Boundary layer effects on the rate of diffusion-controlled reactions

Abstract : The description using the Smoluchowski equation, on which the traditional theory of diffusion-controlled reactions is based, presupposes local equilibrium. Hence it must break down in the vicinity of an absorbing wall, where a kinetic boundary layer is formed. We explore in this paper the effects of this boundary layer on the reaction rate. We start from a description using the Klein-Kramers equation and use two approximate treatments of the boundary layer that gave satisfactory results for the analogous one-dimensional problem. The simplest one leads to a simple analytic correction factor in the Smoluchowski-Debye reaction rate that becomes appreciable for particle radii not very large compared to a typical length, the velocity persistence length. The correction factor always decreases the reaction rate. For constant of piecewise constant potentials between the reacting particles we also work out a somewhat more elaborate approximation, based on Grad's thirteen-moment equations. It yields effects of the same order of magnitude as the simple theory; the differences between the two approximate treatments should give an indication of the errors still contained in each of them.
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Gerald Kneller, U.M. Titulaer. Boundary layer effects on the rate of diffusion-controlled reactions. Physica A: Statistical Mechanics and its Applications, Elsevier, 1985, 129 (3), pp.514-534. ⟨10.1016/0378-4371(85)90183-9⟩. ⟨hal-02156241⟩

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