PHYSICS

alveoli (fig. 6.10). The blood-epithelium-air interface
of the lungs is very large and is approximately
equal to the area of a tennis court. Changes of
surface tension in the lungs are responsible for a
respiratory disease in new born babies, called the
hyaline membrane disease, which is characterized
by the deposition of hyaline substance on the
internal surface of the alveoli. The treatment of
+-lOOlLm-. this disease is associated with the application of
surfactants, species which are able to
Fig. 6.10. A diagrammatic reduce surface tension at the blood-air
cross-section of an alveole interface in the lungs.
6.3.3. Capillarity
A phenomenon caused by the surface tension at the interface
of two nonmixing media is called capillarity and is observed when
a distorted surface of a liquid leads to an elevation or depression
of the liquid when in contact with a solid. It is necessary to take
into account the effects of two opposing forces: adhesion, the
attractive (or repulsive) force between the molecules of the liquid
and those of the container, and cohesion, the attractive force
between the molecules of the liquid. When the liquid-gas interface
is curved, the resultant surface tension produces an additional
pressure difference across the interface. For a hemispherical liquid-gas
interface having radius of curvature R, the pressure
difference is given by the Laplace equation:
2· 0
!:::"p = ±-­
R (6.22)
where c is coefficient of surface of the liquid.
If the interface is not spherical, the Laplace equation is:
!:::"p = ±a .[_1_ + ~ J, (6.23)
R 1
R2
where R] and R 2 are the radii of curvature of two perpendicular
planes.
The sign for Sp is positive for a concave interface and negative
for a convex interface.
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A cylindrical tube with a small internal diameter is called a
capillary. The behavior of liquid in capillary is strongly modulated
by the wettability of the tube walls. If the walls are wettable, the
water rises in the capillary (fig. 6.11). For example, with water in
xylem vessels, the attraction between the water molecules and
the wall is great, causing the liquid to rise.
To calculate the extent of capillary rise, the balance of two
forces, gravity nr'pgh acting downward
and surface tension Znrocosti,
must be determined. Since these forces
are balanced, the extent of rise
h I I~~~t~~~ (h) is given by equating the two
forces (nr 2pgh = 2nrcrcose), which
leads to:
h = 20 cos e
(6.24)
pgr
Fig. 6.11. The fluid in
a narrow tube is puJJed up
by the additional pressure
on the hemisphere at the
liquid-air interface
6.3.4. Capillary Rise
where p is the density of liquid,
e - the contact angle, g - the gravitational
acceleration, r = Rcose ­
the radius of capillary and R - the
radius of surface curvature.
Example. Ifaxylem vessel has a lumen radius of 20 11m, using
equation 6.24, we can determine that water (the density at 20 0 e is
998.2 kg/rn-, surface tension is 0.0728 N/m) will rise to the following
height:
h = 2u cos e = 2·72.8 ·10-' N . m- I cos 90° = 1.49.10- 5 m 2 = 0.745 m
pgr 998.2kg·m 1· 9 .8m · s 2·20·1O- 6m 20·1O- 6(m)
Such a capillary rise would be sufficient to account for the upward
movement of water in small plants (:$; I m in height).
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