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 \documentclass[12pt]{minimal}
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\begin{document}\end{document} is the rms diffusion distance after time t. At short times the number of reactions per unit area, \documentclass[12pt]{minimal}
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\begin{document}\end{document}, is 2nd order in the far-field reactant densities \documentclass[12pt]{minimal}
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\begin{document}\end{document}. For spatial dimensions dabove a critical value \documentclass[12pt]{minimal}
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\begin{document}\end{document}, simple mean field (MF) kinetics pertain, \documentclass[12pt]{minimal}
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\begin{document}\end{document} where Qb is the local reactivity. For low dimensions \documentclass[12pt]{minimal}
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\begin{document}\end{document}, this MF regime is followed by 2nd order diffusion controlled (DC) kinetics, \documentclass[12pt]{minimal}
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\begin{document}\end{document}, provided \documentclass[12pt]{minimal}
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\begin{document}\end{document}. Logarithmic corrections arise in marginal cases. At long times, a cross-over to 1st order DC kinetics occurs: \documentclass[12pt]{minimal}
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\begin{document}\end{document}. A density depletion hole grows on the more dilute A side. In the symmetric case (\documentclass[12pt]{minimal}
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\begin{document}\end{document}), when \documentclass[12pt]{minimal}
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\begin{document}\end{document} the long time decay of the interfacial reactant density, \documentclass[12pt]{minimal}
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\begin{document}\end{document}, is determined by fluctuations in the initial reactant distribution, giving \documentclass[12pt]{minimal}
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\begin{document}\end{document}. Correspondingly, A-rich and B-rich regions develop at the interface analogously to the segregation effects established by other authors for the bulk reaction \documentclass[12pt]{minimal}
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\begin{document}\end{document}. For \documentclass[12pt]{minimal}
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\begin{document}\end{document} fluctuations are unimportant: local mean field theory applies at the interface (joint density distribution approximating the product of A and B densities) and \documentclass[12pt]{minimal}
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\begin{document}\end{document}. We apply our results to simple molecules (Fickian diffusion, z=2) and to several models of short-time polymer diffusion (z>2).
