The determination of the surface tension is complicated by the fact that many of the formu lae containing it involve the contact-angle also. In such cases the contact-angle may be deter mined by an independent observation, as was done by Young in the case of mercury in con tact with glass; but in most cases the liquids examined wet, or seem to wet, the solid walls, and it is then assumed that the contact-angle is evanescent or zero. The results obtained on this assumption may be compared with those ob tained by methods in which the contact-angle is not involved, to test the validity of the as sumption, and if it is found in error, to deter mine the magnitude of the contact-angle.
It is of interest to consider some examples of the constants of capillarity. The units com monly employed are not those of the absolute c. g. s. system. It has been found more con venient to use the millimetre as the unit of length, and the weight of a milligram as the unit of force. Poisson's constant a', being al ways determined as in the example given of the rise of a liquid in a tube, by the product of two lengths, is a number of square millimetres. The surface tension T, or the force which acts across a unit of length in the surface, is ex pressed in milligram weights per millimetre. In these units Poisson's constant for mercury is about 6.75, and the surface tension 45.7. For water at 20° C. we may take 15.0 and T=.75; for chloroform at 23° C., for refined petroleum at 22° C., T°..2.64. These numbers are simply cited as examples of the mavitude of the two constants in typical cases. Their exact deter mination is beset with such difficulties that it is doubtful whether any results have been obtained which can be accepted as definitive.
The constant contact-angle of mercury with glass is about 135°, or a little larger. Most liquids wet glass, and their contact-angles are assumed to be 0°. Evidence has been adduced to show that in some cases, with water or pe troleum, for example, the contact-angle with glass is not 0°, but has a finite, though not a large, value. This question is not yet definitely settled.
The principal difficulty in determining the constants of capillarity with accuracy lies in the effect of impurities on the surface tension. This is especially felt with the liquids which have high surface tension, like mercury or water. The least trace of oil or grease will
spread out over a water surface in a thin film, and alter its surface tension very considerably. It is very difficult to get the vessels clean, which are used in the experiments, and much more difficult to keep them clean, so that the con stants obtained for any liquid are always open to a certain degree of suspicion. Impurities dis solved in the liquid affect the surface tension also, though not to so great a degree as those which spread over its surface.
The surface tensions, of all liquids which have been tested, become less as the temperature rises. It has been shown to be a consequence of the principles of thermodynamics that, pro vided the specific heat of the liquid is inde pendent of the extent of its surface, the amount by which the surface tension changes is pro portional to the change in the absolute tem perature. Most of the older measurements of the temperature coefficients do not confirm this conclusion, but the observations of Knipp on water and of Feustel on various organic liquids are in agreement with it.
The magnitudes of the constants of capil larity manifestly depend on the magnitudes of the forces between molecules and on the range of molecular action. The theory of van der Waals leads to an estimate of the molecular pressure within a liquid, the values obtained for it ranging from 1,430 atmospheres in the case of ether to 10,700 atmospheres in the case of water. The same theory indicates that the range of molecular action is proportional to the linear dimensions of the molecule, and is of about the same magnitude as the radius of the molecule. By the help of a modified form of this theory, Eotvos came to the conclusion that the rate of variation with the temperature of the product of the surface tension and the two thirds power of the molecular volume should be constant, and the same for all liquids, within a certain temperature range, if their molecules are single, and not double or compound. Ob servation shows that this law holds true for many liquids, and in cases in which it fails, there are often other reasons to support the conclusion that the molecules of the liquid are compound.
Before closing, we may consider a few ex amples of the effects produced by surface ten sion.