Biomedical Engineering Reference
In-Depth Information
Finally, we obtain
d
2
R
=
(3.20)
2
cos
(
α θ
-
)
Using the same reasoning with a meniscus oriented in the opposite direction, we
obtain the expression of
R
1
d
1
R
=
(3.21)
1
cos
α θ
+
)
(
Comparing relations (3.20) and (3.21) and noting that
d
2
<
d
1
and cos(
a
-
q
) >
cos(
a
+
q
), we deduce that
R
2
is smaller than
R
1
, and
P
1
>
P
2
. The situation is not
stable. Liquid moves from the high-pressure region to the low-pressure region and
the plug moves towards the narrow gap region. It has also been observed that the
plug accelerates. This is due to the fact that the difference of the curvatures in (3.19)
is increasing when the plug moves to a narrower region. Bouasse [9] noted that the
same type of motion applies for a cone, where the plug moves towards the tip of
the cone. In reality, Bouasse used a conical frustum (slice of cone) in order to let the
gas escape during plug motion.
3.4 Partial or Total Wetting
So far, we have discussed interfaces between two fluids and shown the importance
of the surface tension. In the reality, except for droplets floating in a liquid, inter-
faces must attach somewhere, in general, to a solid surface or sometimes to a third
liquid (Figure 3.16). The intersection of the three domains is called the triple line.
Let us consider first the case of an interface contacting a horizontal solid sur-
face. Liquids spread differently on a horizontal plate according to the nature of the
solid surface and that of the liquid. In reality, it depends also on the third constitu-
ent, which is the gas or the fluid surrounding the drop. Two different situations are
possible: either the liquid forms a droplet and the wetting is said to be partial, or the
liquid forms a thin film, wetting the solid surface (Figure 3.17). For example, water
spreads like a film on a very clean and smooth glass substrate, whereas it forms a
Figure 3.16
Sketch of a liquid/air interface contacting another material (solid or liquid), forming
a triple line.
