Attachment rate calculation
Calculating attachment rates relies on the convectiondespersion equation used in NanoFASE transport modelling. The attachment rate is calculated for the case of favorable attachment, i.e. attachment only by diffusion or advection of the ENMs, using the singlecollector contact efficiency (\(\small \eta_{0}\)). The attachment efficiency is calculated from the attachment rate constant or vice versa. However, the attachment efficiency also takes into account the nonfavorable case, where coatings or electrostatic repulsion lower the rates relative to the favorable case.
1. \(\eta_{0}\) 
1. Calculation of singlecollector contact efficiency according to Tufenkji and Elimelech (2004). 
2. \(\alpha\) 
2. Determine the attachment efficiency using a batch test or column test.

3. \(k_{att}=\alpha \frac{3(1\Theta )v}{2d_{c}}\eta_{0}\) 
3. Calculation of the firstorder attachment rate constant.

4. \(\)\(\Theta \frac{dC}{dt}=v\Theta \frac{dC}{dz}+D\Theta \frac{d^{2}C}{dz^2}k_{att}C\) 
4. Calculation of transport using the convectiondispersion equation.

Execution 
Used in 
\(\small \eta_{0}\) calculation requires knowledge of the effective porosity (\(\Theta\)) and average collector size (\(d_{c}\)). Both can be calculated using pedotransfer functions. The pore velocity is calculated from the rainfall intensity divided by the porosity. The convectiondispersion equation also requires the dispersivity. 
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Tufenkji N, et al. (2004) Transport of Cryptosporidium oocysts in porous media: Role of straining and physicochemical filtration. Environmental Science & Technology. 20:1081810828. http://doi.org/10.1021/es049789u Elimelech M, et al. (1995) Particle Deposition and Aggregation: Measurement, Modeling and Simulation. Oxford: ButterworthHeinemann. 
Contact
Karin Norrfors
Swedish University of Agricultural Sciences (SLU)
Geert Cornelis
Swedish University of Agricultural Sciences (SLU)
Email: geert.cornelis@slu.se