# Straining calculation

Straining, the physical  filtration of particles in soils, is modelled similarly to attachment as an irreversible, first-order loss. There is thus a straining rate coefficient, but contrary to the case of attachment, this coefficient decreases as a function of depth. The idea is that particles will be less frequently found in dead-end pores if it is the case that overall, particles are being transported to deeper and deeper layers in the soil.

 $$k_{straining}=\Psi k$$where$$\Psi = (\frac{d_{50 + z}}{d_{50}})^{-\beta }$$ $$k_{straining}$$ is the straining rate constant and $$\Psi$$ is the depth-dependent straining rate coefficient. $$k$$ expresses the pseudo-first order rate of the interaction itself. This coefficient depends on the distance $$z$$ from the origin/injection point of the nanomaterials in the porous medium and also on the average aggregate (collector) diameter $$d_{50}$$. $$\beta$$ is  an empirical factor expressing the intensity of this depth dependence.

## Execution

 Straining is usually assumed to occur at the same time as other processes such as attachment. There is thus an assumption of a "second type of interaction site" where straining occurs. The straining rate constant itself, however, is a calibration constant fitted to column outflow experiments. Moreover, b is assumed equal to 0.43.

## Used in

 $$\theta \frac{dC}{dt}=v\theta \frac{dC}{dz}$$ $$-\theta (\sum D )\frac{d^{2}C}{(dz)^{2}}$$ $$-\Psi k_{straining} - k_{att}$$ Soil transport calculation Straining

 Consult the NanoFASE Library to see abstracts of these deliverable reports: Bradford, S.A., et al., Modeling Colloid Attachment, Straining, and Exclusion in Saturated Porous Media. Environmental Science & Technology, 2003. 37(10): p. 2242-2250

## Contact Geert Cornelis

Email: geert.cornelis@slu.se