Biomedical Engineering Reference
In-Depth Information
Figure 3.29
Film of water between two glass plates.
separate the plates. This situation is schematized in Figure 3.29. In the first place,
it is observed that the meniscus has a round shape (in order to minimize the free
energy).
Let us write Laplace's law at the free interface. The first (horizontal) radius of
curvature is approximately
R
. The second (vertical) radius of curvature, shown in
Figure 3.30, is given by
h
R
=
(3.35)
2
2 cos
θ
Laplace's law states that
1
2 cos
θ
γ
æ
ö
D =
P
-
(3.36)
ç
÷
è
ø
R
h
In (3.36) the minus sign derives from the concavity of the interface. Because
the vertical gap
h
is much less than the horizontal dimension
R
, we have the ap-
proximation
2
γ θ
cos
D » -
P
h
Figure 3.30
Sketch for the calculation of the vertical curvature.
