Environmental Engineering Reference
In-Depth Information
because a large variety of NMs and complicated application methods exist under
different environmental conditions.
\. .An tue try hnmec
s
"Weil:" flot dilation
" Ti i • eversi hi e" fine c i ihit inn
o°o°o
°o°
W
Figure 15.5
The variation of OT with interparticle separation distance (S). The OT vs. S
curve shows two minima and one maximum: a shallow minimum at large S being
referred to as the secondary minimum, OTSCO a deep minimum, OTpnmaiy; and an energy
maximum at intermediate distances, OTmax (often referred to as the energy barrier).
15.5.1.3 NP Aggregation Kinetics
The stability of a NP system can be characterized by the stability ratio, W:
W= k
llifast
/k
ixslo
w
(Eq. 15.82)
where kn^t
=
8ksT/6|i = the rate constant of fast flocculation (i.e., DLA shown in Fig.
15.5 in the absence of an energy barrier, |i = the viscosity of the medium); and kn
jS
i
o
w
=
2exp (-OTmax /ksT) = the rate constant of slow flocculation (in the presence of an energy
barrier, O
Tm
ax) (Tadros, 2007). W can also be predicted with the DLVO theory
(McGown and Parfitt, 1967):
w
=
(2a+h)
2
(Eq. 15.83)
where h = the surface-to-surface separation distance between two NPs; and (3(h) = the
dimensionless function (Hoing et al., 1971):
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