Biomedical Engineering Reference
In-Depth Information
3.3.1.2 Laplace's Law
Suppose a spherical droplet of liquid surrounded by a fluid (gas or liquid). The
Laplace law links the curvature of the interface to the pressure difference across the
interface
= Ñ
�
D =
P P
-
P
γ
.
n
(3.13)
i
e
where
n
is the unit normal to the surface,
P
i
and
P
e
are, respectively, the internal and
external pressures. This expression derives immediately from (3.9). It can equiva-
lently be written as
γ γ
æ
1
1
ö
D =
P P P
-
=
2
H
=
+
(3.14)
ç
÷
i
e
è
R
R
ø
1
2
For a sphere
R
1
=
R
2
=
R
, and Laplace's law is simply
D =
P P P
-
=
2
γ
R
i
e
and, for a cylindrical interface (Figure 3.12), one of the two radii of curvature is
infinite, and Laplace's law reduces to
D =
P
γ
R
We do not indicate here the derivation of the Laplace law. The reader can refer
to [7, 8]. Let us mention here that the reasoning is based on an energy balance be-
tween the pressure and surface energies
d A
D =
P
γ
(3.15)
dV
Figure 3.12
Laplace's law for a cylindrical interface.
