Biomedical Engineering Reference
In-Depth Information
Figure 4.15
Sketch of the droplet at onset of actuation. If
V
>
V
min
,
q
(
V
) +
a
<
q
0
-
a
and the drop
moves to the right under the action of capillary and electrocapillary forces.
where
dl
is a unit element of the contour line, and
n
the normal unit. Equation
(4.30) can be integrated
�
�
ò
F
=
γ θ
cos
dl n i
.
=
γ θ
cos
e
(4.31)
x
L
where
e
is the width of the electrode, as shown in Figure 4.16. Equation (4.31)
shows that the shape of the triple line above an electrode has no effect on the cap-
illary force. If we remark that the x-direction force on the triple line outside the
electrodes vanishes, we conclude that the x-direction capillary force on the droplet,
whatever its shape, is
(4.32)
F
=
e
γ θ
(cos
-
cos
θ
)
0
This force remains constant during the motion of the droplet between two
electrodes. Now, if we take into account the contact angle hysteresis, we obtain the
advancing and receding capillary forces
F
=
e
γ θ α
cos(
+
)
a x
,
(4.33)
F
= -
e
γ θ α
cos(
-
)
r x
,
0
Figure 4.16
(a) views of droplets on electrodes; (b) sketch of the contact of a drop with the
substrate.
