Environmental Engineering Reference
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7 with NaHCOs and containing either 1.0 mM CaCi2 or water alone with a ZetaPlus
analyzer (Brookhaven Instruments, Holtesville, NY). The zeta potential was calculated
using the following equation:
^
=
l±lL
(Eq. 15.65)
where |i
e
= the measured value of electrophoretic mobility; e = the dielectric constant; f
= the zeta potential, mV;/(Kr) = the Henry's function;
ji =
the dynamic viscosity; r =
the particle radius, L; and
K =
Debye-Hilckel parameter, 1/L (1/K = the double-layer
thickness), which is defined as:
K
* = *>££*
(Eq. 15.66)
where e = the electrical charge = 1.60219 x 10"
1
9
C;
NA =
Avogadro's number; Cj = the
molar concentration, mass (mol)/L
3
; Zj = the valence of the ion;
e. =
the permittivity of
the solution = 7.083 x 10"
1
2
C
2
/cm-J; k
B
= Boltzmann's constant = 1.380666 x 10"
23
J/K;
and T = temperature, K. The Henry's function can be expressed as:
f(icr) = 1.000
(KT < 0.1) (Eq. 15.67)
f (KT) = 1.0275157930 + 0.08576196701og(Kr)+
0.1058385007(log(Kr))
2
+ 0.0464011331(log(Kr))
3
(0.1<KT<3.55) (Eq. 15.68)
f (KT) = 1.0622739775 - 0.07409292261og(ra-)+
0.382612499(log(ra-))
2
-0.1256407214(log(Kr))
3
(3.55< KT < 35.5) (Eq. 15.69)
f (KT) = 0.7682190382 + 0.698870475 llog(Kr)+
0.2263212573(log(Kr))
2
+ 0.0248691121(log(ra-))
3
(35.5< KT < 1000) (Eq. 15.70)
f(xr) = 1.500
(KT> 1000) (Eq. 15.71)
For the 2.4 mg/L nCeo aqueous suspensions at pH 7, containing 1.0 mM CaCl2, the
values of
KT
is 9.0, and the zeta potential is -23.9 mV (Wang et al., 2008a). f can be
manipulated by changing the pH and ionic strength in the solution (Adamson, 1982).
15.5.1.2 Interaction Energies for
NPs
The DLVO theory was developed to combine the van der Waals attraction with
the double-layer repulsion (Verwey and Overbeek, 1948; Tadros, 2007):
*T=*EDL + *V
(Eq. 15.72)
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