Let us consider the crystallization of sugar solution in water at 40°C. We will use the BCF expression (see section 2.3.7):
This rate is unrealistic, but could be reduced if the frequency chosen for the molecular vibrations were lower or if the dissolution heat were positive. In reality, we group these two values together in an empirical coefficient K.
Let us examine the transfer through the diffusion layer (with odiff = 0.2) (see section 2.3.2):
On saturation, the volume fraction of sugar is:
Integration layer and diffusion layer combination
As the integration rate (example I) is extremely high, the crystallization rate is determined by crossing the diffusion layer (example II).
Thus, any experimental value of R must be interpreted by taking the diffusion layer into account in order to correctly assess supersaturation.
Practice of sugar crystallization
The three crystallization techniques
These are the only three techniques that can be used to make crystals (with the exception of chemical precipitation).
1) Vaporization of the solvent by heating with vapor to obtain sugar A occurs with a vapor pressure in the order of 0.18-0.20 bar abs for 3 h at
70°C. Of course, a preparation time of more than 20 mn at 80°C provokes crystal and liquid coloration, particularly if the invert sugar content exceeds a certain limit and if the juice is not sulfated. This is why we often proceed by cooling.
We mix the exit crystallization A syrup with the thick syrup. The solvent’s vaporization then gives the sugar B and green syrup.
2) Cooling by expansion. Depending on the circumstances, cooling by 80-60°C or by 70-40°C (pressure: 0.05 bar abs) can occur. Green syrup must be added to reduce the apparent viscosity of the magma from 1,500 to 150 Pa.s.
This occurs progressively at a cooling rate of 7-11°C.h-1.
Crystallization by cooling is used in the final phase, that is, for sugar C together with the production of seed magma. However, cooling can be produced not only by expansion but also by an exterior agent.
3) Cooling by water or air. The sugar A magma is cooled from 70 to 35°C at a rate of 6°C.h-1, which can increase the production by 30% compared with simply steam vaporizing water. However, for sugar A, the steam vaporization is typically preferred over cooling.
Sugar B magma is cooled from 80 to 50°C with service water at a rate of 10°C.h-1. With air as a cooling agent, we can only cool to 80-60°C in 10 h or 2°C.h-1.
For sugar C, cooling is preferred to vaporization of water in the juice, at a rate of 1-1.5°C.h-1 from 80 to 40°C.
The temperature difference between water and magma is from 10 to 15°C. Cooling occurs with tubes of diameter 10-15 cm through which the magma circulates at a velocity above 0.1 m.s-1. Surface integration is crucial, with viscosity not exceeding 15 Pa.s.
NOTE.- The production of steam vapor during vaporization does not present significant problems of liquid entrainment, since droplets are larger and denser than for standard crystallizations.