Interfacial reaction kinetics

Abstract:

We study irreversible A-B reaction kinetics at a fixed interface separating two immiscible bulk phases, A and B. Coupled equations are derived for the hierarchy of many-body correlation functions. Postulating physically motivated bounds, closed equations result without the need for ad hoc decoupling approximations. We consider general dynamical exponent z, where is the rms diffusion distance after time t. At short times the number of reactions per unit area, , is 2nd order in the far-field reactant densities . For spatial dimensions dabove a critical value , simple mean field (MF) kinetics pertain, where Q_b is the local reactivity. For low dimensions , this MF regime is followed by 2nd order diffusion controlled (DC) kinetics, , provided . Logarithmic corrections arise in marginal cases. At long times, a cross-over to 1st order DC kinetics occurs: . A density depletion hole grows on the more dilute A side. In the symmetric case (), when the long time decay of the interfacial reactant density, , is determined by fluctuations in the initial reactant distribution, giving . Correspondingly, A-rich and B-rich regions develop at the interface analogously to the segregation effects established by other authors for the bulk reaction . For fluctuations are unimportant: local mean field theory applies at the interface (joint density distribution approximating the product of A and B densities) and . We apply our results to simple molecules (Fickian diffusion, z=2) and to several models of short-time polymer diffusion (z>2).