Physical Chemistry of Foods

consequence is that the face does not remain flat on amm scale, but becomes
curved(convex). For most crystal faces a very high supersaturation is needed
to achieve kinetic roughening. It has been observed for some of the faces of
paraffin crystals at high lnb. The shape of these crystals then becomes
almost like a very flat cylinder.

15.2.2 Factors Affecting Growth Rate

The linear growth rates of crystal faces vary enormously. Some approximate
examples of the average rate for crystallization from solution are

Sucrose lnb¼0.1 Rate&100 nm?s
^1

a-Lactose hydrate lnb¼0.4 Rate&1nm?s
^1

Compound fat lnb¼0.4 Rate& 0 :05 nm?s
^1

Moreover, the rates generally vary between the faces of one crystal, and it is
not uncommon that some faces do not grow at all under some conditions.
Below, the main variables affecting growth rate are discussed.

Supersaturation. This has been discussed above. Note that not
only the rate at a certain value of lnbvaries but also the kind of relation
between rate and ln b. Approximating the relation to LC!ðlnbÞn, the
exponent varies considerably, say from 1 to 4, withn&2 being a fairly
common value.

Transport to the Crystal Surface. It is the supersaturation at the
crystal surface that is determinant and that may be below the average value.
If the rate of attachment to the crystal is high, the diffusional transport may
be too slow to keep up with the local depletion of solute, and the rate of
crystallization will bediffusion limited. See Section 5.2.2 for theory on
diffusion. If (mild) stirring enhances the crystallization rate, there is
diffusion limitation. A clear example is crystallization of sucrose during
sugar boiling. Even when stirring, diffusion has to occur through a laminar
boundary layer, thickness about 10–100mm.
If the rate of attachment is small, the system tends to be ideally mixed,
and the crystallization rate then isreaction limitedor interface controlled. Of
course, intermediate situations can occur. In food processing and storage,
most crystallization is reaction limited. However, in foods of high viscosity
or with narrow pores through which the solute has to move, diffusion may
be the limiting step.