Biomedical Engineering Reference
In-Depth Information
Figure 3.25
Cantilever deformed by the presence of a water droplet.
3.5.3.1 Droplet on a Cantilever
In the case of a microcantilever, the presence of a droplet induces capillary forces
along the triple line (Figure 3.25). The deformation results from the resultant of
the capillary forces perpendicular to the cantilever. At rest, this resultant bends the
cantilever, as shown in Figure 3.25. The calculation is lengthy and has been given
by Yu and Zhao [13].
3.5.3.2 Contact Between Three Liquids—Neumann's Construction
Take two immiscible liquids, denoted 1 and 2, with the droplet of liquid 2 deposited
on the interface between liquid 1 and a gas. Even if the density of liquid 2 is some-
what larger than that of liquid 1, the droplet may “float” on the surface, as shown
in Figure 3.26.
The situation is comparable to that of Young's law with the difference that the
situation is now two-dimensional. It is called
Neumann's construction
, and the fol-
lowing equality holds
�
�
�
γ
+
γ
+
γ
=
0
(3.34)
Note that the density of the two liquids condition the vertical position of the
center of mass of the droplet, but at the triple line, it is the
y
-projection of (3.34)
that governs the morphology of the contact [14]. In Figure 3.27 we show some
pictures of floating droplets obtained by numerical simulation (Surface Evolver
software [15]).
L L
1 2
L G
1
L G
2
Figure 3.26
Droplet on a liquid surface.
