SURFACE ENERGY 171 



surface of the liquid the molecules exert an attractive force on one 

 another. This attractive force is appreciable because the molecules are 

 within very minute distances of one another. Since in the interior of 

 the liquid each molecule is surrounded by others on every side, it is 

 therefore subject to attraction in all directions. On the average, over 

 long periods of time as compared with the molecular temperature vibra- 

 tions, the attraction of any molecule is uniform in all directions; hence 

 the molecule is in equilibrium. 



At the surface, however, the molecules of the liquid are attracted only 

 inward and to each side by their neighbors; there is no outward attrac- 

 tion to balance the inward force. The result is that every surface mole- 

 cule is subjected to a resultant inward attraction directed perpendicular 

 to the surface. It is this inward attraction that causes a free surface to 

 maintain its unique shape for given external conditions. It is also this 

 resultant inward attraction that produces the reduction of the area of a 

 free surface. 



The fundamental property of liquid surfaces is that they tend to 

 contract to the smallest possible area permissible by their environment. 

 This tendency is illustrated by the spherical form assumed by small 

 drops of liquid and small gas bubbles, and the shapes assumed by soap 

 films. The departure from spherical forms, noticed in larger liquid 

 drops or gas bubbles, is due to the gravitational effect. The diskoidal 

 form of the mammalian erythrocyte is not well understood, and no 

 satisfactory mathematical expression for the contour has been found. 



Surface Energy 



The fact that an undisturbed liquid surface tends to contract shows 

 that surface energy is associated with it, for energy must be expended to 

 extend such a surface. If we view this extension of the surface from an 

 internal point and in terms of the molecules which form the surface, we 

 observe that, as the surface is extended, more and more molecules must 

 be brought from the interior to be added to the expanding surface. In 

 this molecular rearrangement, work is done to move the internal mole- 

 cules into the surface; hence energy is being expended against the 

 inward-directed molecular forces. An expanding surface is therefore 

 accumulating a greater potential surface energy, and a contracting sur- 

 face is accompanied by a loss in surface energy. When a surface con- 

 tracts, either it must wrinkle, or molecules must be forced out of it. If 

 an appreciable surface molecular attraction comparable to what might be 

 called tangential tension exists, then a liquid surface must wrinkle on 

 contraction. This result is contrary to experimental evidence; hence 

 no tangential surface force can exist. 



