Page 13 - AN INTRODUCTION TO SURFACE CHEMISTRY By ERIC KEIGHTLEY RIDEAL

8 SURFACE TENSION OF LIQUIDS

4. The capillary rise method.
Of the methods of measuring surface tension that depending on
the rise of liquid in a capillary tube has been more widely used
than any, with the possible exception of the drop-weight method.
This is because, of all the static methods, of methods, that is, which
give an equilibrium value for the surface tension, the conditions
are the most clearly defined, and the calculations based upon them
have a greater degree of certainty. It can be used equally at high
and at very low temperatures: by this means Ramsay carried out
determinations of the surface tension of organic liquids up to their
critical points, and Kammerlingh Onnes that of hydrogen almost
to its freezing point.
When a glass capillary tube is dipped into water the liquid
rises in the tube above the general level of the water to a height
which is approximately in inverse proportion to the radius of the
tube, We may explain this event somewhat as follows: Water
wets glass; it tends, that is, to spread over its surface and displace
therefrom the air. In order that this may occur the sum of the
surface energies involved must be reduced, and if nothing hinders
(that is if the contact angle be zero), the water will continue to
spread until all the glass is covered or all the water has been used
to form a thin continuous film. When a vertical tube provides the
surface over which the water must spread we have however
a balancing tendency due to the effect of gravity on the water
raised up in the tube. If the tube is narrow enough the rise of
level is easy to calculate from the principle of virtual work. Let
00% 0 represent the surface tension of water-air, glass-air and
glass-water respectively. Imagine an infinitesimal rise of the
liquid in the tube above its equilibrium position, without change
of shape of the meniscus and therefore without altering the total
free surface energy water-air. If h be the equilibrium height
of the liquid, Sh the increase to this and r the radius of the
tube, the surface glass-air will be diminished and the surface
glass-water increased by an amount 2nr Sh cm.' 'The surface
energy will thus be diminished by (a,-o,) 2mr8h. 'The potential
energy due to gravity will be at the same time increased by
grh(p-p) &h where p, p are the densities of water and air