Biomedical Engineering Reference
In-Depth Information
where
s
sg
,
s
sl
, and
s
lg
are the tensions at the solid/gas, solid/liquid, and liquid/gas interface, resulting
in the relation between the contact angle
q
and the applied voltage
DF
(
Fig. 6.33
(b)):
q ¼
arccos
cos
q
0
þ
2
1
s
lg
c
DF
:
(6.27)
2
From the above equation, the condition for the applied voltage to make an originally hydrophobic
surface
q
0
>
90
hydrophilic (
q <
90
) is:
q
2
s
lg
cos
q
0
=
DF >
c
:
(6.28)
Increasing the voltage decreases the contact angle until a critical voltage is reached. At voltages higher
than that critical value, the contact angle does not follow the Lippmann relation
(6.25)
.
Electrowetting on dielectric
. The drawbacks of direct electrowetting are the fixed capacitance per
unit surface and electrolysis reaction at the electrodes. If the electrode is coated with a hydrophobic
and dielectric material such as Teflon, the capacitance per unit surface can be controlled by the
thickness
d
of the dielectric coating (
Fig. 6.34
):
c ¼
3
r
3
0
d
:
(6.29)
The relative dielectric coefficient of Teflon is approximately
3
r
¼
2. The contact angle can be
formulated as a function of the applied voltage by combining
(6.25)
and
(6.27)
.
Thermocapillary actuation
utilizes the temperature dependency of the surface tension or the
interfacial tension
[44]
.
Figure 6.35
depicts a simple model of this actuation concept. A liquid plug is
positioned in a capillary between two external heaters. The capillary with two open ends is considered
long compared to the distance between the two heaters. The rest of the capillary is filled with air. The
transient temperature distribution in the capillary can be described with a transient 1-D heat
conduction equation. With the known temperature as a function of position and time, the temperature
difference across the liquid plug and, consequently, the thermocapillary force can be determined. The
velocity and the position of the plug are then determined by solving the balance equation of forces
acting on the liquid plug.
FIGURE 6.34
Electrowetting on dielectric: (a) the hydrophobic dielectric layer acts as a capacitor and (b) an applied voltage
changes the contact angle.
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