Interstitial transport of solutes in non-steady state accumulating and compacting sediments

A general one-dimensional equation for interstitial transport in accumulating and compacting sediments under non-steady state conditions is derived. As a consequence of compaction the metric along the path of a given horizon, i.e. the spatial distance between neighbouring particles, changes continually. Special emphasis is put on the treatment of advection caused by compaction. The resulting partial differential equation for the interstitial concentration of a given solute contains terms which can be evaluated based on data from a single sediment core. In addition, an integral over the time-derivative of porosity appears which would make it necessary to compare cores from the same site but at different times. Under quite general assumptions this last term may, however, be transformed into a form for which evaluation from a single core becomes possible. Several special solutions are treated such as total steady state, steady state at the surface, non-constant sedimentation rate with steady state compaction, and non-steady state with steady state compaction. The last case applies, e.g., to diffusion under the influence of changing boundary conditions at the water/sediment interface while the accumulation process remains in steady state.