Modelling chemical depletion profiles in regolith

Chemical or mineralogical profiles in regolith display reaction fronts that document depletion of leachable elements or minerals. A generalized equation employing lumped parameters was derived to model such ubiquitously observed patterns:C = frac(C₀, frac(C₀ - C_{x = 0}, C_{x = 0}) exp (Γ_ini · over(k, ̂) · x) + 1)Here C, C_{x = 0}, and C_o are the concentrations of an element at a given depth x, at the top of the reaction front, or in parent respectively. Γ_ini is the roughness of the dissolving mineral in the parent and k̂̂ is a lumped kinetic parameter. This kinetic parameter is an inverse function of the porefluid advective velocity and a direct function of the dissolution rate constant times mineral surface area per unit volume regolith. This model equation fits profiles of concentration versus depth for albite in seven weathering systems and is consistent with the interpretation that the surface area (m² mineral m^{- 3} bulk regolith) varies linearly with the concentration of the dissolving mineral across the front. Dissolution rate constants can be calculated from the lumped fit parameters for these profiles using observed values of weathering advance rate, the proton driving force, the geometric surface area per unit volume regolith and parent concentration of albite. These calculated values of the dissolution rate constant compare favorably to literature values. The model equation, useful for reaction fronts in both steady-state erosional and quasi-stationary non-erosional systems, incorporates the variation of reaction affinity using pH as a master variable. Use of this model equation to fit depletion fronts for soils highlights the importance of buffering of pH in the soil system. Furthermore, the equation should allow better understanding of the effects of important environmental variables on weathering rates.