NanoFASE - sedimentation-rate

Sedimentation rate \(k_{settle}\)determines the speed at which particles (whether nanoparticles or suspended particulate matter, SPM) are removed from the water through sedimentation (sediment deposition). The higher the rate, the faster particles are removed. Predicting the sedimentation rate is needed in order to predict movement of particles from the water column to the sediment layer. A key variable in determining the rate is the settling velocity \(w\) - the speed at which a particle falls through the water. A higher sedimentation rate requires either a higher settling velocity or a shorter sedimentation path-length, i.e. a shallower water column (see algorithm (i) below).

Irrespective of their density, nanoparticles (diameter below 100 nm) are expected not to settle/sediment, because the slow sedimentation movement is overwhelmed by the fast diffusion of the particles. Free nanoparticles are thought to move with the water (advective transport) and must aggregate or heteroaggregate to SPM to acquire a substantial sedimentation rate. Also, when the water flows in a turbulent manner, as in a river, the movement of particles is more influenced by the turbulent water flow than by the downward fall of sedimentation.

There are multiple approaches to calculate the settling velocity, which are applicable to both nanoparticles and SPM. The algorithm links below provide (ii) a general example of settling velocity calculation using Stokes’ law, valid for laminar (non-turbulent) flows, and (iii) a description of the settling velocity calculation for SPM in the NanoFASE water-soil-organism (WSO) model, more accurate for turbulent flows (and thus more applicable to natural rivers). Heteroaggregation of nanoparticles to SPM is a key process in their removal from waters, due to subsequent settling of the sediments. The NanoFASE WSO model does not simulate the settling of free nanoparticles, but models only the sedimentation of SPM to which nanoparticles may be attached.

	Used for
	Sedimentation

Algorithms

\(k_{settle}=\frac{w}{D}\)	(i) Calculation of settling rate from settling velocity \(w\) and river depth \(D\).
\(w=\frac{2(\rho _{\rho }-\rho _{f})gr^{2}}{9\mu }\)	(ii) A general example of calculating settling velocity using Stokes’ law, valid for laminar (non-turbulent) flows.
\(w_{\text{spm}} = \frac{\eta}{d} d_^3 \left( 38.1 + 0.93 d_^{12/7} \right)^{-7/8}\)	(iii) Settling velocity of SPM as calculated in the NanoFASE WSO model, more applicable for natural rivers with turbulent flows.