Once crystallization is concluded, equilibrium is set up between the crystals of pure solute and the residual mother liquor, the balance being determined by the solubility (concentration) and the temperature. The driving force making the crystals grow is the concentration excess (supersaturation) of the solution above the equilibrium (saturation) level. The resistances to growth are the resistance to mass transfer within the solution and the energy needed at the crystal surface for incoming molecules to orient themselves to the crystal lattice.
Solubility is defined as the maximum weight of anhydrous solute that will dissolve in 100 g of solvent. In the food industry, the solvent is generally water.
Solubility is a function of temperature. For most food materials increase in temperature increases the solubility of the solute as shown for sucrose in Fig. 9.8. Pressure has very little effect on solubility.
To remove more salt, this solution would have to be concentrated by removal of water, or else cooled to a lower temperature.
When a solution is cooled to produce a supersaturated solution and hence to cause crystallization, the heat that must be removed is the sum of the sensible heat necessary to cool the solution and the heat of crystallization. When using evaporation to achieve the supersaturation, the heat of vaporization must also be taken into account. Because few heats of crystallization are available, it is usual to take the heat of crystallization as equal to the heat of solution to form a saturated solution. Theoretically, it is equal to the heat of solution plus the heat of dilution, but the latter is small and can be ignored. For most food materials, the heat of crystallization is positive, i.e. heat is given out during crystallization. Note that heat of crystallization is the opposite of heat of solution. If a material takes in heat, i.e. has a negative heat of solution, then the heat of crystallization is positive. Heat balances can be calculated for crystallization.
Heat lost in the
solution = sensible heat + heat of crystallization
40.8 x 104 + 4.07 x 104 = 4 x 104 + 3.14 x 104 + heat removed by cooling.
Heat removed in cooling = 37.7 x 104 kJ
Once nucleii are formed, either spontaneously or by seeding, the crystals will continue to grow so long as supersaturation persists. The three main factors controlling the rates of both nucleation and of crystal growth are the temperature, the degree of supersaturation and the interfacial tension between the solute and the solvent. If supersaturation is maintained at a low level, nucleus formation is not encouraged but the available nucleii will continue to grow and large crystals will result. If supersaturation is high, there may be further nucleation and so the growth of existing crystals will not be so great. In practice, slow cooling maintaining a low level of supersaturation produces large crystals and fast cooling produces small crystals.
Nucleation rate is also increased by agitation. For example, in the preparation of fondant for cake decoration, the solution is cooled and stirred energetically. This causes fast formation of nucleii and a large crop of small crystals, which give the smooth texture and the opaque appearance desired by the cake decorator.
Once nucleii have been formed, the important fact in crystallization is the rate at which the crystals will grow. This rate is controlled by the diffusion of the solute through the solvent to the surface of the crystal and by the rate of the reaction at the crystal face when the solute molecules rearrange themselves into the crystal lattice.
These rates of crystal
growth can be represented by the equations
where dw is the increase in weight of crystals in time dt, A is the surface area of the crystals, c is the solute concentration of the bulk solution, ci is the solute concentration at the crystal/solution interface, cs is the concentration of the saturated solution, Kd is the mass transfer coefficient to the interface and Ks is the rate constant for the surface reaction.
These equations are not easy to apply in practice because the parameters in the equations cannot be determined and so the equations are usually combined to give:
and dL/dt is the rate of growth of the side of the crystal and rs is the density of the crystal.
It has been shown that at low temperatures diffusion through the solution to the crystal surface requires only a small part of the total energy needed for crystal growth and, therefore, that diffusion at these temperatures has relatively little effect on the growth rate. At higher temperatures, diffusion energies are of the same order as growth energies, so that diffusion becomes much more important. Experimental results have shown that for sucrose the limiting temperature is about 45°C, above which diffusion becomes the controlling factor.
Impurities in the solution retard crystal growth; if the concentration of impurities is high enough, crystals will not grow.
When the first crystals have been separated, the mother liquor can have its temperature and concentration changed to establish a new equilibrium and so a new harvest of crystals. The limit to successive crystallizations is the build up of impurities in the mother liquor which makes both crystallization and crystal separation slow and difficult. This is also the reason why multiple crystallizations are used, with the purest and best crystals coming from the early stages.
For example, in the manufacture of sugar, the concentration of the solution is increased and then seed crystals are added. The temperature is controlled until the crystal nucleii added have grown to the desired size, then the crystals are separated from the residual liquor by centrifuging. The liquor is next returned to a crystallizing evaporator, concentrated again to produce further supersaturation, seeded and a further crop of crystals of the desired size grown. By this method the crystal size of the sugar can be controlled. The final mother liquor, called molasses, can be held indefinitely without producing any crystallization of sugar.
Calculate the yield of sugar in each evaporator and the concentration of sucrose in the mother liquor leaving the final evaporator.
The sugar solubility figures are taken from the solubility curve, Fig. 9.7.
MASS BALANCE (weights in kg)
Basis 5000 kg sugar solution h-1
Total Sugar - Sugar crystallized 2975 kg : Liquor from effect 275 kg
Yield in first effect
Total yield 91.6%
Quantity of sucrose in final syrup 275 kg/h-1
Concentration of final syrup 73.5% sucrose
Crystallizers can be divided into two types: crystallizers and evaporators. A crystallizer may be a simple open tank or vat in which the solution loses heat to its surroundings. The solution cools slowly so that large crystals are generally produced. To increase the rate of cooling, agitation and cooling coils or jackets are introduced and these crystallizers can be made continuous. The simplest is an open horizontal trough with a spiral scraper. The trough is water jacketed so that its temperature can be controlled.
An important crystallizer in the food industry is the cylindrical, scraped surface heat exchanger, which is used for plasticizing margarine and cooking fat, and for crystallizing ice cream. It is essentially a double-pipe heat exchanger fitted with an internal scraper, see Fig. 6.3(c). The material is pumped through the central pipe and agitated by the scraper, with the cooling medium flowing through the annulus between the outer pipes.
A crystallizer in which considerable control can be exercised is the Krystal or Oslo crystallizer. In this, a saturated solution is passed in a continuous cycle through a bed of crystals. Close control of crystal size can be obtained.
Evaporative crystallizers are common in the sugar and salt industries. They are generally of the calandria type. Vacuum evaporators are often used for crystallization as well, though provision needs to be made for handling the crystals. Control of crystal size can be obtained by careful manipulation of the vacuum and feed. The evaporator first concentrates the sugar solution, and when seeding commences the vacuum is increased. This increase causes further evaporation of water which cools the solution and the crystals grow. Fresh saturated solution is added to the evaporator and evaporation continued until the crystals are of the correct size. In some cases, open pan steam-heated evaporators are still used, for example in making coarse salt for the fish industry. In some countries, crystallization of salt from sea water is effected by solar energy which concentrates the water slowly and this generally gives large crystals.
Crystals are regular in shape: cubic, rhombic, tetragonal and so on. The shape of the crystals forming may be influenced by the presence of other compounds in the solution, even in traces. The shape of the crystal is technologically important because such properties as the angle of repose of stacked crystals and rate of dissolving are related to the crystal shape. Another important property is the uniformity of size of the crystals in a product. In a product such as sucrose, a non-uniform crystalline mixture is unattractive in appearance, and difficult to handle in packing and storing as the different sizes tend to separate out. Also the important step of separating mother liquor from the crystals is more difficult.
Contact-Equilibrium Processes - APPLICATIONS > MEMBRANE SEPARATIONS
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