Supersaturation limiting

Figure 3.4a shows a normal crystallization curve with the spinodal (supersaturation limit) curve (CD) and equilibrium curve (AB). At point P neither nuclei nor crystal growth will occur since the solution is superheated by the amount RP. Once the saturation line (AB) is crossed, either through cooling or increase in concentration, nuclei and crystals may or may not form in the metastable region. Metastable point Q is shown between point R and the crosshatched line CD. 

Figure 4.1 Nucleation process. As time proceeds, the concentration increases until eventually reaching the supersaturation limit. At this point, nucleation occurs, relieving the high concentration stress.

When the concentration is closer to the supersaturation limit, heterogeneous nucleation occurs most often. The nucleus develops onto the substrate, with which it makes a contact angle a. Solution of the equations for the nucleus size and activation energy imply that the critical radius is the same as for homonuclear... 

Many experimental results have been reported which show that materials other than the solute and solvent present in the solution may inhibit crystal growth and induce a greater degree of supersolubility than usual. For example, many years ago, Marc (M6) showed that the presence of even small amounts of the dye Ponceau 2R extends the supersaturation limit of potassium chlorate solution. The general effects of impurities and additives on nucleation and growth are discussed further below and in detail by Buckley (B8). 

A second reason for staging continuous crystallizers is to control the process stream concentration-temperature profile for products with a steep solubility curve (i.e., exponential increase in solubility with temperature). Even though the volumetric flow rates would permit a single crystallizer of reasonable size, staged temperature for adiabatic cooling crystallization requires multiple vessels to prevent the local concentration at the hot concentrated feed entrance from exceeding its supersaturation limit when it is diluted and mixed with the circulating bulk. 

Figure 3.45 shows a schematic demonstrating the idealized stages involved in the formation of a dense particle from a droplet of solution [224, 225]. The droplet experiences evaporation, when the solute concentration in the outer layer increases to a value of above the supersaturation limit, thus resulting in the precipitation of fine particles. Precipitation is followed by a drying stage, in which the vapor phase diffuses through the pores in the precipitated layer. Decomposition of the... 

Bishnoi, R., Englezos, P., Gibbs fiee energy analysis for the supersaturation limits of methane in hquid water and the hydrate-gas-hquid water phase behavior. Fluid Phase Equilib., 42 (1988) 129-140. 

There are, however, practical limitations to minimizing RSS. Precipitates that are extremely insoluble, such as Fe(OH)3 and PbS, have such small solubilities that a large RSS cannot be avoided. Such solutes inevitably form small particles. In addition, conditions that yield a small RSS may lead to a relatively stable supersaturated solution that requires a long time to fully precipitate. For example, almost a month is required to form a visible precipitate of BaS04 under conditions in which the initial RSS is 5. ... 

In the absence of a suitable soHd phase for deposition and in supersaturated solutions of pH values from 7 to 10, monosilicic acid polymerizes to form discrete particles. Electrostatic repulsion of the particles prevents aggregation if the concentration of electrolyte is below ca 0.2 N. The particle size that can be attained is dependent on the temperature. Particle size increases significantly with increasing temperature. For example, particles of 4—8 nm in diameter are obtained at 50—100°C, whereas particles of up to 150 nm in diameter are formed at 350°C in an autoclave. However, the size of the particles obtained in an autoclave is limited by the conversion of amorphous siUca to quartz at high temperatures. Particle size influences the stabiUty of the sol because particles <7 nm in diameter tend to grow spontaneously in storage, which may affect the sol properties. However, sols can be stabilized by the addition of sufficient alkaU (1,33). 

Supersaturation reaches the metastable limit and nucleation is initiated supersaturation drops rapidly as crystals formed begin to grow... 

Better product characteristics are obtained through control of the rate at which supersaturation (cooling, evaporation, and addition of a nonsolvent or precipitant) is generated. An objective of the operation may be to maintain the supersaturation at some constant prescribed value, usually below the metastable limit associated with primary nucleation. For example, the batch may be cooled slowly at the beginning of the cycle and more rapidly at the end. 

Control of a batch ciystaUizer is almost always the most difficult part and veiy often is not practiced except to permit homogeneous nucleation to take place when the system becomes supersaturated. If control is practiced, it is necessary to have some means for determining when the initial solution is supersaturated so that seed of the appropriate size, quantity, and habit may be introduced into the batch. Following seeding, it is necessaiy to limit the coohng or evaporation in... 

The time elapsed from the ereation of the initial supersaturation to the detee-tion of the first erystals formed in the system is known as the induetion period. The level of supersaturation attained is then akin to the metastable limit . Neither quantity (viz. the induetion time and metastable limit) is therefore a fundamental quantity. Both are useful measures, however, of the propensity of a solution to nueleate. Measurement of the induetion time as a funetion of supersaturation ean be used to help determine erystallization kineties and meehanism. Thus, the induetion time may be expressed by (Walton, 1967)... 

Now, if nueleation ean be eonsidered negligible by operation at a low level of supersaturation then the eooling eurve needed to maintain the supersaturation within the metastable limit may be expressed by (Mullin and Nyvlt, 1971)... 

Carbon dioxide gas diluted with nitrogen is passed continuously across the surface of an agitated aqueous lime solution. Clouds of crystals first appear just beneath the gas-liquid interface, although soon disperse into the bulk liquid phase. This indicates that crystallization occurs predominantly at the gas-liquid interface due to the localized high supersaturation produced by the mass transfer limited chemical reaction. The transient mean size of crystals obtained as a function of agitation rate is shown in Figure 8.16. 

The solubility of oxygen in water is influenced by several factors but, generally, most waters contain, at equilibrium, about 8mg/kg at 25°C, although supersaturation may increase this considerably. Some indication of the amount of dissolved oxygen relevant in different situations is shown, on the one hand, by the value of 0-1 mg/kg found in central heating systems and, on the other hand, by the value of 0 005 mg/kg specified by most users of large boilers as the upper limit at the economiser inlet (see Section 5.5). 

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