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Sessile drop experiments on metal/ceramic systems have shown that an important improvement in wetting may be produced by introduction of alloying elements which form, by reaction at the metal/ceramic interface, a continuous layer of solid that is better wetted by the metal than the original substrate. We present results from a finite-difference analysis of the kinetics of reactive wetting under conditions where the rate of spreading is controlled by the rate of diffusion of the reactive solute element.