Environmental Engineering Reference
In-Depth Information
situation, only a fraction of collisions,
(collision effi ciency factor), are successful.
The collision effi ciency factor expresses the ratio of the number of collisions leading
to aggregation to the number of collisions due to Brownian motion according to
Equation 4.13 :
α
( )
( )
( )
( )
1
k
h
hR
β
Vh
kT
h
hR
β
Vh
kT
11
A
T
α
==
(
=
exp
dh
exp
dh
)
2
2
W
k
(
+
2
)
(
+
2
)
11
B
B
fast V
,
=
0
(4.13)
0
0
R
W is the stability ratio, which is defi ned as the ratio of the fast, diffusion limited
aggregation rate to the slow, reaction limited aggregation rate (Elimelech et al. ,
1995b ).
4.5.4
Non - DLVO Interactions
Recently, DLVO theory has been found unable to fully describe colloidal behaviour
in aquatic and terrestrial environments (Grasso et al. , 2002 ; Sander et al. , 2004 ). The
structure of water, adsorbed or dissolved entities (e.g. organic molecules) close
to the colloid surface in the water body may result in non-DLVO effects. Much
research has been conducted to understand these forces such as hydration, hydro-
phobic, steric and bridging interactions, and to extend DLVO theory to account for
them. Although understanding has improved signifi cantly, much environmental
research has ignored them (Grasso et al. , 2002). However, in many aggregation
studies, reversible aggregation cannot be fully interpreted by DLVO theory (van
der Waals and electrostatic forces) alone. Therefore, in such situations, some other
short range forces should be considered.
4.5.4.1
Hydration Effect
In aquatic systems most colloidal particle surfaces carry a surface charge and
surface functional groups, which are expected to be hydrated, analogously to ions
in solution. Therefore, aquatic colloids such as humic substances, clay particles and
metal oxides are generally expected to be surrounded by a layer of water. The
nature of this hydration layer can be different from that of the bulk water (Figure
4.7). This hydration layer plays an important role in the interactions of these col-
loids, and usually gives an extra repulsion to that induced by the double layer. For
true contact to occur between particles, surfaces need to become dehydrated, hence
a repulsion due to hydration occurs (Grasso et al. , 2002 ).
Direct evidence for the hydration repulsion comes from force measurements.
Atomic force microscopy (AFM) enables direct measurement of forces between a
planar surface and an individual colloid particle (Butt et al. , 1995 ; Cappella and
Dietler, 1999). Measurements using AFM tips or, more quantitatively, silica parti-
cles generally show good agreement with DLVO forces, although at short separa-
tion distances (2-3 nm) a deviation was observed (Figure 4.8) (Ducker et al. , 1991,
1992). At these distances the DLVO theory predicts that attractive van der Waals
force will exceed the repulsive double layer force, although the measured repulsive
force was greater than the predicted, which has been attributed to hydration forces.
This force is dependent on solution conditions. Hydration forces are more impor-
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