176 SURFACES AND MEMBRANES 



bottom of the urine. The surface energy of the normal urine, because 

 of the presence of the bile salts, is changed from about 66 to 55 ergs/cm 2 . 

 Oil is sprayed on water as a larvicide to suppress mosquitoes. The 

 larvae of mosquitoes normally suspend themselves from the water-air 

 interface by means of three hairlike appendages attached to their breath- 

 ing tubes. Substituting a water-oil interface for the water-air interface 

 reduces the surface energy. To be effective the oil must reduce the 

 surface energy sufficiently to prevent the larvae from suspending them- 

 selves by their breathing tubes, so that they sink and suffocate. 



Surface Energy in Living Systems 



Since living cells are immersed in liquids, it follows that the interface 

 surface energy must be much less than that found at air-water inter- 

 faces. Recent work shows that invariable, very low tensions exist 

 between the cell and liquid interface. Protoplasm in sea water, for 

 instance, may have a surface energy as low as 1 erg/cm 2 . The work by 

 Harvey [1938] on the physical properties of protoplasm shows that such 

 " naked " cells as amebas, leucocytes, and plant cells removed from 

 their cellulose walls possess surface energies even less than 1 erg/cm 2 . 

 With the microscope centrifuge, first constructed by Harvey in 1932, 

 some very low values for this interface tension were found for numerous 

 invertebrate eggs. 



Plateau's Principle of Minimal Area 



When the disturbing effects of gravity are absent to distort the shape 

 of a fluid body at rest, liquid surfaces always assume a curvature such 

 that the mean curvature along two planes at right angles is constant. 



— + — = Constant 



where #1 and R 2 are these principal radii of curvature at any point. 

 Hence, when one decreases the other must increase to keep the reciprocals 

 of the sum constant. A spherical soap bubble, for example, has two 

 equal curvatures along two planes at right angles. If this bubble is 

 stretched, one radius of curvature increases as the one at right angles 

 decreases. Geometrically it can be shown that surfaces to which this 

 equation applies are surfaces of minimum area. 



The forms of living cells and protoplasmic masses, such as vacuoles, 

 plasmolyzed protoplasts, and amebas, are also illustrations of this 

 principle. Barnes [1937] even found that fatty material in such cells as 

 intestinal epithelium occurs as spherical droplets. 



