Diffusion and kinetic control of weathering layer development

The formation of porous weathering rinds (layers of chemical alteration) on the exterior of rocks is a consequence of dissolution and precipitation of minerals occurring at the mineral-fluid interface within the pores. The speed at which the developed rind advances is controlled by both kinetic reaction rates and the transport of reaction products away from the pore spaces into the outside fluid. We show, using both reaction-diffusion theory and numerics, that under diffusion limitations, the weathering rate depends on the size and curvature of the sample. This leads to a relationship between rind thickness, delta, and age, t. As the rind thickens, the result in three dimensions differs substantially from the one-dimensional result of delta similar to root t. We describe the conditions under which the one-dimensional and diffusion-limited approximations apply and how they evolve as the rock weathers. Under chemical kinetic limitations, the rind advances at a constant rate, d/dt=v. We defend the application of a spherical approximation to irregular non-spherical rocks and apply our results to field observations reported in the literature to show consistency with established methods. Finally, we argue that the variability in size, as well as in mineralogy, over ensembles of grains contributes to heterogeneous weathering rates. We demonstrate that this heterogeneity can contribute to the aging, or gradual decrease with time, of weathering rates previously observed in laboratory and field measurements.