Surfactant - Tissue Functioning and Remodeling in the Circulatory and Ventilatory Systems - page 784

curvature radius decreases, when the surface tension is constant. 3 In a bialveolar
model with 2 communicating alveoli of different curvature radii, the pressure of the
small alveolus is higher than the pressure of the large one. Such a bialveolar model
is not synchronized. The force exerted on a very thin curved shell is equal to twice
the tension divided by the surface curvature radius. For a surface tension of 5 N/m 2
(physiological magnitude) and a radius of 50 m, the force is equal to 200 kPa. The

superficial tension is then minimized in proportion to the alveolar volume by the
secretion of a wetting agent.
The interface forces govern adhesion, friction, wettability (wetting or non-
wetting) 4 of solids by liquids (Fig. 13.2 ), capillarity of liquids in small-bore tubes 5
and the curvature of gas-liquid or solid-liquid interfaces.
In the liquid domain, the time and space-averaged attraction force (resultant)
exerted on any liquid molecule by its neighbors is equal to zero, even though the
molecules diffuse and undergo random collisions. But at the interface of the liquid
with the surrounding medium, no molecule can balance the effects of the interior
liquid molecules (symmetry rupture). Cohesion forces are hence responsible for

3 The Laplace law indicates that the pressure within a spherical structure with surface tension
associated with a liquid-gas interface is inversely proportional to the radius of the sphere:

p = 2 T / R

( T : surface tension, R : sphere radius). At a constant surface tension, small hollow spheres generate
greater pressures than large spheres. Small spherical tanks connected in parallel to large spherical
reservoirs can therefore empty into large ones.
4 The criterion for the wetting and non-wetting of solids by liquids is the value of the contact angle
between the solid and the liquid. A liquid wets a solid when the contact angle ranges between
0 and 90 degrees (concave meniscus in capillarity experiments). When the contact angle is greater
than 90 degrees, the liquid does not wet the solid (convex meniscus in capillarity experiments).
Three interfaces exist when a liquid droplet contacts a solid or a liquid rises in a capillary tube:
(1) the gas-solid (GS), (2) liquid-solid (LS), and (3) gas-liquid (GL) interface. Each interface
is associated with a surface tension T GS / LS / GL . The contact angle α can be calculated from the

following formula:

.
Partial or total wetting can be characterized by a spreading coefficient. When it is positive, the
energy of the dry surface is greater than that of the wetted surface, and conversely when the
spreading coefficient is negative. The droplet volume change can modify the contact angle without
disturbing the equilibrium between the liquid droplet and the more or less rough solid wall.
However, when the contact angle is greater than the expansion limit or smaller than the retraction
limit, the droplet configuration changes.
5 The motion of liquid in capillary tubes (rise or fall whether the liquid wets or not the solid wall
of the tube of small radius ( R < 5 mm) plunged into the liquid bath, according to the magnitude
of capillarity forces, pressure and opposing gravity) is characterized by a meniscus (downward or
upward meniscus whether the liquid wets or not the solid wall) at a height given by the Jurin law :

cos α =( T GS − T LS ) / T GL

H = 2 T s cos α / ( R ρ g ) .

Water barometers must then be based on tubes of inner diameter equal to 8 mm at least in order to
avoid disturbed measurements.