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

TL;DR

This paper investigates how bulk-mediated excursions influence long-term behavior in catalytic reactions, revealing that mixing fails to restore equilibrium under steady inflow conditions due to superdiffusive transport effects.

Contribution

It demonstrates that bulk-mediated excursions do not restore chemical equilibrium in steady inflow reactions, contrasting with their mixing effect in batch reactions, and characterizes the relaxation dynamics.

Findings

Bulk-mediated excursions lead to superdiffusive transport along the catalytic plane.

Steady inflow reactions do not reach mean-field equilibrium due to insufficient mixing.

Relaxation to steady-state follows a power-law decay, not exponential.

Abstract

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 \to 0 reactions in systems in which a catalytic plane (CP) is in contact with liquid phase, containg 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 intial detachment point. This process which 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 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 \to \infty, in which the limiting value of the mean coverages of the CP depends on the particles' diffusion coefficient in the bulk liquid phase and the spatial distributions of adsorbed particles are strongly correlated. Moreover, we show that the relaxation to such a steady-state is described by a power-law function of time, in contrast to the exponential time-dependence describing the approach to equilibrium in perfectly stirred systems.