Biomedical Engineering Reference
In-Depth Information
electric double layer builds up at the surface of the insulator. The system now com-
prises two capacitors in series, namely the double layer at the solid surface specific
capacitance
C
H
and the dielectric layer specific capacitance
C
D
given by
ε ε
0
D
C
=
(4.7)
d
Comparing
C
H
(4.3) and
C
D
(4.7), we find
C
ε
ε
d
D
D H
=
C
d
H
l
This relation shows that
C
D
<<
C
H
because
d
H
<<
d
and
e
D
<
e
l
. Thus, the total
capacitance
C
, given by the relation
1
1
1
=
+
C C
C
D
H
can be approximated by
C
»
C
D
. This relation shows that the voltage drop occurs
within the dielectric layer and (4.4) is replaced by
C
ε ε
( )
eff
2
0
D
2
γ
V
=
γ
-
V
=
γ
-
V
(4.8)
SL
SL
SL
2
2
d
where the potential at no charge
V
pzc
has been neglected assuming that the insulat-
ing layer does not give rise to spontaneous adsorption of charge. Using Young's law,
and considering that the potential at no charge on a dielectric is zero, we find the
Berge-Lippmann-Young law for electrowetting on dielectric
C
2
cos
θ
=
cos
θ
+
V
(4.9)
0
2
LG
γ
The last term on the right hand side of (4.9) is dimensionless, and is called the elec-
trowetting number
h
C
ε ε
2
0
D
2
η
=
V
=
V
(4.10)
2
γ
2
d
γ
LG
LG
For a usual dielectric like Teflon or parylene 1
m
m thick and a droplet of water, the
coefficient
e
0
e
D
0/2
dg
LG
is of the order of 10
-4
V
-2
. In order to obtain a substantial
change of contact angle, applied electric potentials should be of the order of 30 to
80V.
Electromechanical Approach
The electromechanical approach was introduced by Jones at al. [7], Kang [8], and
recently reviewed by Zeng and Korsmeyer [9]. Let us start from the Maxwell stress
tensor
æ
1
2
ö
2
T
=
ε ε
E E
-
δ
E
(4.11)
ç
÷
ik
0
i k
ik
è
ø
