Units supersaturation

Table 3.3. Conversion factors for supersaturation units (Mullin, 1973)... 

Mullin, J.W. (1973) Solution concentration and supersaturation units and their conversion factors. The Chemical Engineer, No. 274, 316-317. 

The central quantity of interest in homogeneous nucleation is the nucleation rate J, which gives the number of droplets nucleated per unit volume per unit time for a given supersaturation. The free energy barrier is the dommant factor in detenuining J J depends on it exponentially. Thus, a small difference in the different model predictions for the barrier can lead to orders of magnitude differences in J. Similarly, experimental measurements of J are sensitive to the purity of the sample and to experimental conditions such as temperature. In modem field theories, J has a general fonu... 

Aragonite. Calcium carbonate is a common deposit in shallow tropical waters as a constituent of muds, or in the upper part of coral reefs where it precipitates from carbon dioxide-rich waters supersaturated with carbonate from intense biological photosynthesis and solar heating. Deposits of ooHtic aragonite, CaCO, extending over 250,000 km in water less than 5 m deep ate mined for industrial purposes in the Bahamas for export to the United States (19). 

Crystallization batches range from 30,000 to 60,000 Hters for each pan. Continuous centrifugals are typically used for second, third, and affination steps continuous vacuum pans are less common but are used in the U.S. for intermediate strikes. Most horizontal batch crystallizers have been replaced by continuous units, and all are designed for controlled cooling of the massecuite to maintain supersaturation. 

Since the effluent from a softening unit is usually supersaturated with calcium carbonate at the usually high pH values, it is necessary to reduce the pH to a value that allows the solution to be exactiy saturated for the calcium-ion and carbonate-ion concentrations present. The relationship is... 

Evaporative crystalli rs generate supersaturation by removing solvent, thereby increasing solute concentration. These crystallizers may be operated under vacuum, and, ia such circumstances, it is necessary to have a vacuum pump or ejector as a part of the unit. If the boiling poiat elevation of the system is low (that is, the difference between the boiling poiat of a solution ia the crystallizer and the condensation temperature of pure solvent at the system pressure), mechanical recompression of the vapor obtained from solvent evaporation can be used to produce a heat source to drive the operation. 

Another type of crystallizer is the Oslo-type unit shown in Figure 24. In units of this type, the object is to form a supersaturated solution in the upper chamber and then reHeve the supersaturation through growth in the lower chamber. The use of the downflow pipe in the crystallizer provides good mixing in the growth chamber. 

The seeond-order dependenee of the growth rate on the supersaturation ean be explained by a number of growth theories. The most eonvineing, however, is that of Burton etal. (1951). In their BCF theory about the serew disloeation eentred surfaee spiral step, it is assumed that growth units enter at kinks with a rate proportional to cr and that the kink density is also proportional to cr whieh gives the faetor cr in the rate expression. 

It is supposed that water is to be cooled at a mass rate L per unit area from a temperature 0L2 to Ql - The air will be assumed to have a temperature 6G, a humidity Jf ], and an enthalpy Hoi (which can be calculated from the temperature and humidity), at the inlet point at the bottom of the tower, and its mass flow per unit area will be taken as G. The change in the condition of the liquid and gas phases will now be followed on an enthalpy-temperature diagram (Figure 13.16). The enthalpy-temperature curve PQ for saturated air is plotted either using calculated data or from the humidity chart (Figure 13.4). The region below this line relates to unsaturated air and the region above it to supersaturated air. If it is assumed that the air in contact with the liquid surface... 

A carboxylate derivative of a fully aromatic, water-soluble, hyperbranched polyphenylene is considered as a unimolecular micelle due to its ability to complex and solubilize non-polar guest molecules [23]. The carboxylic acid derivative of hyperbranched polyphenylene polymer (HBP) (My,=5750-7077, Mn=3810-3910) consists of 40-60 phenyl units that branch outward from a central point forming a roughly spherical molecule with carboxylates on the outer surface. The free acid form of HBP was suspended in distilled water and dissolved by adding a minimum quantity of NaOH. The solution was adjusted to pH 6.2 with aqueous HCl. Calcium carbonate crystals were growth from supersaturated calcium hydrogencarbonate solution at room temperature. HBP gave... 

For a number of reasons, using saturation indices as measures of the mineral masses to be formed as a fluid approaches equilibrium is a futile (if commonly undertaken) exercise. First, a mineral s saturation index depends on the choice of its formula unit. If we were to write the formula for quartz as Si2C>4 instead of Si02, we would double its saturation index. Large formula units have been chosen for many of the clay and zeolite minerals listed in the llnl database, and this explains why these minerals appear frequently at the top of the supersaturation list. 

