Supersaturation fractional

The command and control mechanism must take account of the particular instability of each wine so as to eliminate only the supersaturated fraction of potassium hydrogen tartrate and calcium salts. 

Hydrolysis of phenolates into phenolic acids whose supersaturated fraction can be separated by direct settling. 

Eeactive crystalli tion addresses those operations ia which a reaction occurs to produce a crystallizing solute. The concentration of the solute formed generally is greater than that corresponding to solubiHty. In a subset of systems, the solubiHty is nearly zero and, concomitantly, the supersaturation produced by reaction is large. These are often referred to as precipitation operations, and crystal size distributions from them contain a large fraction of fine crystals. 

Another method of fractional crystallization, in which advantage is taken of different ciystallization rates, is sometimes used. Thus, a solution saturated with borax and potassium chloride will, in the absence of borax seed ciystals, precipitate only potassium chloride on rapid coohng. The borax remains behind as a supersaturated solution, and the potassium chloride crystals can be removed before the slower borax crystalhzation starts. 

Crystal growth is a layer-by-layer process, and the retention time required in most commercial equipment to produce crystals of the size normally desired is on the order of 2 to 6 h. On the other hand, nucleation in a supersaturated solution can be generated in a fraction... 

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... 

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. 

As discussed in Section 15.5.2, the separation of two or more sublimable substances by fractional sublimation is theoretically possible if the substances form true solid solutions. Gillot and Goldberger(10°) have reported the development of a laboratory-scale process known as thin-hlm fractional sublimation which has been applied successfully to the separation of volatile solid mixtures such as hafnium and zirconium tetrachlorides, 1,4-dibromobenzene and l-bromo-4-chlorobenzene, and anthracene and carbazole. A stream of inert, non-volatile solids fed to the top of a vertical fractionation column falls counter-currently to the rising supersaturated vapour which is mixed with an entrainer gas. The temperature of the incoming solids is maintained well below the snow-point temperature of the vapour, and thus the solids become coated with a thin film (10. im) of sublimate which acts as a reflux for the enriching section of the column above the feed entry point. 

Gels are obtained for concentrations shown in the temperature-concentration phase diagram (Figure 1). Electron spin resonance (ESR) shows (10) that for a given temperature only a fraction (p) of the initial steroid concentration is transferred from the solution to the gel network. The picture of this gel is thus of a supersaturation gel there is a dynamic equilibrium between free molecules in solution and aggregated steroid molecules included in the long objects which constitute the gel network. The free steroid molecules concentration at a temperature where the gel state is stable is (1-p), while C p is the steroid concentration within the solid-iike gel aggregates. 

Finally, the term A/to can be expressed as a function of the molar fractions C and Coo (he. concentration, or activity, or partial pressure, depending on the system), the concentrations near the growing surface, and around an infinite planar surface of the sohd formed, respectively. The supersaturation parameter S is generally defined as the ratio C/Coo, thus ... 

Gillani, Leaitch, and co-workers (1995) carried out a detailed study of the fraction of accumulation mode particles (diameters from 0.17 to 2.07 /Am) that led to cloud droplet formation in continental stratiform clouds near Syracuse, New York. When the air mass was relatively clean, essentially all of the particles were activated to form cloud droplets in the cloud interior and the number concentration of cloud droplets increased linearly with the particle concentration. However, when the air mass was more polluted, the fraction of particles that were activated in the cloud interior was significantly smaller than one. This is illustrated by Fig. 14.40, which shows the variation of this fraction (F) as a function of the total particle concentration, Nun. In the most polluted air masses (as measured by large values of Nun), the fraction of particles activated was 0.28 + 0.08, whereas in the least polluted, it was as high as 0.96 + 0.05. The reason for this is likely that in the more polluted air masses, the higher number of particles provided a larger sink for water vapor, decreasing the extent of supersaturation. 

When the supersaturation ratio S becomes greater than unit, the small liquid droplets (i.e. molecular clusters) commence to appear. Almost all the droplets are immediately destroyed due to evaporation and only small fraction of the droplets (critical clusters) with radii greater than a critical radius r have a chance to survive and grow by accretion of vapor molecules (monomers) onto their surface. It is assumed that macroscopic thermodynamics is applied to the critical clusters that are considered as liquid droplets containing the large number of monomers, that is nx>>i. The number of the critical clusters formed per unit time per unit volume is the nucleation rate J so that the number density of dust grains is Nd = JJdt. Expressions for calculation of the nucleation rate and other quantities can be found in the review paper by Draine (1981). 

Figure 16.5. Supersaturation behavior, (a) Schematic plot of the Gibbs energy of a solid solute and solvent mixture at a fixed temperature. The true equilibrium compositions are given by points b and e, the limits of metastability by the inflection points c and d. For a salt-water system, point d virtually coincides with the 100% salt point e, with water contents of the order of 10-6 mol fraction with common salts, (b) Effects of supersaturation and temperature on the linear growth rate of sucrose crystals [data of Smythe (1967) analyzed by Ohara and Reid, 1973],...

In this particular case, there is no transport of component B towards the surface. BO is homogeneously precipitated in the region < F, and the BO fraction corresponds to the concentration of B in the initially homogeneous alloy. Although the BO fraction is spatially constant in this case, the size of the BO particles is not. The increase in supersaturation becomes slower as the reaction front F advances. Thus, the number of precipitating particles becomes smaller with increasing time and, consequently, their volumes become larger since the local product of number times volume remains constant. 

Solution. Important assumptions include that the interfacial free energy is isotropic, that elastic strain energy is unimportant, and that the nucleation rates mentioned are for steady-state nucleation. The critical barrier to nucleation, AQe, can be calculated for the 0.3 atomic fraction B alloy using the tangent-to-curve construction on the curves in Fig. 19.18b to provide the value Aga = —9 x 107 Jm-3 for the chemical driving force for this supersaturation at 800 K. AQc is given for a spherical critical nucleus by... 

It can precipitate as potassium hydrogen tartrate (KHT) or as calcium tartrate (CaT), the latter being practically insoluble in aqueous solutions. Their equilibrium solubility varies with temperature, pH, and alcohol content, while the presence of a few wine components, such as polysaccharides and mannoproteins, may hinder spontaneous nucleation even if the solution is supersaturated. From Figure 14 that shows the equilibrium tartaric acid-dissociated fractions versus pH and ethanol volumetric fraction (Berta, 1993 Usseglio-Tomasset and Bosia, 1978), it can be seen that in the typical pH range (3 4) of wines KHT is predominant. As temperature is reduced from 20 to 0°C, KHT solubility in water or in a 12% (v/v) hydro-alcoholic solution reduces from 5.11 to 2.45 kg/m3 or from 2.75 to 1.1 kg/m3, respectively (Berta, 1993). Each of these data also varies with pH and reaches a minimum at the pH value associated with the maximum concentration of the hydrogen tartrate anions. For the above-mentioned solutions, the solubility minimum shifts from pH 3.57 to pH 3.73 as the ethanol content increases from 0 to 12% (v/v) (Berta, 1993). 

In precipitation, particle formation is extremely fast due to high supersaturations which in turn lead to fast nucleation. At least in the beginning, size distributions are narrow with particle sizes around one 1 nm. Nanomilling in stirred media mills is characterized by relatively slow particle formation kinetics, particle sizes ranging from several microns down to 10 nm and high sohds volume concentrations of up to 40%. Large particles may scavenge the fine fractions. The evolution of the particle size distribution can be described for both cases by population balance equations (Eq. (7)),... 

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