Biomedical Engineering Reference
In-Depth Information
Figure 4.13
Sketch of the hysteresis curves. Actuated contact angles are not identical if the volt-
ages are increasing or decreasing. Advancing and receding curves are approximately shifted by the
hysteresis angle
a
.
Let us assume now that the two contact angles are the actuated and not ac-
tuated Young contact angles, plus or minus the hysteresis angle, as sketched in
Figure 4.14 [20].
The advancing and receding limit contact angles are then
q
+
a
and
q
0
−
a
where
q
is the actuated contact angle and
q
0
the nonactuated contact angle. This notation
stems from the Hoffman-Tanner law [21] indicating that the advancing and reced-
ing contact angles are respectively larger and smaller than their Young values. The
minimum actuation potential is then the potential required for obtaining a net posi-
tive electrocapillary force
θ
(
V
)
+
α θ α
£
-
(4.29)
min
0
This relation is illustrated by the sketch of Figure 4.15.
The electro-capillary force in the direction x (unit vector
i
) on the hydrophilic
electrode is given by
�
�
=
ò
(4.30)
F
γ θ
cos
dl n i
.
x
L
Figure 4.14
Sketch of the advancing and receding contact angles with and without the hysteresis
angle.
