Definition.--_The tension of a liquid surface across any line drawn on
the surface is normal to the line, and is the same for all directions of
the line, and is measured by the force across an element of the line
divided by the length of that element._
_Experimental Laws of Surface-Tension._--1. For any given liquid
surface, as the surface which separates water from air, or oil from
water, the surface-tension is the same at every point of the surface and
in every direction. It is also practically independent of the curvature
of the surface, although it appears from the mathematical theory that
there is a slight increase of tension where the mean curvature of the
surface is concave, and a slight diminution where it is convex. The
amount of this increase and diminution is too small to be directly
measured, though it has a certain theoretical importance in the
explanation of the equilibrium of the superficial layer of the liquid
where it is inclined to the horizon.
2. The surface-tension diminishes as the temperature rises, and when the
temperature reaches that of the critical point at which the distinction
between the liquid and its vapour ceases, it has been observed by
Andrews that the capillary action also vanishes. The early writers on
capillary action supposed that the diminution of capillary action was
due simply to the change of density corresponding to the rise of
temperature, and, therefore, assuming the surface-tension to vary as the
square of the density, they deduced its variations from the observed
dilatation of the liquid by heat. This assumption, however, does not
appear to be verified by the experiments of Brunner and Wolff on the
rise of water in tubes at different temperatures.
3. The tension of the surface separating two liquids which do not mix
cannot be deduced by any known method from the tensions of the surfaces
of the liquids when separately in contact with air.
When the surface is curved, the effect of the surface-tension is to make
the pressure on the concave side exceed the pressure on the convex side
by T (1/R1 + 1/R2), where T is the intensity of the surface-tension and
R1, R2 are the radii of curvature of any two sections normal to the
surface and to each other.
[Illustration: FIG. 3.]
If three fluids which do not mix are in contact with each other, the
three surfaces of separation meet in a line, straight or curved. Let O
(fig. 3) be a point in this line, and let the plane of the paper be
supposed to be normal to the line at the point O. The three angles
between the tangent planes to the three surfaces of separation at the
point O are completely determined by the tensions of the three surfaces.
For if in the triangle abc the side ab is taken so as to represent on a
given scale the tension of the surface of contact of the fluids a and b,
and if the other sides bc and ca are taken so as to represent on the
same scale the tensions of the surfaces between b and c and between c
and a respectively, then the condition of equilibrium at O for the
corresponding tensions R, P and Q is that the angle ROP shall be the
supplement of abc, POQ of bca, and, therefore, QOR of cab. Thus the
angles at which the surfaces of separation meet are the same at all
parts of the line of concourse of the three fluids. When three films of
the same liquid meet, their tensions are equal, and, therefore, they
make angles of 120 deg. with each other. The froth of soap-suds or
beaten-up eggs consists of a multitude of small films which meet each
other at angles of 120 deg.
If four fluids, a, b, c, d, meet in a point O, and if a tetrahedron ABCD
is formed so that its edge AB represents the tension of the surface of
contact of the liquids a and b, BC that of b and c, and so on; then if
we place this tetrahedron so that the face ABC is normal to the tangent
at O to the line of concourse of the fluids abc, and turn it so that the
edge AB is normal to the tangent plane at O to the surface of contact of
the fluids a and b, then the other three faces of the tetrahedron will
be normal to the tangents at O to the other three lines of concourse of
the liquids, and the other five edges of the tetrahedron will be normal
to the tangent planes at O to the other five surfaces of contact.
If six films of the same liquid meet in a point the corresponding
tetrahedron is a regular tetrahedron, and each film, where it meets the
others, has an angle whose cosine is -1/3. Hence if we take two nets of
wire with hexagonal meshes, and place one on the other so that the point
of concourse of three hexagons of one net coincides with the middle of a
hexagon of the other, and if we then, after dipping them in Plateau's
liquid, place them horizontally, and gently raise the upper one, we
shall develop a system of plane laminae arranged as the walls and floors
of the cells are arranged in a honeycomb. We must not, however, raise
the upper net too much, or the system of films will become unstable.
When a drop of one liquid, B, is placed on the surface of another, A,
the phenomena which take place depend on the relative magnitude of the
three surface-tensions corresponding to the surface between A and air,
between B and air, and between A and B. If no one of these tensions is
greater than the sum of the other two, the drop will assume the form of
a lens, the angles which the upper and lower surfaces of the lens make
with the free surface of A and with each other being equal to the
external angles of the triangle of forces. Such lenses are often seen
formed by drops of fat floating on the surface of hot water, soup or
gravy. But when the surface-tension of A exceeds the sum of the tensions
of the surfaces of contact of B with air and with A, it is impossible to
construct the triangle of forces; so that equilibrium becomes
impossible. The edge of the drop is drawn out by the surface-tension of
A with a force greater than the sum of the tensions of the two surfaces
of the drop. The drop, therefore, spreads itself out, with great
velocity, over the surface of A till it covers an enormous area, and is
reduced to such extreme tenuity that it is not probable that it retains
the same properties of surface-tension which it has in a large mass.
Thus a drop of train oil will spread itself over the surface of the sea
till it shows the colours of thin plates. These rapidly descend in
Newton's scale and at last disappear, showing that the thickness of the
film is less than the tenth part of the length of a wave of light. But
even when thus attenuated, the film may be proved to be present, since
the surface-tension of the liquid is considerably less than that of pure
water. This may be shown by placing another drop of oil on the surface.
This drop will not spread out like the first drop, but will take the
form of a flat lens with a distinct circular edge, showing that the
surface-tension of what is still apparently pure water is now less than
the sum of the tensions of the surfaces separating oil from air and
water.
The spreading of drops on the surface of a liquid has formed the subject
of a very extensive series of experiments by Charles Tomlinson; van der
Mensbrugghe has also written a very complete memoir on this subject
(_Sur la tension superficielle des liquides_, Bruxelles, 1873).
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
contact of the two fluids meets the surface of the solid depends on the
values of the three surface-tensions. If a and b are the two fluids and
c the solid then the equilibrium of the tensions at the point O depends
only on that of thin components parallel to the surface, because the
surface-tensions normal to the surface are balanced by the resistance of
the solid. Hence if the angle ROQ (fig. 4) at which the surface of
contact OP meets the solid is denoted by [alpha],
T_(bc) - T_(ca) - T_(ab) cos[alpha] = 0,