Supersaturation ratio

In principle, nucleation should occur for any supersaturation given enough time. The critical supersaturation ratio is often defined in terms of the condition needed to observe nucleation on a convenient time scale. As illustrated in Table IX-1, the nucleation rate changes so rapidly with degree of supersaturation that, fortunately, even a few powers of 10 error in the preexponential term make little difference. There has been some controversy surrounding the preexponential term and some detailed analyses are available [33-35]. 

Because of the large surface tension of liquid mercury, extremely large supersaturation ratios are needed for nucleation to occur at a measurable rate. Calculate rc and ric at 400 K assuming that the critical supersaturation is x = 40,000. Take the surface tension of mercury to be 486.5 ergs/cm. ... 

Calculate what the critical supersaturation ratio should be for water if the frequency factor in Eq. IX-10 were indeed too low by a factor of 10 . Alternatively, taking the observed value of the critical supersaturation ratio as 4.2, what value for the surface tension of water would the corrected theory give ... 

Since the critical supersaturation ratio for homogeneous nucleation is typically greater than 3, it is not often reached in process equipment. 

For ionie systems, however, the definition of the appropriate driving foree beeomes more eomplex sinee the ionie eoneentrations are not neeessarily in stoiehiometrie ratio and the solubility produet generally applies. Thus the supersaturation ratio of sparingly soluble systems ean be deseribed by... 

Supersaturation can be expressed as the concentration driving force Ac, the supersaturation ratio, S, or the relative supersaturation, a ... 

Li S, Xu J, Luo G (2007) Control of crystal morphology through supersaturation ratio and mixing conditions. J Cryst Growth 304(l) 219-224... 

Calculation of Supersaturation Ratios of Flue Gas Scrubbing Slurries... 

The scaling tendency of the lime or limestone processes for flue gas desulfurization is highly dependent upon the supersaturation ratios of calcium sulfate and calcium sulfite, particularly calcium sulfate. The supersaturation ratios cannot be measured directly. They are determined by measuring experimentally the molalities of dissolved sulfur dioxide, sulfate, carbon dioxide, chloride, sodium and potassium, calcium, magnesium, and pH. Then by calculation, the appropriate activities are determined, and the supersaturation ratio is determined. Using the method outlined in Section IV, the concentrations of all ions and ion-pairs can be readily determined. The search variables are the molalities of bisulfite, bicarbonate, calcium, magnesium, and sulfate ions. The objective function is defined from the mass balance expressions for dissolved sulfur dioxide, sulfate, carbon dioxide, calcium, and magnesium. This equation is... 

These values are based upon a pH of 5.5, temperature of 50°C, carbon dioxide partial pressure of 0.12 atm, calcium sulfite supersaturation ratio of 1.0, and calcium sulfate supersaturation ratio of 1.25. 

At 293 K, a supersaturated solution of sucrose contains 2.45 kg sucrose/kg water. If the equilibrium saturation value is 2.04 kg/kg water, what is the supersaturation ratio in terms of kg/kg water and kg/kg solution ... 

From a kinetic point of view, the homogeneous nucleation rate (Nr) [57] and the growth rate (Gr) [58] can be expressed as a function of the supersaturation ratio ... 

Equation 7 shows the exponential variation of the homogeneous nucleation rate with an increasing supersaturation ratio. Equation 8, coming from the model of Strickland-Constable [59], establishes that a linear relation exists between growth rate and supersaturation ratio. The direct comparison of Nr and Gr is difficult because of their different units. However, Fig. 7, although only schematic, shows the variation of these two rates versus S, predicting that for a certain value of S the nucleation rate will become preponderant on the growth rate. Moreover, it also shows, that, in the case of preponderance... 

Both these succinct theoretical models, derived from both a thermodynamic and kinetic perspective, underline the role of the supersaturation ratio during nucleation and growth steps. They strongly indicate that control of this supersaturation parameter will improve the processes by which chemical vapour deposition occurs. 

As soon as S > 0, a supersaturated liquid enters a metastable state and must degas to recover a supersaturating ratio equal to zero. In the case of Champagne wines, just after uncorking the bottle, Cl is the equilibrium concentration of CO2 in the liquid bulk corresponding to a partial... 

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