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Nanoparticle Transport, Aggregation, and Deposition 259

is the single collector contact efficiency for transport by gravity. Eq. 18
G
is based on the additivity assumption where is determined by summa-
0
tion of the three independently determined transport mechanisms.
It is instructive to look at the components of plotted as a func-
0
tion of particle size (Figure 7.16). For particles in the micron size
range, transport to a collector surface is largely governed by inter-
ception and gravitational settling mechanisms. However, nanoparti-
cle transport to a collector will typically be dominated by diffusion
[10]. It is evident that as particle size approaches that of the nanoscale
(d 100 nm) the interception and gravity terms begin to approach
zero. On the other hand, once particle size is smaller than approxi-
mately 300 nm, the particle contact efficiency is largely controlled by
. The diffusion component is a function of the porosity of the
D
D
transporting medium, the aspect ratio between the collector and
particle sizes, the particle approach velocity to the collector surface,
and the Hamaker constant for the interacting surfaces. With the high
diffusion component for nanoparticles their mobility may be espe-
cially low in porous media characterized by low flow rates or Peclet
numbers, such as groundwater aquifers.
We obtain a similar picture of particle mobility when the efficiency of
single collectors is integrated across a length of the porous medium that

0.10 0.014
Diffusion
0.012
Interception
0.08
Gravity 0.010

0.06
0.008
η D η
0.006
0.04
0.004
0.02
0.002

0.00 0.000
0.01 0.1 1 10
dp (µm)
Figure 7.16 Respective contributions to the total single collector contact efficiency from
each of three transport mechanisms: diffusion ( D ), interception ( I ), and gravitational
settling ( G ). The magnitude of each mechanism is plotted as a function of particle size
while holding other particle characteristics constant.