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Surface Tension

liquid, sphere, molecule, position, attraction and force

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SURFACE TENSION, that property of liquids in virtue of which they tend to take such a form as to have the smallest surface possible. The name °surface tension° has ref erence to the. fact that liquids, when freed from the action of gravity and other compara tively powerful forces, behave as though their surfaces were elastic membranes, whic.h are everywhere in a state of uniform tension. Be ginners in the study of physics often fortn the idea, from their textbooks, that this hypothet ical tension is real and that the surface of a liquid really is membranous in nature, and sub ject to an actual, physical tension. This is not at all the case; for the behavior of the liquid is due to an entirely different cause, as will be understood by reference to Fig. 1. AB here represents a liquid surface, and m m m et represents a molecule of the liquid, which is originally in the interior of the liquid, but which is removed from it in the manner illus trated by the successive figures 1, 2. 3, 4 and 5. Consider, first, the state of the molecule m in the position 1. It is here surrounded by the liquid on all sides, and the attractive influence that the other molecules of the liquid exert upon it is sensibly the same in all directions. The circle that is drawn about m represents a sphere whose radius is the °radius of sensible molecular attraction2; that is, it is equal to the (unknown) distance at which we may suppose that the attraction of one molecule of the liquid for another one ceases to be sensible. The at tractive influence of those parts of the liquid which are external to this sphere being by hypothesis insensible, we may regard m as in fluenced solely by such molecules as are within a sphere of the radius shoW11. It is easily seen, therefore, that the attraction of the liquid for m will be the same in all directions (and therefore without any resultant effect), so long as the sphere remains totally submerged. But when the molecule m approaches the surface so nearly that a part of its sphere projects into the air as shown at 2, it is equally evident that the attractive force upon in is no longer the same in all directions. In order to make it so,

we should have to cut off, from the bottom of the sphere at 2, a segment equal to the segment that projects into the air, as indicated by the little shaded area. The mass of fluid that lies between this shaded segment and the surface of the liquid is without any resultant effect upon m, on account of its symmetry with respect to m; and hence in the position 2 we may regard m as subject only to the unbalanced downward attraction that the shaded segment exerts upon it. In position 3 the molecule has reached the surface of the liquid, and it is subject to a downward attractive force due to the mass of liquid contained in the entire lower half of the sphere. In bringing the molecule from position I to position 3, we therefore have to move it upward against a force which tends to pull it back into the liquid again; this force becoming active from the moment that the sphere of sensible molecular attraction first becomes tan gent to the surface of the liquid: and increasing in magnitude until it attains its maximum value when the molecule actually reaches that sur face. Hence we have to perform work, in order to transport a molecule from the interior of a liquid to the surface; and this amounts to say ing that we have to perform work in order to increase the surface of a liquid. But this is just what we should have to do if the surface of the liquid were an elastic membrane; and hence it is permissible to imagine that the sur face is such a membrane; and it is found that such a conception makes it easier to under stand and describe the phenomena that result from molecular attractions in liquids. It will be noted, however, that in extending the sur face of a liquid we do not actually stretch the existing surface. We merely bring more mole cules from the interior, where the forces acting upon them are balanced, to the surface, where these forces are not balanced.

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