Hardware Reference
In-Depth Information
Fig. 1.1
Side view of the
setup for observation of
electrowetting on dielectric
phenomenon
In the electrowetting-on-dielectric setup shown in Fig.
1.1
, there are three phases
that are in contact with each other [
12
]. Phase 1 is the solid dielectric layer; Phase
2 is the droplet. If the droplet is in direct contact with air, then Phase 3 is the vapor;
if the droplet is surrounding by the filler medium, such as silicone oil, then Phase
3 is the surface of the filler medium. If no voltage is applied to the droplet, it will
maintain its equilibrium shape. The contact angle between the phase of the droplet
and the solid insulator is referred to as , which is defined as shown in Fig.
1.1
.
Each interface has an interfacial energy, referred as
ij
,wherei and j are
the indices that represent the corresponding phases.
Interfacial Energy
is defined
as “the amount of energy, G, that must be used under reversible and isothermal
conditions to increase the surface A of an interface at constant volume” [
12
-
15
].
The mathematical expression of this definition is:
ˇ
ˇ
ˇ
T D
const
;V D
const
dG
dA
ij
D
(1.1)
According to
the Principle of Minimum Total Potential Energy
, the total free
energy of a droplet (G) should obtain its minimum value at the equilibrium state
[
12
-
15
]. From Eq. (
1.1
), we obtain the basic correlation between the interfacial
energy , the total free energy G, and the surface A, as:
dG
dA
D
sl
sv
C
lv
cos
D
0
(1.2)
where the subscripts “l ”, “s”, and “
v
” refer to liquid, solid, and vapor, respectively.
Thus
sl
represents the interfacial energy for the interface between the solid phase
and the liquid phase. The symbols
sv
and
lv
are defined in a similar way. From
the above equation, we can get the
Young equation
, which shows that the value of
the contact angle is a function of the interfacial energies [
6
,
12
-
15
]:
sv
sl
lv
cos
D
(1.3)
When a voltage is applied to the droplet, the total free energy will contain additional
terms [
6
,
12
]:
dG
D
sl
dA
sv
dA
C
lv
dAcos
C
dU
dW
(1.4)
