Supersaturation Measurements

In general, it is very difficult to measure directly the activity or concentration of reactive species independently one from another. Unless a sufficiently sensitive, quick dynamic response, species-specific probe-electrode can be applied for each of the reactants, the direct measurement of such a fundamental precipitation property as momentary supersaturation is rarely possible. Therefore, often the ratio of concentration of one of the reagents whose concentration can be monitored independently, to its solubility, is used as a measure of supersaturation. As a further simplification, a ratio between the concentration of the influx reagent stream and the solubility, i.e., an initial supersaturation ratio, can be used to characterize supersaturation at the onset of nucleation, Tanaka and Iwasaki (1985). 

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Gas bubble separation time of petroleum oils NFT 60-149 ASTM D 3427 Time for air liberation after supersaturation (measurement of density)... 

In both sexes, CCM-OJ provided an alkali load that significantly increased urinary pH compared to basal levels and versus milk consumption, and also increased urinary citrate excretion versus basal levels. An elevated urine pH and citrate level are generally considered to reduce Ca oxalate supersaturation and crystallization potential (Odvina, 2006). However, in this study the relative supersaturation measurement for Ca oxalate was not different between the CCM-OJ and milk treatment groups, or between either treatment and the basal levels. Although the alkalizing effect of milk was less than that of CCM-OJ, it also induced a higher urinary pH compared to basal levels (p <. 01 and p <. 05 in women and men, respectively). 

Table 3 Supersaturation measurement methods in liquid solution ...

Growth rates of crystals also must be measured in the laboratory or pilot plant, although the suitable condition may be expressed simply as a residence time. Table 16.3 gives a few growth rate data at several temperatures and several extents of supersaturation for each substance. In most instances the recommended supersaturation measured as the ratio of operating to saturation concentrations is less than 1.1. It may be noted that at a typical rate of increase of diameter of 10 7 m/sec, the units used in this table, the time required for an increase of 1 mm is 2.8 hr. 

Values of 12 can be monitored as time passes to determine whether equilibrium between a solid phase and a soil solution exists. If 12 < 1, the soil solution is termed undersaturated with respect to the solid phase if 12 > 1, the soil solution is supersaturated. Measurements of 12 thus lead to one or more of the following conclusions about the reaction of Eq. 3.1 whenever 12 1 ... 

Yedur, S.K. Berglund, K.A. Use of fluorescence spectroscopy in concentration and supersaturation measurements in citric acid solutions. Appl. Spectrosc. 1996, 50 (7), 866-870. 

Also discussed are precipitation specific experimental techniques, such as supersaturation measurements, constant composition (CC) method, instantaneous mixing devices, maximum (critical) growth rate experiments, and sizing. Due to the intrinsic difficulties with the direct supersaturation measurements and the microsecond characteristic time scale of precipitation reaction and nucleation, the CC method is used to study the precipitation kinetics. For the same reasons, the critical growth experiments are used to delineate the domain of the reactant feed rate that assures a renucleation-free process and a unimodal CSD. 

The use of the supersaturation as the measured variable for a control algorithm was first suggested by Han (1969). Rousseau and Howell (1982) used simulations to demonstrate that the substitution of the supersaturation for in Eq. (9.10) could stabilize a cycling crystallizer. While the on-line supersaturation measurement is in general more easily obtained than the determination of properties of the CSD, it is pointed out that the scheme based on supersaturation measurement is more sensitive to measurement noise. 

Here, r is positive and there is thus an increased vapor pressure. In the case of water, P/ is about 1.001 if r is 10" cm, 1.011 if r is 10" cm, and 1.114 if r is 10 cm or 100 A. The effect has been verified experimentally for several liquids [20], down to radii of the order of 0.1 m, and indirect measurements have verified the Kelvin equation for R values down to about 30 A [19]. The phenomenon provides a ready explanation for the ability of vapors to supersaturate. The formation of a new liquid phase begins with small clusters that may grow or aggregate into droplets. In the absence of dust or other foreign surfaces, there will be an activation energy for the formation of these small clusters corresponding to the increased free energy due to the curvature of the surface (see Section IX-2). 

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. ... 

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... 

Solutions vaiy greatly in their ability to sustain measurable amounts of supersaturation. With some materials, such as sucrose, it is possible to develop a supersaturation coefficient of 1.4 to 2.0 with little danger of nucleation. With some common inorganic solutions such as sodium chloride in water, the amount of supersaturation which can be generated stably is so small that it is difficult or impossible to measure. 

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)... 

Induction period measurements can also be used to determine interfacial tensions. To validate the values inferred, however, it is necessary to compare the results with an independent source. Hurley etal. (1995) achieved this for Cyanazine using a dynamic contact angle analyser (Calm DCA312). Solid-liquid interfacial tensions estimated from contact angle measurements were in the range 5-12 mJ/m which showed closest agreement with values (4—20mJ/m ) obtained from the log-log plots of induction time versus supersaturation based on the assumption of — tg. 

Garside elal. (1979) measured size distributions of seeondary nuelei and reported their variation with supersaturation. Signifieant inerease of nuelei with supersaturation is observed. Thus the proeess is not simply an attrition event alone, but is also related to the level supersaturation at whieh parent erystal is growing. Jones elal. (1986) also observed anomalous growth of seeondary nuelei in a study of the eontinuous MSMPR erystallization of potassium sulphate with eonsequenees inferred for seeondary nueleation rates. Girolami and Rousseau (1986) demonstrate the importanee of initial breeding meehanism in seeded potash alum bateh erystallization. The number of erystals... 

It is evident that most studies reported to date have used number density, average size or weight per eent as eontrol variables. Often these variables are inferred from other measurements, ineluding density, solution supersaturation, refraetive index ete. Inferential teehniques have been shown to be partieularly suitable for industrial seale applieations where laser seattering deviees for on-line size distribution measurement are not yet praetieal for industrial eontrol purposes, although substantial progress is being made to that end. Even when usable, however, these measurement deviees are often eharaeterized by noise and require operation at very low solids eoneentration. 

Dunuwila, D. and Berglund, K.A. 1997. ATR FTIR spectroscopy for in situ measurement of supersaturation. Journal of Crystal Growth, 179, 185-193. 

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