relate theoretically the
ensemble mean of the length of the contact line, of the gradients along it and
of the modulus of the rate of decrease of the space averaged reactant
concentrations (here called the chemical speed) to the joint statistics of the
finite time Lyapunov exponent with two equivalent times. The inverse of the
Lyapunov exponent measures the stretching time scale of a Lagrangian parcel on
a chaotic orbit up to a finite time t, while the first equivalent time measures
it in the recent past before t and the second equivalent time in the early part
of the trajectory. We show that the chemical speed scales like the square root
of the diffusion and that its time evolution is determined by rare large events
in the finite time Lyapunov exponent distribution. The case of smooth initial
gradients is also discussed. The theoretical results are tested with an
ensemble of direct numerical simulations (DNS) using a pseudospectral model.

Chaotic Dynamics;Atmospheric and Oceanic Physics;Fluid Dynamics