Spontaneous contraction of a liquid surface

Spontaneous contraction of a liquid surface. The fundamental property of liquid surfaces is that they tend to contract to the smallest possible area. This tendency is shown in the spherical form of small drops of liquid, in the tension exerted by soap films as they tend to become less extended, and in many other properties of liquid surfaces. Plateau1 has undertaken a prolonged study of the forms assumed by liquid surfaces, under conditions when the disturbing effect of gravity is absent he showed that the surfaces always assume a curvature such that, if and are the principal radii of curvature at any point, 

It is a geometrical fact that surfaces for which the relation (1) holds are surfaces of minimum area. 

The methods of eliminating the effect of gravity on the form of the surfaces were two Plateau used soap films, which are practically weightless and he suspended masses of olive oil in a mixture of alcohol and water of practically the same density. By the latter device, spheres many centimetres in diameter were obtained. 

Under conditions where the weight of the liquid cannot be neglected, the shapes are more complicated. The effect of gravity can, however, be allowed for (see equation (4) below). Plateau s experiments give a very complete experimental proof of the tendency of liquid surfaces to contract the various forms assumed with different supports are of more interest to the mathematician than the physicist, and reference should be made to Plateau s book, Boys s Soap Bubbles,2 or Maxwell s article8 for further details of them. 

Molecular explanation of the tendency to contract. The simplest properties of molecules in liquids suffice to account for this tendency of the surfaces to contract. Molecules are small objects, possessing definite size and shape, in all states of matter in all fluids they are free to move relative to one another, and in liquids they are kept close to each other, by the cohesions forces between them. Liquids are thus distinguished from solids by their fluidity, that is, the freedom of the molecules to move and from gases by the fact that the attraction between the molecules restrains the motions sufficiently to prevent more than a small 

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