an oil layer. Also the solutions of Eqs. (10.10) and (10.11) represent
minimum values of the interfacial free energy of the system. The equations
given can also be derived by minimizing interfacial free energy.
10.6.2 Wetting
In Figure 10.22a the material of the capillary—say, glass—is completely
wetted by the liquid—say, water. In other words, the contact angle equals
zero. If the contact angle is finite, the radius of curvature of the meniscus is
rand it will be given byr/cosy. Consequently, Eq. (10.8) is modified to
h¼2 gcosy
rrgð 10 : 13 ÞThis implies that the capillary rise is decreased. Ify¼ 908 , there is no
capillary rise, and fory> 908 , there is capillary depression. In Figure 20.22c
as compared to b, the capillary depression is reduced by a factor cos 135/cos
180 ¼0.71.
Contact angles can be modified by the addition of asurfactant, since
that alters interfacial tension. This is illustrated in Figure 10.25a, for
spherical solid particles (S) at an O–W interface. The contact angle in the
aqueous phase decreases as the surfactant concentration increases, and it
can even become zero, implying that the particle enters the aqueous phase,
being dislodged from the O–W interface. Figure 10.25b gives a kind of state
diagram. Straight lines of constantygo through the origin. At or above the
line fory¼0, the solid would be completely wetted by the aqueous phase; at
or belowy¼ 1808 , it is completely wetted by oil; in between, there is partial
wetting.
The system to which the data in Figure 10.25 roughly apply is of solid
triacylglycerols (saturated, long-chain;b^0 -crystals), liquid triacylglycerol oil
and a solution of Na-lauryl sulfate (SDS). It is seen that, without surfactant,
the solid is far better wetted by the oil than by water, as is to be expected.
From Table 1, we obtaingOW¼30 mN?m^1 , and it is generally found that
the contact angle for fat crystals at a pure O–W interface& 1508. This leads
togOWcosy¼26 and taking from Table 1gOS¼4 (value derived from
crystallization kinetics; see Chapter 15), we obtaingWS&30 mN?m^1 , i.e.,
(nearly) the same value asgOW. If SDS is added,gOWandyboth decrease, in
such a way that the curve in Figure 20.25b is practically straight and of slope
1; this implies that the value ofgOSremains constant. The Young equation
(10.10) then predicts that the differencegWS–gOW(which we presumed to be
almost zero in the absence of SDS) remains constant. Application of the
Gibbs equation (10.2) then leads to the conclusion that SDS must adsorb to