Catalytic reactions with bulk-mediated excursions: mixing fails to restore chemical equilibrium

In this paper we analyze the effect of the bulk-mediated excursions (BME) of reactive species on the long-time behavior of the catalytic Langmuir-Hinshelwood-like A+B-->0 reactions in systems in which a catalytic plane (CP) is in contact with a liquid phase, containing concentrations of reactive particles. Such BME result from repeated particles desorption from the CP, subsequent diffusion in the liquid phase, and eventual readsorption on the CP away from the initial detachment point. This process leads to an effective superdiffusive transport along the CP. We consider both "batch" reactions, in which all particles of reactive species were initially adsorbed onto the CP, and reactions followed by a steady inflow of particles onto the CP. We show that for batch reactions the BME provide an effective mixing channel and here the mean-field-type behavior emerges. On the contrary, for reaction followed by a steady inflow of particles, we observe essential departures from the mean-field behavior and find that the mixing effect of the BME is insufficient to restore chemical equilibrium. We show that a steady state is established as t--> infinity, in which the limiting value of the mean coverage of the CP depends on the particles' diffusion coefficient in the bulk liquid phase, and that the spatial distributions of adsorbed particles are strongly correlated. Moreover, we show that the relaxation to such a steady state is a power-law function of time, in contrast to the exponential time dependence describing the approach to equilibrium in perfectly stirred systems.