cos[alpha] = (T_(bc) - T_(ca))/T_(ab).
As an experiment on the angle of contact only gives us the difference of
the surface-tensions at the solid surface, we cannot determine their
actual value. It is theoretically probable that they are often negative,
and may be called surface-pressures.
[Illustration: FIG. 4. ]
The constancy of the angle of contact between the surface of a fluid and
a solid was first pointed out by Dr Young, who states that the angle of
contact between mercury and glass is about 140 deg. Quincke makes it
128 deg. 52'.
If the tension of the surface between the solid and one of the fluids
exceeds the sum of the other two tensions, the point of contact will not
be in equilibrium, but will be dragged towards the side on which the
tension is greatest. If the quantity of the first fluid is small it will
stand in a drop on the surface of the solid without wetting it. If the
quantity of the second fluid is small it will spread itself over the
surface and wet the solid. The angle of contact of the first fluid is
180 deg. and that of the second is zero.
If a drop of alcohol be made to touch one side of a drop of oil on a
glass plate, the alcohol will appear to chase the oil over the plate,
and if a drop of water and a drop of bisulphide of carbon be placed in
contact in a horizontal capillary tube, the bisulphide of carbon will
chase the water along the tube. In both cases the liquids move in the
direction in which the surface-pressure at the solid is least.
[In order to express the dependence of the tension at the interface of
two bodies in terms of the forces exercised by the bodies upon
themselves and upon one another, we cannot do better than follow the
method of Dupre. If T12 denote the interfacial tension, the energy
corresponding to unit of area of the interface is also T12, as we see
by considering the introduction (through a fine tube) of one body into
the interior of the other. A comparison with another method of
generating the interface, similar to that previously employed when but
one body was in question, will now allow us to evaluate T12.
The work required to cleave asunder the parts of the first fluid which
lie on the two sides of an ideal plane passing through the interior, is
per unit of area 2T1, and the free surface produced is two units in
area. So for the second fluid the corresponding work is 2T2. This having
been effected, let us now suppose that each of the units of area of free
surface of fluid (1) is allowed to approach normally a unit area of (2)
until contact is established. In this process work is gained which we
may denote by 4T'12, 2T'12 for each pair. On the whole, then, the work
expended in producing two units of interface is 2T1 + 2T2 - 4T'12, and
this, as we have seen, may be equated to 2T12. Hence