Biomedical Engineering Reference
In-Depth Information
ζ
= zeta potential of particle in suspension
η
= viscosity of medium
1
κ
= Debye length
r
= radius of particle
k
′ = dielectric constant of medium (
ε
/
ε
o
[28])
The function
f
(
κr
) varies from 1 to 1.5 according to the size of the particle compared to
the Debye length
1
κ
[19].
For particles that are small relative to the Debye length (
f
(
κr
) ≈ 1;
κr
<< 1), the Hückel
formula, given in Equation 3.7, applies:
k
2
2
εεζ
η
2
ε ζ
η
=
0
=
0
(3.7)
3
3
For particles that are large relative to the Debye length (
f
(
κr
) ≈ 1.5;
κr
>> 1), the Smoluchow-
ski formula, given in Equation 3.8, applies:
k
2
εεζ
η
ε ζ
η
=
=
0
(3.8)
0
where:
μ
= electrophoretic mobility of particle
ε
= permittivity of medium
ε
o
= permittivity of vacuum
ζ
= zeta potential of particle in suspension
η
= viscosity
k
′ = dielectric constant of medium (
ε
/
ε
o
[28])
Zeta Potential
As mentioned, the zeta potential is used widely to assess the magnitude of the electrical
charge at the double layer. It also is known as the
electrokinetic potential
. Figure 3.3 illus-
trates that the zeta potential is the electrical potential at the interface between the station-
ary adsorbed liquid layer and the mobile medium beyond it.
For effective suspension of particles, which generally is a prerequisite to electrophoretic
deposition, a high and uniform surface charge on the particles is desirable [21]. In this
regard, the zeta potential is important to this process by determining the following:
• Level of repulsive interaction and consequent suspension stabilization
• Direction and speed of particle migration
• Green (unfired) bulk density of the deposit
It is possible to manipulate the zeta potential through the use of
charging agents
, including
acids, bases, and adsorbed ions and polyelectrolytes [19]. This manipulation can extend to
complete reversal of the sign of the zeta potential (positive versus negative).
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