Agitation also tends to decrease the width of the crystal size distribution,
because local variation in supersaturation is reduced.
Question
Assume a solution supersaturated with one crystallizable solute. To part of the
solution, a crystal growth inhibitor is added. It is established that in both cases the
relationLC¼a(lnb)^2 holds, only the constantabeing different. Assume now that
both solutions have the same initial, rather weak, supersaturation and that
crystallization is started by adding tiny seed crystals. Would the ratio of the overall
crystallization rates dj/dtnow be the same as the ratio of bothavalues?
Answer
Assuming for the momentLCto remain constant in time, and the crystals to have
spherical shape, we may assume that
dj
dt
¼Npr^2 LCwhereNis the number of crystals per unit volume.ris crystal radius, and it will of
course increase during crystallization, its magnitude being given byLCt(neglecting
the radius of the seed crystal). Insertion and integration then yields
j¼
1
3
pNL^3 Ct^3 ¼
1
3
pNa^3 ½lnbðtÞ^2 t^3The growth rate would thus be proportional toa^3. Sincebdecreases with time in a
manner depending on the value ofa, the relation will become more complicated, but
the growth rate will be always more than proportional toa.
15.3 CRYSTALLIZATION FROM AQUEOUS
SOLUTIONS
Crystallization in aqueous systems is by far the most common case in foods
and food processing. Either water or the solute(s) can crystallize, and in
some cases both. We will in this section primarily consider crystallization of
a single solute. Moreover, the formation and properties of ice are briefly
discussed.