Natural Colloids and Nanoparticles in Aquatic and Terrestrial Environments - Environmental and Human Health Impacts of Nanotechnology - page 144

1000

1: d col. = 10 mm, vf = 10 m/d, density = 1 g/cm?
2: d col. = 10 mm, vf = 1 m/d, density = 1 g/cm?
3: d col. = 10 mm, vf = 1 m/d, density = 3 g/cm?
4: d col. = 1 mm, vf = 1 m/d, density = 3 g/cm?

100

10

1

2

1

3

4

0,1

0,001 0,01 0,1 1 10

colloid size [ m m]

Figure 4.19 Effect of colloid density, fl ow velocity and collector grain diameter on fi ltration/
deposition effi ciencies calculated by Equations 4.14 to 4.21. d coll = grain size diameter of the
collector, v f = apparent fl ow velocity of the fl uid within the porous media.

Once the colloid is attached to the surface of the collector it can be remobilized
by hydrodynamic drag or lift forces. These two forces are balanced by an
adhesive force, which can be quantifi ed in terms of free energy of adhesion
using an extended DLVO type approach (Section 4.5). The fl uid drag and lift forces
on a retained colloid can be calculated as summarized by Ryan and Elimelech
(1996). For small colloids the lift force, that is the force due to different pressure
acting on the top and bottom of the particle, can be neglected. The adhesive force
can be calculated using different scaling models, such as the Johnson- Kendall -
Roberts model or the Derjaguin- Mullen -Toporov model (Derjaguin et al. , 1975 ;
Johnson et al. , 1971; Kendall, 2001). Drag forces are typically signifi cant only for
particles larger than a few hundred nanometers and when deposition occurs in the
primary minimum (according to DLVO theory, Section 4.5). However, for deposi-
tion of nanoparticles 100 nm in the secondary minimum, hydrodynamic drag

forces play a larger role due to weaker thermodynamic interactions (Hahn and
O' Melia, 2004 ).

<

4.7.2 Unsaturated Porous Media

In unsaturated porous media, in addition to the mechanism mentioned in Section
4.7.1 , liquid -gas and liquid- solid -gas interfaces have to be taken into account.
Colloids can also attach to these interfaces (Chen and Flury, 2005). Colloids in
unsaturated media also are subject to straining in thin fl uid fi lms when fl uid satura-
tion becomes small (i.e. drying of the soil). This effect is called fi lm straining and
was described fi rst by (Wan and Tokunaga, 1997; Wan and Wilson, 1994). There, the