Biomedical Engineering Reference
In-Depth Information
Double layer repulsion (
V
R
)
+
Energy barrier (
E
B
)
B
Total potential energy (
V
T
)
E
B
Distance between particles (
D
)
C
Secondary minimum
van der Waals attraction(
V
A
)
A
FIGURE 3.4
Schematic of interaction energy between two particles. (Adapted from Sarkar, P. and Nicholson, P.S.
J. Am.
Ceram. Soc.,
79 [8] 1987-2002 (1996).)
• As the distance between the particles increases, the balance between the attrac-
tive potential energy (
V
A
) and repulsive potential energy (
V
R
) shifts in favor of the
former.
• Point C.
At the secondary minimum (the primary minimum is off-scale, beyond
point A), if the concentration of counterions is sufficient,
flocculation
occurs.
Electrophoretic Mobility
Electrophoresis generally occurs when the distance over which the double layer charge
falls toward zero is large compared to the particle size [20]. Hence, the effect of an applied
electric field is greater on the particle and so it will move under its influence. The velocity
at which this occurs is given by Equation 3.5 [19]:
v
=
μE
(3.5)
where:
v
= particle velocity
μ
= electrophoretic mobility
E
= applied electric field
The electrophoretic mobility for a rigid spherical particle is given by Equation 3.6 [20]:
2
2
2
k
εεζ
η
ε ζ
η
0
o
=
f
(
r
)
=
f
(
r
)
(3.6)
κ
κ
3
3
where
μ
= electrophoretic mobility of particle
ε
= permittivity of medium
ε
o
= permittivity of vacuum
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