course impossible. In that case,y¼0 and the solid is said to be fully wetted
by the liquid: given enough space, the liquid will spread in a thin layer over
the solid. Many liquids, including water and nearly all aqueous solutions,
give zero contact angle at clean glass. The other extreme is thaty¼ 1808 ;in
that case the solid is not wetted at all, and a small drop tends to ‘‘float’’ on
the solid, making no contact.
All these configurations are, however, modified if also other forces
are acting on the system. In most situations, gravity plays a part, and the
shapes given would then only be true if it concerned very small drops
(e.g.,< 0.1 mm). Figure 10.24b shows by a broken line the effect of
gravity for a certain case. The drop becomes flatter and attains a larger
diameter, but the contact angle (in this case 90 8 ) remains the same.
In the case depicted in Figure 10.24a, the vertical component of the
interfacial tension A–L, which equalsgAL?sin y, is balanced by elastic
reaction forces of the solid. Such forces cannot be exerted by (Newtonian)
liquids, and for three fluid phases alensas depicted in Figure 10.24d may be
formed; the example given concerns paraffin oil, water, and air. Now two
equations for a balance of forces must be met,
gaw¼gAOcosy 1 þgOWcosy 2
gAOsiny 1 ¼gOWsiny 2ð 10 : 11 Þ(Note: For convenience, we have taken the contact angley¼y 1 þy 2 ,inthe
oil phase, rather than in the denser water phase.) The three interfacial
tensions can be determined (see data in Table 10.1) and the configuration of
the drop at the interface can thus be calculated. The shape of the drop and
of the A–W interface near the drop will also be affected by gravity. Ifyis
fairly small, a large drop will attain a shape as in Figure 10.24e.
Following Eq. (10.11), a two-dimensionalspreading pressurecan be
defined,
Ps¼gAWðgAOþgOWÞð 10 : 12 ÞIfPs>0, spreading of oil over the A–W interface will occur, as depicted in
Figure 10.24f. For example, if the oil is a triglyceride oil, the data in Table
10.1 givePs¼ 72 (30þ35)¼7mN?m^1 ; hence the oil will spread over
the surface. Given sufficient space, the oil layer can spread until it is one
molecule thick. The data in Table 10.1 also indicate that paraffin oil will not
spread over an A–W surface. Actually, Eq. (10.12) also applies to solid
surfaces, but it is generally not so well obeyed (see Section 10.6.2).
For the case that Eq. (10.12) applies andPs>0, it is easy to see that
the total interfacial free energy is smallest if the water surface is covered by