and the thickness of the film between approaching globules may then remain
greater than the distance over which crystals protrude. A higherCvalue
leads to a greater shear stress,forcing the globules together. A threshold
value ofCfor partial coalescence to occur is often observed; above that
value, the coalescence rate is about proportional toC: see curve 2. The
threshold value and the magnitude ofaat higherCvary considerably with
composition and structure of the system. For the same shear stress,larger
globulesare pressed together with a greater force and will thus be less stable,
which may explain part of the trend in frame (c).
Subjecting the system toturbulent flowleads to even faster aggrega-
tion.
- Protruding crystals. Actually, it concerns two variables: how many
crystals protrude and how large they are. The number is strongly dependent
on the fraction solid of the fat (js); cf. frame (d). IfjSis below a certain
threshold value, the crystals cannot form a network spanning the diameter
of the globule. This follows from fractal aggregation theory: see Formula
(13.18). In practice, the threshold value is of the order of 0.1. Below that
value, crystals will generally not protrude very far, and they may even be
pushed into the oil on encountering another globule. Presumably,
protrusion does especially arise from the shrinking of the globule due to
ongoing crystallization after the network has formed. As more fat
crystallizes, more crystals will protrude and over a greater distance. The
distance may also depend on the size of the crystals in the network. Several
other factors will determine the results, including triglyceride composition
and crystallization history, which primarily implies temperature history; see
Section 15.4. Exceptionally, crystals may grow out of the globules, making
very long protrusions. In such a case, the system is extremely unstable:
merely pouring it causes immediate formation of very large lumps or even a
solid network of globules; presumablya&1.
Another factor affecting the effective number of protruding crystals is
theglobule size. This is because the area of the film between approaching
spheres is proportional to sphere diameter; see Figure 13.15b. Moreover,
large globules may contain larger crystals that protrude farther. The effect
of globule size on partial coalescence rate is always large; see frame (c). - Contact angle. To allow wetting of the crystal by the oil in the
second globule, the contact angleyshould be between 90 and 180 degrees. If
crystals have the freedom to move to an equilibrium position in the O–W
interface, the three interfacial tensions will determine the contact angle: see
Eq. (10.10). A smalleryvalue will mean fartherprotrusionof the crystal into
the aqueous phase, as is illustrated in Figure 10.25. It has indeed been
observed that the partial coalescence rate increases when one adds more
sodium dodecyl sulfate (as in Figure 10.25) prior to crystallization. For