The kinetics of release of dissolved silicon from compacted sediments under close to natural conditions were studied on the basis of a semi-infinite diffusion model taking into account the dissolution of the support. A general theoretical framework suitable for the description and modelling of such processes was developed.
The basic equation describing release of silicon from sediments is

where D is the diffusion coefficient of dissolved silicon in the pore water, k is the dissolution rate constant, c_in is the initial concentration of silicon in the pores measured at the beginning of the experiment, γ(t) is the concentration of silicon in the overlying solution recorded in the course of the experiment, and c_s is its saturation concentration at the pH of the experiment. The x-axis is normal to the sediment/solution interface and directed to the sediment. The general solution to the above equation can be represented in the form

G being the Green function. To determine γ(t), the mass balance requirement should be imposed,

where l is the depth of the overlying solution and p is the porosity of the sediment. By combining eqn.(2) and (3), the desired time-dependence of silicon concentration is obtained,

where L -1 denotes the inverse Laplace transform. Based on the above equations, the dynamics of the concentration profile of dissolved silicon in the sediment phase was calculated (see Figure to the right), and by adjusting the model parameters to an extensive set of experimental data on concentration profiles measured in natural sediments and in a fluvarium channel-bed, the diffusion coefficient and generation rate constant of dissolved silicon were determined.