Biomedical Engineering Reference
In-Depth Information
where V pzc is the potential at no charge: spontaneous charges appear at the surface
of a solid when immersed into electrolyte solutions at zero voltage, and the poten-
tial at no charge is the voltage required to compensate this spontaneous charging.
Equation (4.4) is the original Lippmann's law. Using Young's law, we can translate
the change of g    e ff
SL in a change of the contact angle. Young's law applied successively
at zero potential and at potential V can be written
γ γ γ
-
=
cos
θ
SG
SL
LG
0
(4.5)
eff
SL V
(
)
cos
γ γ
-
=
γ
θ
SG
LG
where q and q 0 are the actuated and not-actuated contact angles. Upon subtraction
of these two equations and a substitution in (4.4), we obtain the Berge-Lippmann-
Young law
C
H
2
cos
θ
=
cos
θ
+
(
V V
-
)
(4.6)
0
pzc
2
γ
LG
Equation (4.6) shows that the contact angle decreases with an increase of the ap-
plied voltage. However, direct applications of Lippmann's law to a liquid contacting
a metallic surface are of little use because of the limitation of the voltage due to hy-
drolysis phenomena. For water, d H ~ 2 nm, e l ~ 80, g SL ~ 0.040 N/m, and the maxi-
mum voltage difference is of the order of 0.1V, so that the relative change of the
value of the surface tension is D g SL / g SL ~ 2%. In terms of contact angle, using g LG =
0.072 N/m, we find (cos q - cos q 0 ) < 0.01. Since Berge [3], modern electrowetting
applications circumvent this problem by introducing a thin dielectric film, which
insulates the liquid from the electrode.
The specific capacitance is decreased by the presence of the dielectric, but this
effect is compensated by much larger working voltages. This technique is called
electrowetting on dielectric (EWOD) (Figure 4.3). In this new configuration, the
Figure 4.3  Scheme of the electrowetting setup used to verify the Lippmann-Young equation. The
specific capacitance C of the system is the sum of the specific capacitances of the different layers
between the electrode and the liquid. The zero potential electrode may be placed anywhere in the
conducting drop. Upon actuation of a voltage V , the droplet spreads on the substrate. The value of
the contact angle depends on the value of the actuation potential V , according to the BYL law.
 
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