Law of LaPlace

The second effect of surface tension is that it causes the alveolus to become as small as possible. As the water molecules pull toward each other, the alveolus forms a sphere, which is the smallest surface area for a given volume. This generates a pressure directed inward on the alveolus, or a collapsing pressure. The magnitude of this pressure is determined by the Law of LaPlace ... 

Figure 17.2 Effects of surface tension and surfactant on alveolar stability, (a) Effect of surface tension. According to the law of LaPlace (P = 1ST/r), if two alveoli have the same surface tension (ST), the alveolus with the smaller radius (r), and therefore a greater collapsing pressure (P), would tend to empty into the alveolus with the larger radius, (b) Effect of surfactant. Surfactant decreases the surface tension and thus the collapsing pressure in smaller alveoli to a greater extent than it does in larger alveoli. As a result, the collapsing pressures in all alveoli are equal. This prevents alveolar collapse and promotes alveolar stability.

The presence of fluid in the alveoli, albeit only a thin layer, will exert a force on the interstitial space. This force may be calculated by use of the law of Laplace. This law is expressed for a single spherical curved surface by the following equation ... 

The Law of Laplace expresses the relationship between pressure and geometry at equilibrium ... 

The Law of Laplace can be used for cylindrical shapes without the factor 2. Thus, smaller conduits such as the capillaries would be expected to resist high blood pressures with thinner walls than would the arteries just because the capillaries are smaller in radins. 

Of what importance is the Law of Laplace to biological organisms How does the Law of Laplace explain shapes common in biology ... 

The integrity of certain types of bacteria depends on cell walls that they construct. The antibiotic penicillin was effective because it interfered with this construction process (Palumbi, 2001). From the Law of Laplace (Section 2.9.4) ... 

We shall now illustrate the use of dimensional analysis with the appHcation of Laplace s law to mammalian hearts. The beat-to-beat pumping ability of the mammalian heart is determined by its force-generating capability and the lengths of its constituent muscle fibers, as governed by the Starling s experimental observations on the heart. The formula for calculating force or tension, however, has been based on the law of Laplace... 

The first equation is the famihar law of Laplace for a cylindrical tube with internal radius q. It indicates that the force due to internal pressure, pj, must be balanced by a tensile force (per unit length), T, within the wall. This tension is the integral of the circumferentially directed force intensity (or stress, a ) across the wall ... 

The membrane deformation is calculated from observed macroscopic changes in cell geometry, usually with the use of simple geometric shapes to approximate the cell shape. The membrane force resultants are calculated from force balance relationships. For example, in the determination of the area expansivity modulus of the red cell membrane or the cortical tension in neutrophils, the force resultants in the plane of the membrane of the red cell or the cortex of the white cell are isotropic. In this case, as long as the membrane surface of the cell does not stick to the pipette, the membrane force resultant can be calculated from the law of Laplace ... 

Incorporation of the definition of the surface curvature into the equation of the capacitive energy variation in the system and the condition of nullity of this one when the system is at equilibrium (energy minimum) lead to the law of Laplace (here expressed in general, without the hypothesis of sphericity)... 

Basford JR. The Law of Laplace and its relevance to contemporary medicine and rehabilitation. Arch Phys Med Rehabil 2002 83(8) 1165—70. 

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