is depicted by the broken line in Figure 10.25b; it applies to solid tristearate,
water, and a triacylglycerol oil with various oil-soluble surfactants.
Adhesion. Solid particles can thus become lodged in a fluid
interface, like fat crystals in an O–W or A–W interface. This is often
calledadhesion. An important parameter is the strength of the adhesion, for
instance when considering so-called Pickering stabilization of emulsion
droplets by small particles (see Section 13.4.2), or flotation (small particles
in a liquid can be removed by adsorption onto air bubbles in the liquid and
subsequent creaming). The free energy needed to remove a particle from the
interface, i.e., forygoing from its equilibrium value to zero, is for spherical
particles given by
Dy 0 G¼pr^2 gOWð 1 cosyÞ^2 ð 10 : 14 ÞTaking as an example the particles in Figure 10.25a forc¼0, we havegOW
¼0.03 N?m^1 ,y¼ 1508 , and assuming a particle radiusr¼ 1 mm, we obtain
forDG3.3? 10 ^13 J, corresponding to about 8? 107 timeskBT. This means
that the particle will never become dislodged spontaneously (i.e., owing to
its Brownian motion). In other words, fat crystals do very strongly adhere to
an O–W interface, illustrating again that surface forces can have large
effects. Even for a particle as small as 10 nm radius, withg¼0.002 andy¼
458 (Fig. 10.22a, No. 4),DGwould amount to about 13 timeskBT, implying
that it would not readily become dislodged (e^13 & 2? 10 ^6 ). For still
smaller particles, we enter the realm of macromolecules, and a molecular
treatment as given in Section 10.2 would be needed.
Complications. Several factors affect the contact angles and
thereby wetting. The interfacial tensions may differ from the tabulated
values and change with time if the liquids involved are to some extent
mutually soluble; dissolution may be a slow process. Such changes become
more important if surfactants are present. In most cases, the surfactant
(mixture) is added to one phase, and upon contact between the phases it
may go not only to phase boundaries, which takes some time but also
dissolve in one of the other phases, which would probably take a longer
time. All these processes may affect contact angle and wetting, the latter
especially if the spreading pressure [Eq. (10.12)] is close to zero.
Important complications often arise for thewetting of solids, say of
water on a solid surface in contact with air or with oil (Fig. 10.24, upper
row). These include
The solidsurface is inhomogeneous. This is virtually always the case if
the material contains several components that are not fully mixed,
which is very common in foods; consider, e.g., chocolate, biscuits,