CHAPTER 9
CONTACT EQUILIBRIUM PROCESSES - APPLICATIONS (cont'd)

CRYSTALLIZATION

Crystallization Equilibrium
Solubility
Heat of crystallisation
Rate of Crystal Growth
Stage-equilibrium Crystallization
Crystallization Equipment


Crystallization is an example of a separation process in which mass is transferred from a liquid solution, whose composition is generally mixed, to a pure solid crystal. Soluble components are removed from solution by adjusting the conditions so that the solution becomes supersaturated and excess solute crystallizes out in a pure form. This is generally accomplished by lowering the temperature, or by concentration of the solution, in each case to form a supersaturated solution from which crystallization can occur. The equilibrium is established between the crystals and the surrounding solution, the mother liquor. The manufacture of sucrose, from sugar cane or sugar beet, is an important example of crystallization in food technology. Crystallization is also used in the manufacture of other sugars, such as glucose and lactose, in the manufacture of food additives, such as salt, and in the processing of foodstuffs, such as ice cream. In the manufacture of sucrose from cane, water is added and the sugar is pressed out from the residual cane as a solution. This solution is purified and then concentrated to allow the sucrose to crystallize out from the solution.

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 and Saturation

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.

Figure 9.8 Solubility and saturation curves for sucrose in water

During crystallization, the crystals are grown from solutions with concentrations higher than the saturation level in the solubility curves. Above the supersaturation line, crystals form spontaneously and rapidly, without external initiating action. This is called spontaneous nucleation. In the area of concentrations between the saturation and the supersaturation curves, the metastable region, the rate of initiation of crystallization is slow; aggregates of molecules form but then disperse again and they will not grow unless seed crystals are added. Seed crystals are small crystals, generally of the solute, which then grow by deposition on them of further solute from the solution. This growth continues until the solution concentration falls to the saturation line. Below the saturation curve there is no crystal growth, crystals instead dissolve.

EXAMPLE 9.8. Crystallization of sodium chloride
If sodium chloride solution, at a temperature of 40°C, has a concentration of 50% when the solubility of sodium chloride at this temperature is 36.6 g / 100 g water, calculate the quantity of sodium chloride crystals that will form once crystallization has been started.

Weight of salt in solution = 50 g / 100 g solution
                                     = 100 g / 100 g water.
Saturation concentration  = 36.6 g / 100 g water

Weight crystallized out    = (100 - 36.6) g / 100 g water
                                     = 63.4 g / 100 g water

To remove more salt, this solution would have to be concentrated by removal of water, or else cooled to a lower temperature.

Heat of crystallization

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.

EXAMPLE 9.9. Heat removal in crystallization cooling of lactose
Lactose syrup is concentrated to 8 g lactose per 10 g of water and then run into a crystallizing vat which contains 2500 kg of the syrup. In this vat, containing 2500 kg of syrup, it is cooled from 57°C to 10°C. Lactose crystallizes with one molecule of water of crystallization. The specific heat of the lactose solution is 3470 J kg^-1 °C^-1. The heat of solution for lactose monohydrate is -15,500 kJ mol^-1. The molecular weight of lactose monohydrate is 360 and the solubility of lactose at 10°C is 1.5 g / 10 g water. Assume that 1% of the water evaporates and that the heat loss through the vat walls is 4 x 10⁴ kJ. Calculate the heat to be removed in the cooling process.

Heat lost in the solution = sensible heat + heat of crystallization

Heat removed from solution = heat removed through walls + latent heat of evaporation + heat removed by cooling                                        
Heat Balance: Heat lost in the solution = Heat removed from solution
       Sensible heat lost from solution when cooled from 57°C to 10°C = 2500 x 47 x 3.470
                                              = 40.8 x 10⁴ kJ

Heat of crystallization       = -15,500 kJ mole^-1
                                      = -15,500/360
                                      = - 43.1 kJ kg^-1
Solubility of lactose at 10°C, 1.5 g / 10 g water,
Anhydrous lactose crystallized out = (8 - 1.5)
                                      = 6.5 g / 10 g water
Hydrated lactose crystallized = 6.5 x (342 + 18)/(342)
                                      = 6.8 g / 10 g water
Total water                      = (10/18) x 2500 kg
                                      = 1390 kg
Total hydrated lactose crystallized out = (6.8 x 1390)/10
                                      = 945 kg
Total heat of crystallization = 945 x - 43.1
                                      = 4.07 x 10⁴
Heat removed by vat walls = 4.0 x 10⁴ kJ.
Water evaporated             = 1% = 13.9 kg
The latent heat of evaporation is, from Steam Tables, 2258 kJ kg^-1
Heat removed by evaporation    = 13.9 x 2258 kJ
                                             = 3.14 x 10⁴ kJ.

Heat balance

            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

Rate of Crystal Growth

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
                    dw/dt = K_dA(c - c_i)                                                                                       (9.13)
                    dw/dt = K_s(c_i - c_s)                                                                                       (9.14)

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, c_i is the solute concentration at the crystal/solution interface, c_s is the concentration of the saturated solution, K_d is the mass transfer coefficient to the interface and K_s 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:

             dw/dt = KA(c - c_s)                                                                                       (9.15)

where
               1/K = 1/K_d + 1/K_s
or          dL/dt = K(c - c_s)/r_s                                                                                     (9.16)
since        dw = Ar_sdL

and dL/dt is the rate of growth of the side of the crystal and r_s 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.

Stage-equilibrium Crystallization

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.

EXAMPLE 9.10. Multiple stage sugar crystallisation by evaporation
The conditions in a series of sugar evaporators are:
First evaporator: temperature of liquor at 85°C, concentration of entering liquor 65%, weight of entering      liquor 5000 kg h^-1, concentration of liquor at seeding, 82%.
Second evaporator: temperature of liquor 73°C, concentration of liquor at seeding 84%.
Third evaporator: temperature of liquor 60°C, concentration of liquor at seeding 86%.
Fourth evaporator: temperature of liquor 51°C, concentration of liquor at seeding 89%.

Calculate the yield of sugar in each evaporator and the concentration of sucrose in the mother liquor leaving the final evaporator.

SUGAR CONCENTRATIONS (g / 100 g water)

The sugar solubility figures are taken from the solubility curve, Fig. 9.7.

	Into effect	At seeding	Sugar crystallized	Liquor from effect
First effect
Water	1750	713	-	713
Sugar	3250	3250	506	2744
Second effect
Water	713	522	-	522
Sugar	2744	2744	1018	1726
Third effect
Water	522	279	-	279
Sugar	1726	1726	912	814
Fourth effect
Water	279	99	-	99
Sugar	814	814	539	275

Total Sugar - Sugar crystallized 2975 kg : Liquor from effect 275 kg

Yield in first effect
         506 kg h^-1 506/3250 = 15.6%
Yield in second effect
     1018 kg h^-1 1018/3250 = 31.3%
Yield in third effect
         912 kg h^-1 912/3250 = 28.1%
Yield in fourth effect
         539 kg h^-1 539/3250 = 16.6%
Lost in liquor
         275 kg h^-1 275/3250 = 8.4%

                          Total yield 91.6%

                          Quantity of sucrose in final syrup 275 kg/h^-1

                          Concentration of final syrup 73.5% sucrose

Crystallization Equipment

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

Back to the top