PrintAs the rainfall contacts the rock, cations and anions are released from the rock. The processes change properties of both solid and aqueous phases. However, the solid rock is dense in terms of amount of chemical mass compared to the aqueous phase so that the solid phase properties change at rates that are orders of magnitude slower than the aqueous phase. The system therefore often reaches steady state where the concentrations of species relatively constant over time.
The relative magnitude of advection, diffusion/dispersion and mineral dissolution are often compared using dimensionless numbers. The dimensionless numbers are quantitative measures of the relative magnitude of the characteristic time scales of different processes. In this case we have three characteristic time scales: the residence time related to advection $\tau\ \text{advection}=\frac{l}{v}$, the time for diffusion/dispersion $\tau\ \text {diffusion/dispersion}=\frac{l^{2}}{D_{h}}$, and the reaction time to reach equilibrium $\tau\ \text {reaction }=\frac{C_{e q}}{k A}$. Here we introduce two dimensionless numbers comparing the different time scales: DaI (Damköhler number for advection), DaII (Damköhler number for dispersion):
where l is the characteristics length of a domain (m), k is the rate constant (moles m−2 s−1), A is the reactive surface area (m2m−3), Dh is the diffusion coefficient in porous media (m2 s−1), and Ceq is the mineral solubility (moles m−3). When Damköhler number >>1, reaction times are much faster than transport times so that the system is transport controlled. The relative importance of advective versus dispersive transport is compared by the Péclet number that we have introduced before.
when Pe>>1, advective transport dominates and dispersive and diffusive transport are negligible.