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Understanding the behaviour of particulate matter and chemicals at the sediment-water interface (SWI) is of interest in environmental studies and risk assessments. These processes are still poorly understood, and this work aims to gain relevant insights by using a kinetic reactive transport model. It merges early diagenetic processes and box models for the uptake kinetics. Numerical solutions have been found for synthetic scenarios and for studying real cases from the literature (210Pb and Chernobyl fallout radionuclides in Lake Sniardwy, Poland, and 7Be in sediments from Tema Harbour, Ghana). The study identifies a series of factors that dynamically interact to govern the final fate of tracers in the SWI region, leading to a wide diversity of behaviours. When a term of eddy diffusivity is included in the upper regions of the pore fluid, which seems feasible for some energetic scenarios, it is possible to explain the observed large penetration depths for Cs and Be, while high particle-reactive elements are retained in thinner sediment layers. Desorption from the sediment occurs through the pore fluid as diffusive fluxes. Transient depth profiles of tracer concentrations can last from months up to a year, and they can show subsurface maxima at positions unrelated with the accretion rate. In the application cases, the model explained a wide set of observational data that was beyond the capabilities of other approaches involving physical mixing of solids and equilibrium k d. This modelling study could provide useful guidance for future research works. • A kinetic reactive transport model of pollutants in surficial sediments is coded. • Applications to atmospheric fallout radiotracers in lake and harbour sediments. • Eddy diffusivity in the pore fluid explains desorption and large penetration depths. • Transient inventories and profiles appear over time scales of months up to a year. • Tracer-specific kinetics explains differential behaviour of 7Be, 137Cs and 210Pb. [ABSTRACT FROM AUTHOR]