Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 75 / 3 / a / Solution

Vertical turbulence carries particles upward as well as downward. Its mixing time $h/u^{\prime }$ should be short relative to the settling time $h/V_s$; hence $u^{\prime }\gg V_s$ is a useful well-mixed criterion, subject also to the eddy correlation time and particle response time. A more resolved description balances turbulent diffusion against downward settling velocity. A nearly uniform interior concentration does not eliminate the downward drift.

At an absorbing bed, particles crossing the boundary settle and do not return unless sediment resuspension is separately supplied. With well-mixed concentration $\varphi$, the particle volume deposition flux is $V_s\varphi$ per unit horizontal area. Thus stirring can preserve an almost uniform suspension while its total particle content decreases. The present model neglects sediment resuspension and any significant change of bulk fluid volume due to the dilute particles.