Capillarity and Surface Forces (Liquids) - Surface and Colloid Chemistry: Principles and Applications - page 26

The pendant drop method is very useful under specific conditions:

1. Technically, only a drop (a few microliters) is required. For example, eye
fluid can be studied since only a drop of one microliter is needed.

2. It can be used under very extreme conditions (very high temperature or cor-
rosive fluids).

3. It can be used under very high pressure and temperatures. Oil reservoirs
are found typically at 100°C and 300 atm pressure. The surface tension of
such systems can be conveniently studied by using high pressure and tem-
perature cells with optical clear windows (sapphire windows 1 cm thick;
up to 2000 atm). For example, γ of inorganic salts at high temperatures (ca.
1000°C) can be measured using this method. The variation in surface ten-
sion can be studied as a function of various parameters (temperature and
pressure; additives [gas, etc.]).

2.6.2 T h e r I n g m e T h o d
A method that has been rather widely used involves the determination of the force to
detach a ring or loop of wire from the surface of a liquid. Originally developed by du
Nouy, this method is based on using a ring (platinum) and measuring the force when
it is dipped in the liquid surface.
This is one of the many detachment methods of which the drop weight and the
Wilhelmy slide methods are also examples. As with all detachment methods, one
supposes that, within an accuracy of a few percent, the detachment force is given
by the surface tension multiplied by the periphery of the surface (liquid surface)
detached (from a solid surface of a tubing or ring or plate). This assumption is also
found to be acceptable for most experimental purposes. Thus, for a ring, as illus-
trated in Figure 2.12,

W total = W ring + 2 (2 π R ring ) γ (2.35)

= W ring + 4 π R ring γ (2.36)

where W total is the total weight of the ring, W ring is the weight of the ring in air, and
R ring is the radius of the ring. The circumference is 2 π R ring , and factor 2 is because
of the two sides of contact.
This relation assumes that the contact between the fluid and the ring is geometri-
cally simple. It is also found that this relation is fairly correct (better than 1%) for
most working situations. However, it was observed that Equation 2.36 needed a cor-
rection factor in much the same way as was done for the drop weight method. Here,
however, there is one additional variable, so that the correction factor f now depends
on two dimensionless ratios.
Experimentally, the method is capable of good precision. A so-called chainomatic
balance has been used to determine the maximum pull, but a popular simplified ver-
sion of the tensiometer, as it is sometimes called, makes use of a torsion wire and is
quite compact. Among experimental details to mention are that the dry weight of the