Biomedical Engineering Reference
In-Depth Information
��
�
�
ò
ò
F
=
f i dl
.
=
γ θ
cos
n i dl
.
(3.52)
W
W
Equation (3.52) can be simplified and cast under the form
e
�
�
�
�
ò
ò
ò
ò
F
=
γ θ
cos
n i dl
.
=
γ θ
cos
n i dl
.
=
γ θ
cos
cos
α γ θ
dl
=
cos
dl
¢
W
W
W
0
Finally we obtain the expression
F
=
eγ θ
cos
(3.53)
Equation (3.53) shows that the resulting force on a triple contact line in any
direction does not depend on the shape of the interface [21]; it depends only on the
distance between the two ends of the triple line normal to the selected direction.
3.6.7 Examples of Capillary Forces in Microsystems
It is very common in biotechnology to use plates comprising thousands of micro-
holes or cusps. The position of the free surface of the liquid in the cusps is of utmost
importance. In particular, the liquid must not exit the holes under the action of
capillary forces.
As an example, Figure 3.37 shows a free liquid interface in a square hole, cal-
culated with the Surface Evolver numerical software [15].
Figure 3.37
The surface of a liquid in a microwell is not flat due to capillary forces. The figure is a
simulation with the Surface Evolver software. (a) Case of water in a hydrophilic well (contact angles
of 140°). (b) Case of water in a hydrophilic well (contact angles 60°). The “free” surface is tilted
downwards or upwards depending on the contact angle. The walls have been dematerialized for
clarity.
