Surfactant - Tissue Functioning and Remodeling in the Circulatory and Ventilatory Systems - page 786

Fig. 13.3 Soap bubble in air.

G

p i − p e = p i − p L + p L − p e ∼

L

p e

2 . A spherical bubble

provides the smallest surface
containing a given volume.
The higher the surface area,
the greater the associated
energy. The equilibrium is
reached when the energy,
hence the area, is minimal

( 2 T s / R ) G

p i

Re Ri

radius of a surface and the pressure. At the interface, a pressure difference exists
between the concave and the convex sides of the surface. When a stretched zero-
thickness membrane is crossed, an increment of pressure is observed from the
convex side to the concave side that is given by the Laplace law. The excess pressure
p on the concave side over the convex side is indeed expressed by the principal radii
of curvature of the surface R c 1 and R c 2 :

Δ p = T s ( 1 / R c 1 + 1 / R c 2 ) . (13.2)

Using this principle, the vapor pressure p is greater for small bubbles in a liquid:

ln p / p 0 = 2 T s / ( ρ R c )( M / ( R g T )) , (13.3)

where p 0 is the vapor pressure over a liquid plane surface (infinite curvature radius)
and M the molecular weight.
Any hollow bubble is characterized by 2 interfaces, an inner (convex with respect
to the liquid domain) between the liquid and the internal gas (curvature radius R i ),
and an outer (concave with respect to the liquid domain) between the liquid and the
external gas (curvature radius R e ∼ R i ≡ R ). The Laplace law ( p = 2 T s / R ) applied

to both interfaces then leads to: p i − R (Fig. 13.3 ).

In Eustachian tubes, surfactant slightly lowers surface tension and reduces
opening pressure for better aeration and middle ear drainage. Eustachian tube
surfactant is a much weaker surface tension lowering agent than pulmonary
surfactant. Eustachian tube surfactant primarily acts as an anti-adhesive agent.
Alveolus surface tension is associated with neonatal respiratory distress syn-
drome [ 1596 ]. A greater pressure is required to inflate lungs filled with air than
with aqueous solution. Surfactant effects were studied in 1950s by various teams
of investigators [ 1597 - 1601 ]. The surface tension hampers transudation from
capillaries to alveoli through the alveolocapillary membrane. Furthermore, the
absence of a lung lining substance can cause neonatal atelectasis [ 1602 ]. Surface
tension varies with lung compression and expansion, i.e., with changes in the surface
area of the lung parenchyma. Surface tension rises with lung expansion to prevent
the lung from overexpanding and helps lungs to deflate. Conversely, surface tension

p e = 4 T s /