Diffusion-controlled first-order surface reaction in turbulent flow

The effect of advective diffusion on the rate of reactant consumption by a first-order surface reaction is analyzed in the fast-reaction limit. The decay of reactant concentration is described by the function n(t) ∼ exp(-λt). In the limit of well-developed turbulence, the scaling estimates λ ∼ L-1κ3/4μ1/4 and λ ∼ fκ3/4μ1/4 are obtained, respectively, for a confined flow with characteristic length scale L and in the case when the reactants are contained near the surface by an external field with potential U/T = fx, where κ is molecular diffusivity and μ is the constant parameter in the eddy diffusivity Dadv = μx4 (x is distance to the wall). The coefficients in the scaling laws are evaluated by a variational method and by numerical solution of the governing equations