Hardware Reference
In-Depth Information
where W represents the work done by the voltage source with voltage V when
the charge q is redistributed, and U represents the energy required to establish an
electric field between the liquid and the dielectric insulation.
The following equations [
12
,
16
] can be used to calculate U :
U
D
Z
E
DdV ol
(1.5)
V
ol
D
Z
d
0
U
A
1
2
E
Dd
z
D
1
2
d
E
D
(1.6)
where
E and
D denote the electric field and the electric displacement, respectively.
dU
dA
1
2
d
V
D
d
q
(1.7)
where V
ol
represents the volume of the droplet, and d represents the thickness of the
dielectric insulation layer on the surface of the electrode. In addition to the above
equations, we also have:
dW
dA
D
Vq
(1.8)
and
Gauss's law
[
16
]:
"
0
"
r
V
d
q
D
(1.9)
Now, we can search for the minimum value of total free energy, G, by setting the
derivative
dG
dA
equal to zero, which results in the following equation [
6
,
12
]:
dG
dA
D
sl
sv
C
lv
cos
1
2
"
0
"
r
d
V
2
D
0
(1.10)
According to Eq. (
1.10
), we can express
cos
as the function of voltage applied on
the electrode. Thus we get the
Young-Lippman Equation
:
sv
sl
lv
1
2
"
0
"
r
lv
d
V
2
cos.V /
D
C
(1.11)
Equation (
1.11
) shows that, when voltage is applied to the electrode, the solid-
electrolyte contact angle can be adjusted by applying voltage to the droplet
[
17
-
19
]. On the digital microfluidic platform, when control voltage is applied
on the electrode, the surface of the insulator will change from hydrophobic to
hydrophilic [
17
]. Thus, the droplet is repelled by the hydrophobic surface and
