Biomedical Engineering Reference
In-Depth Information
wedge tend to spread in the corner (Figure 3.54). This motion results from the fact
that the interface curvature is strongly reduced in the corner. In the case of Figure
3.54, the vertical curvature radius is small; the Laplace pressure is low in the corner
and liquid tends to spread in the corner. Concus and Finn [25] have investigated this
phenomenon and they have derived a criterion for capillary motion in the corner of
the wedge. If
q
is the Young contact angle on both planes and
a
is the wedge half-
angle, the condition for capillary self-motion is
π
θ
<
-
α
(3.79)
2
This case corresponds to wetting walls. Conversely, when the walls are nonwet-
ting, the condition for de-wetting of the corner is
π
θ
>
+
α
(3.80)
2
In Figure 3.55, the Concus-Finn relations have been plotted in a (
q
,
a
) coordi-
nates system. One verifies that, for a flat angle, the Concus-Finn relations reduce to
the usual capillary analysis. The Concus-Finn relations can be numerically verified
using the Surface Evolver software. Figure 3.56 shows the spreading of the liquid in
the corner when condition (3.79) is met.
In microtechnology, wedges and corners most of the time form a 90° angle, so
that a droplet disappears in the form of filaments if the wetting angle on both planes
is smaller than 45°. One must be wary that, when coating the interior of microsys-
tems with a strongly wetting layer, in order to have very hydrophilic (wetting) sur-
face, droplets may disappear; they are transformed into filaments in the corners.
The converse can also be verified. For a rectangular channel, if the coating
is strongly hydrophobic, and the contact angles on both planes are larger than
Figure 3.54
A liquid interface is deformed in the corner of a wedge made of two wetting plates.
This phenomenon is due to a decrease of curvature at the edge.