The saturation state of aragonite (Fig. 24.5), on the other hand, is affected little by temperature. Aragonite remains supersaturated by a factor of about ten (one log unit) over the gamut of analyses. The supersaturation probably arises from the effect of orthophosphate, present at concentrations of about 100 mg kg-1 in Mono Lake water orthophosphate is observed in the laboratory (Bischoff et al., 1993) to inhibit the precipitation of calcite and aragonite. 

In this chapter, you learned about solutions. A solution is a homogeneous mixture composed of a solvent and one or more solutes. Solutions may be unsaturated, saturated, or supersaturated. Solution concentration units include percentage, molarity, molality, and mole fraction. The solubility of solids in liquids normally increases with increasing temperature, but the reverse is true of gases dissolving in liquids. The solubility of gases in liquids increases with increasing pressure. 

At a high degree of supersaturation, the nucleation rate is so high that the precipitate formed consists mostly of extremely small crystallites. Incipiently formed crystallites might be of a different polymorphous form than the final crystals. If the nucleus is smaller than a one-unit cell, the growing crystallite produced initially is most likely to be amorphous substances with a large unit cell tend to precipitate initially as an amorphous phase ("gels"). 

There are many ways of expressing the relative amounts of solute(s) and solvent in a solution. The terms saturated, unsaturated, and supersaturated give a qualitative measure, as do the terms dilute and concentrated. The term dilute refers to a solution that has a relatively small amount of solute in comparison to the amount of solvent. Concentrated, on the other hand, refers to a solution that has a relatively large amount of solute in comparison to the solvent. However, these terms are very subjective. If you dissolve 0.1 g of sucrose per liter of water, that solution would probably be considered dilute 100 g of sucrose per liter would probably be considered concentrated. But what about 25 g per liter—dilute or concentrated In order to communicate effectively, chemists use quantitative ways of expressing the concentration of solutions. Several concentration units are useful, including percentage, molarity, and molality. 

A vacuum crystalliser operates on a slightly different principle from the reduced-pressure unit since supersaturation is achieved by simultaneous evaporation and adiabatic cooling of the feedstock. A hot, saturated solution is fed into an insulated vessel maintained under reduced pressure. If the feed liquor temperature is higher than the boiling point of the solution under the low pressure existing in the vessel, the liquor cools adiabatically to this temperature and the sensible heat and any heat of crystallisation liberated by the solution evaporate solvent and concentrate the solution. 

Once a particular class of unit has been decided upon, the choice of a specific unit depends on initial and operating costs, the space available, the type and size of the product, the characteristics of the feed liquor, the need for corrosion resistance and so on. Particular attention must be paid to liquor mixing zones since the circulation loop includes many regions where flow streams of different temperature and composition mix. These are all points at which temporary high supersaturations may occur causing heavy nucleation and hence encrustation, poor performance and operating instabilities. As Toussaint and Donders(72) stresses, it is essential that the compositions and enthalpies of mixer streams are always such that, at equilibrium, only one phase exists under the local conditions of temperature and pressure. 

Mullin(3) has used this procedure for the design of a unit for the crystallisation of potassium sulphate at 293 K. The data are given in Table 15.5 from which it will be noted that the cross-sectional area depends linearly on the relative degree of de-supersaturation and the production rate depends linearly on the area but is independent of the height. If the production rate is fixed, then the crystalliser height may be adjusted by altering the sizes of the seed or product crystals. Mullin and Nyvlt(75) have proposed a similar procedure for mixed particle-size in a crystalliser fitted with a classifier at the product outlet which controls the minimum size of product crystals. 

The metastable compressed films described above bear rough analogy to a supersaturated solution, since a larger number of molecules are contained per unit area than would be stable under true equilibrium conditions in the presence of a second denser phase. On... 

Consider a situation in which a concentrated polymeric solution enters the extraction zone of, say, an extruder in circumstances when the pressure in the extraction zone. Pa, is less than the equilibrium partial pressure of the volatile component in the feed solution. Under these conditions the solution will be supersaturated at the extraction pressure, flashing of the volatile component will occur, gas bubbles of radius Rq will be formed, and the concentration will immediately fall from Wi to wq. If bubble formation occurs by homogeneous nucleation, the rate at which these bubbles will be formed per unit volume of solution should depend on the difference between the equilibrium partial pressure of the volatile component and the devolatilization pressure. Since this pressure difference is greatest when the solution first enters the extraction zone, the rate of formation of bubbles will at first be high but as devolatilization pro-... 

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