Supersaturation maximum

The dynamic picture of a vapor at a pressure near is then somewhat as follows. If P is less than P , then AG for a cluster increases steadily with size, and although in principle all sizes would exist, all but the smallest would be very rare, and their numbers would be subject to random fluctuations. Similarly, there will be fluctuations in the number of embryonic nuclei of size less than rc, in the case of P greater than P . Once a nucleus reaches the critical dimension, however, a favorable fluctuation will cause it to grow indefinitely. The experimental maximum supersaturation pressure is such that a large traffic of nuclei moving past the critical size develops with the result that a fog of liquid droplets is produced. 

Sodium borate solutions near the Na20 B202 ratio of maximum solubihty can be spray-dried to form an amorphous product with the approximate composition Na20 4B202 4H20 commonly referred to as sodium octaborate (64). This material dissolves rapidly in water without any decrease in temperature to form supersaturated solutions. Such solutions have found apphcation in treating ceUulosic materials to impart fire-retardant and decay-resistant properties (see Cellulose). 

These design aspeets may be subjeet to eonstraints ineluding maximum supersaturation level (whieh may affeet sealing or enerustation), ete. Thus for any given duty, the size of the vessel, the operating poliey and performanee of the erystallizer are interrelated. 

In general, both nucieation and crystal growth depend on supersaturation and to lesser extent temperature and magma characteristics. Such data must therefore be collected to gain maximum benefit from the population balance approach (Jones and MuIIin, 1974 Jones, 1974). Further simplifications to the describing equations are also possible, however (as follows). 

Either a spore suspension or mycelium can be used to inoculate the production vessel. The medium contains a maximum glucose concentration of 15%. The upper limit reflects the low solubility of caldum gluconate which is normally about 4% at 30°C, but it can form supersaturated solutions up to about 15% without risk of predpitation. 

If we could prevent the mixture from separating into two phases at temperatures below Tc, we would expect the point of inflection to develop into curves similar to those shown in Figure 8.17 as the dotted line for /2, with a maximum and minimum in the fugacity curve. This behavior would require that the fugacity of a component decreases with increasing mole fraction. In reality, this does not happen, except for the possibility of a small amount of supersaturation that may persist briefly. Instead, the mixture separates into two phases. These phases are in equilibrium so that the chemical potential and vapor fugacity of each component is the same in both phases, That is, if we represent the phase equilibrium as... 

Also, hydrates are more soluble in water-miscible solvents than are the corresponding anhydrous forms. For example, the solubility of caffeine hydrate is lower than that of anhydrous caffeine in water but higher in ethanol. The maximum concentration seen may be due to the solubility of the anhydrous crystalline phase or due to a temporary steady state in which the rate of dissolution of the metastable anhydrous form and the rate of crystallization of the stable hydrate are equal. The decreasing concentration represents crystallization of the stable hydrate from a solution supersaturated with respect to it. If the maximum concentration of the solute in the dissolution experiment corresponds to the solubility, then the initial increase in concentration follows the Noyes-Whitney equation [15]. Van t Hoff plots of log solubility versus the reciprocal of temperature give linear relationships (Fig. 16). 

A solution containing the maximum amount of solute per given amount of solvent at a given temperature is a saturated solution. An unsaturated solution has less than that maximum amount of solute dissolved. Sometimes, there may be more that that maximum amount of solute, resulting in a supersaturated solution. Supersaturated solutions are unstable and eventually expel the excess solute, forming a saturated solution. 

A saturated solution is one in which the maximum amount of solute is dissolved for a given amount of solvent at a given temperature. Any solution with less than the maximum solute is called unsaturated. A solution with greater than maximum solute is supersaturated (an unstable state). 

In these pictures, the growth rates of the step surfaces In both directions are quite similar to each other, and they are roughly evaluated to be 0.05 mm/mln.MPa under a supersaturation of 4 MPa. On the other hand, there Is scarcely any growth In the maximum length and width of the parlally melted crystal during the shape healing. 

Literature has revealed limited kinetic data on secondary nucleation of alumina trihydrate in the precipitator of the Bayer Process for alumina production. A batch agitated, isothermal, three litre crystallizer was used in the study. A Coulter-Counter was utilized as the particle sizing equipment. The effects of seed density, supersaturation and temperature on secondary nucleation were investigated. Maximum nucleation rates were found to occur at about 70 C and for any crystallization temperature, the nucleation rate passed through a maximum. The correlated equation for the effective secondary nucleation rate of alumina trihydrate is... 

The nucleation rate increased from 65°C to 70°C and dropped from 70°C to 80°C. Thus 70°C seems to be the optimum temperature for maximum nucleation. Published work on alumina trihydrate by Misra and White (5) and Brown (9 10) revealed that the nucleation rate decreases with increasing temperature, at greater than 70 C by the former but from 50 to 75°C by the latter. This nucleation rate dependence on temperature differs with normal chemical reaction where the reaction rate increases with increase in temperature. It is not clear whether then-studies at different temperatures in the published work were conducted at constant initial absolute supersaturation (AC7C ) for all the temperatures studied or at constant initial concentration. The latter would account for the higher nucleation rates obtained at lower temperatures as the AC/C is higher at lower temperatures since C decreases with temperature. 

Figure 5(b) illustrates that the nucleation rate goes through a maximum in any batch run. These results seem to agree witii the findings of Brown (9,10). It is not expected that a higher nucleation rate results at a lower supersaturation. 

For any fixed batch crystallization temperature, the effective nucleation rate passes through a maximum even at high seed densities. It is suggested that the induction period r uired to activate the seed surfaces may be responsible for the lower initial nucleation rate observed when the supersaturation was higher. It is also suggested that agglomeration may have caused the observed phenomenon. 

The soln. below —18 3 are supersaturated and unstable since there is a maximum in the solubility curve at —18"3° corresponding with the formation of the dihydrate, HC1.2H20, as indicated in Fig. 14. 

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