A stochastic approach to model bottom boundary conditions and compute efficiency in a settling tank

When the diffusion term is supposed not to be zero at the boundary of a settling tank, we show that an alternate (and equivalent) description to the basic advection-diffusion equation for the concentration of micro pollutant consists in modelling the micro pollutant particles' trajectories as a diffusion stochastic process. Indeed, the density of this latter satisfies the same Pde as the advectiondiffusion equation. Our emphasis here is on the computation of the so called tank efficiency and on the bottom boundary conditions. We claim that our interpretation in terms of a diffusion process helps to enlighten the choice of the appropriate mathematical boundary conditions. What is more, we introduce a scouring parameter and give its range as well as its physical interpretation.