Biomedical Engineering Reference
In-Depth Information
3.7  Pinning and Canthotaxis
3.7.1  Theory
Solid surfaces are not always smooth or chemically homogeneous. They can have
edges and chemical heterogeneities. These surface discontinuities (geometrical or
chemical) modify the behavior of an interface. The shape of an interface is modified
locally by a point or line inhomogeneity. Let us suppose that an interface is coming
to contact a straight edge (Figure 3.38), and that the Young contact angle q is the
same on both sides of the edge. If the liquid is slowly pushed over the edge, the con-
tact line on the angle stays fixed or pinned as long as the contact angle is not forced
over the limit a + q , where a is the angle between the two planes. The condition for
pinning is then
θ φ α θ
£ £
+
(3.54)
where q is the contact angle. In the case where the two planes have a different
chemical surface, the Young contact angles can be denoted q 1 and q 2 , and the con-
dition (3.54) becomes
£ £ + (3.55)
The pinning condition between the two angles q and a + q is called can-
thotaxis .
θ φ α θ
1
2
3.7.2  Pinning of an Interface Between Pillars
Microsystems for biotechnology often make use of pillars to perform microfluidic
functions. Let us consider the example in which the role of the pillars is to block and
maintain fixed an interface between two immiscible fluids [22, 23] (Figure 3.39).
This is the case of capillary valves, liquid-liquid extraction devices, and so forth.
Figure 3.38  Droplet pinning on an edge: the droplet is pinned as long as the contact angle varies
between the natural Young contact angle q to the value q + a . Above this value, the interface moves
over the right plane and the interface is suddenly released.
 
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