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Effective rates in dilute reaction-advection systems

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A dilute system of reacting particles transported by fluid flows is considered. The particles react as A+A -> O with a given rate when they are within a finite radius of interaction. The system is described in terms of the joint n-point number spatial density that obeys a hierarchy of transport equations. An analytic solution is obtained in either the dilute or the long-time limit by using a Lagrangian approach where statistical averages are performed along non-reacting trajectories. In this limit, it is shown that the moments of the number of particles have an exponential decay rather than the algebraic prediction of standard mean-field approaches. The effective reaction rate is then related to Lagrangian pair statistics by a large-deviation principle. Numerical simulations in a smooth, compressible, random delta-correlated-in-time Gaussian velocity field support the theoretical results.

Author(s):

Giorgio Krstulovic    
Laboratoire Lagrange, Observatoire de la Côte d'Azur
France