When a solid body is in contact with two fluids the surface of the solid cannot alter its form but the angle at which the surface of con tact of the two fluids meets the surface of the solid must depend on the values of the three tensions. For equilibrium 32 = Cr2i cosa.
The angle a is known as the angle of contact.
For pure substances the angle is definite. It varies from zero (or very nearly so) for liquids that "wet" the solid to 13o° or 140° for mercury on glass.
In regard to the experimental behaviour of water on mercury the wealth of papers is equalled by the remarkable lack of uni formity in the results obtained even when elaborate precautions are taken. A drop of water which fails to spread when placed on a mercury surface is often caused to spread by the action of pouring the mercury out of the dish—thus involving the creation of a new surface ! Water shows a positive tendency to spread in vacuo on a drop formed in vacuo! (Burdon, Faraday Society, May, 1927).
This will be the case, for example, near a flat plate dipped into the liquid. Let be the vertical plate supposed to be so wide that the edge effects do not count. We will consider the forces per unit depth (perpendicular to the paper) and will consider as the standard level of the liquid far from the plate. The curvature of the surface at the point x, y, is The shape of the surface is there fore the elastica, i.e., the form taken by a uniform spring when equal and opposite forces are ap plied at its ends (see Thomson and Tait, Natural Philosophy, vol. i. p. 455). The equation might have been found by con sidering the elementary volume of a strip of liquid, dx, sustained above the normal level of the liquid by the surface forces at its outer and inner edges. The differ ence of the vertical component of these is and the weight of the strip is gpydx but since d (sin 0) d (cos 8) the same result is obtained.
dx dy If the angle of contact is a the value of 0 at the plate is —a; in which the coefficients are claimed to be correct to the approxi mation given. The equation can only be used in the case when r is small compared with h. It may be mentioned that a very near approach to the equation can be obtained by considering the sur face as ellipsoidal with its minor axis vertical. This was first shown by Hagen and Desains. Various methods are employed for
determining surface tension experimentally : (a) From the rise in a capillary tube making use of the above equation.
(b) Sentis's Method.--A capillary tube is partly immersed in the liquid. It is then withdrawn vertically and a drop remains clinging to the lower end ; the position A of the vertex of the drop is noticed. The liquid in the vessel is then raised until it touches the vertex (when the column falls) and then raised further till the upper surface is at the same level C as at first. The liquid in the vessel is then at the level B. The vertical dis tance AB corresponds to h in the ordinary method but in the correcting terms h must be put negative. The width of the drop is in this case to be small corn pared with h.
(c) Jaeger's Method.—In this method an orifice (a "tip") is placed just under the surface of the liquid and the pressure of gas is increased until bubbles form. The maximum pressure of the gas (which is fairly sharply marked) is observed. The deduction of the applicable equation is a some what delicate matter because the problem is really a kinetic, not a static, one. The formula em ployed is As a means for measuring surface tension this method is ob viously not satisfactory; but for rough comparative values for liquids of like kind it is a very quick and easy method.
Wide Tubes.—When a is not small the approximations made above for narrow tubes are not suitable.
The question has been fully discussed by the late Lord Ray leigh to whose papers reference should be made (v. Rayleigh, Proc. Roy. Soc. A, 92, 184, Bubbles and Drops.—These can be dealt with by similar methods. Air bubbles in a liquid can be formed of any size, from minute ones which are nearly spherical to large ones shaped like a flat cake. The excess pressure p— which is easily found by experiment, determines the total curvature at the lowest point N; where is the maximum dif ference of pressure between the level of the end of tube inside and outside, and r is the internal radius of the tube. The bubble is assumed to form within the internal circumference. In practice, however, it sometimes forms on the outside circumference. To obviate the uncertainty it is recommended to make the two circumferences as nearly equal as possible, but this is an experimental matter of great difficulty. The final accuracy depends chiefly on the measurement of the radius r. The subject of the formation of bubbles and drops requires much more study than it has received.