Heterogeneous kinetics and diffusion boundary layers: The example of reaction in a fracture

Abstract

At steady state both surface‐ and transport‐controlled reaction rates can be expressed in a single form which resembles a first‐order rate law. This rate law includes a dimensionless parameter analogous to the Biot number of heat transfer, and the Damköhler number of combustion physics. This parameter is useful for predicting the rate‐controlling step reaction for overall mineral dissolution or growth. For cases in which this parameter is much larger than 1, the reaction rate is controlled by solute transport through a boundary layer. When the parameter is much less than 1, the reaction rate is surface controlled. Because the activation energies for surface‐controlled reactions are generally much larger than those of diffusion, one anticipates that reaction mechanisms may vary from surface to transport control with increased temperature. As an illustration, this parameter is used to predict the rate‐controlling step reaction for quartz, calcite, and brucite dissolution as a function of temperature.