Soil advective transport calculation
Transport of nanoparticles in soils is usually described using a onedimensional convectiondispersion equation. This equation equates the change in concentration at a certain depth to: (i) percolation, i.e. downward flow of nanoparticles due to flowing water; (ii) the dissipating effects of diffusion and dispersion; and (iii) loss of nanoparticles to soil surfaces because of attachment and straining. The sum of these processes is used within NanoFASE to model breakthrough curves obtained during the saturated soil column procedure, mainly to obtain the attachment efficiency. That fate descriptor is then used in the NanoFASE soil model.
\(\Psi = (\frac{d_{50}+z}{d_{50}})^{\beta }\)  1. Straining calculation 
\(k_{att}=\alpha \frac{3(1\theta )v}{2d_{c}}\eta _{0}\) 
2. Calculation of the attachment rate coefficient for the whole soil profile using the soil  nanoparticle specific attachment efficiency. 
\(\theta \frac{dC}{dt}=v\theta \frac{dC}{dz}\theta (\Sigma D)\frac{d^{2}C}{(dz)^{2}}\Psi k_{straining}k_{att}\)  3. Solving the convection dispersion equation numerically. 

Execution 
Procedure 
Straining (step 1) is not always included in the convection dispersion equation shown in step 3, which affects the value of the attachment efficiency one obtains via step 2. The equation of step 3 is not solved analytically, even when applying it to breakthrough curves of the saturated column test. 
Read more 
Read also 
Consult the NanoFASE Library to see abstracts of these deliverable reports: NanoFASE Report D7.2 Soil property  NM fate relationships NanoFASE Report D7.4 Module for NM exposure prediction in soils to couple to overall framework 
Cornelis, G.; Pang, L.; Doolette, C.; Kirby, J.K.; McLaughlin, M.J., 2013. Transport of silver nanoparticles in saturated columns of natural soils. Sci. Tot. Environ. 463464. 120130. 
Contact
Geert Cornelis
Swedish University of Agricultural Sciences (SLU)
Email: geert.cornelis@slu.se