Environmental Engineering Reference
In-Depth Information
As shown in Table 15.4, the importance of each collision mechanism varies as a
function of system properties. Small NPs (e.g., 1-100 nm) are removed mainly by
diffusion, which is reduced with an increase in Darcy velocity. Larger NPs (e.g., 1000
nm) are removed mainly by sedimentation, which is reduced with an increase in Darcy
velocity and a decrease in NPs' density. Interception would be important only when the
particle size of the porous media, d c is very small; the removal of NPs would increase
greatly as d c decrease (data not shown). Thus, the stability and the attachment efficiency
of NMs need to be incorporated into the fundamental clean-bed filtration models.
Table 15.4 Comparison of different collision mechanisms 3 .
Diameter (nm)
Hematite, density
Total r\
ID
= 5.3 g/cm 3 ,
0.737
0.159
0.0342
0.00736
= 5.3 g/cm 3 ,
0.106
00.0228
0.00491
0.00106
"Hi
Darcy velocity U =
1.22X10 4 1
1.22x10-'
1.22x10-'
1.22xlO- 5
Darcy velocity U =
1.22x10-"
1.22x10-'
1.22x10-'
1.22xlO- 5
Is
100 cm/d b
1.56x10-'
1.56xlO- 5
0.00156
0.156
1836 cm/d b
8.48x10-'
8.48x10-'
8.48xlQ- 5
0.00848
density 0 = 1.4 g/cm , Darcy velocity U = 100 cm/d
0.737
0.737
0.159
0.0357
0.163
Hematite, density
0.106
0.0228
0.00499
0.00955
Carbon nanotube,
0.737
0.159
0.0343
0.0219
Yao's model (Table 15.3) was used for calculation, with the following conditions: soil particle <^ =
0.035 cm; T = 283 K; the dynamic viscosity of water = 0.0103 g/cm-s; and water density = 0.9997 g/cm 3 .
b U = 100 cm/d (Logan, 1999); and U = 153 (cm/h)*0.5 (porosity)*24, which was used in column tests
reported by Kretzschmar and Sticher (1997). ° wikipedia (2008).
1.22x10-"
1.45x10-*
0.159
0.0342
0.00736
1.22x10-'
1.22x10-'
1.22xlO- 5
1.45x10-'
0.000145
0.0145
For the models listed in Table 15.3, several points need to be discussed. First, in
these models all the factors that affect particle transport are lumped into A, such as fluid
velocity, temperature, media, and particle size. However, the derivation of A involves
the construction of a mass balance and the prediction of the frequency of particle-
collector collisions (T|). The mass balance can be different because fluid flow around a
collector can be defined in different ways. In these models, analytical and empirical
correlations are used to predict individual collector efficiencies (T|D, T|I, and T|S). The RT
model includes attractive effects due to London-van der Waals forces and reduced
collisions due to viscous resistance of the water between the particles and collector (the
lubrication effect). The major shortcoming of the RT model, however, is the omission of
the influence of hydrodynamic and van der Waals interactions on the deposition of
particles that are dominated by Brownian diffusion. The latter removal mechanism may
be mainly valid for NPs, but can extend to particles as large as a few micrometers for
filtration at low Peclet numbers or flow rates (such as in subsurface environments), thus
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