Desupersaturation

Bubbles in a liquid originate from one of three general sources (1) They may be formed by desupersaturation of a solution of the gas or by the decomposition of a component in the liqiiid (2) They may be introduced directly into the liquid by a bubbler or sparger or by mechanical entrainment and (3) They may result from the disintegration of larger bubbles already in the liquid. 

Garside, J., Gibilaro, L.G. and Tavare, N.S., 1982. Evaluation of crystal growth kinetics from a desupersaturation curve using initial derivatives. Chemical Engineering Science, 37, 1625-1628. 

For a polymorphic drug, the polymorph obtained depends on the physical conditions, such as temperature, pressure, solvent, and the rate of desupersaturation. For a solvated drug, in addition to these conditions, the thermodynamic activity of the solvating solvent may also determine the solvate obtained. However, kinetic factors may sufficiently retard the crystallization of a stable form or the solid-state transition to the stable form that an unstable form may be rendered metastable. 

Y. Hu, J.K. Liang, A.S. Myerson and L.S. Taylor, Crystallization monitoring by Raman spectroscopy Simultaneous measurement of desupersaturation profile and polymorphic form in flufenamic acid systems, Ind. Eng. Chem. Res., 44, 1233-1240 (2005). 

Tavare and Garside ( ) developed a method to employ the time evolution of the CSD in a seeded isothermal batch crystallizer to estimate both growth and nucleation kinetics. In this method, a distinction is made between the seed (S) crystals and those which have nucleated (N crystals). The moment transformation of the population balance model is used to represent the N crystals. A supersaturation balance is written in terms of both the N and S crystals. Experimental size distribution data is used along with a parameter estimation technique to obtain the kinetic constants. The parameter estimation involves a Laplace transform of the experimentally determined size distribution data followed a linear least square analysis. Depending on the form of the nucleation equation employed four, six or eight parameters will be estimated. A nonlinear method of parameter estimation employing desupersaturation curve data has been developed by Witkowki et al (S5). 

An alternative scheme, proposed by Garside et al. (16,17), uses the dynamic desupersaturation data from a batch crystallization experiment. After formulating a solute mass balance, where mass deposition due to nucleation was negligible, expressions are derived to calculate g and kg in Equation 3 explicitly. Estimates of the first and second derivatives of the transient desupersaturation curve at time zero are required. The disadvantages of this scheme are that numerical differentiation of experimental data is quite inaccurate due to measurement noise, the nucleation parameters are not estimated, and the analysis is invalid if nucleation rates are significant. Other drawbacks of both methods are that they are limited to specific model formulations, i.e., growth and nucleation rate forms and crystallizer configurations. 

Figure 4(a). Effect of seed size on nucleation at 70°C, 200 g/1 seed density. Desupersaturation curve. 

Figure 6. Desupersaturation curve at different temperatures for seed density of200g/l.

Zipp, G. L. and Rodriguez-Hornedo, N. (1989) Determination of crystal growth kinetics from desupersaturation measurement. J. Pharm., 51 147-156. 

Crystallization from supersaturated solutions can occur by two processes, formation of new crystals or nucleation and growth on existing crystals. The internal surfaces of the scrubber can provide nucleation sites, thus resulting in scale formation. For many crystal systems, growth will occur without nucleation if suflBcient seed crystals are provided. Work by other investigators (3) has shown that supersaturated calcium sulfate solutions can be effectively desupersaturated by circulation of 1-5% gypsum seed crystals. 

Rader, P. C., Bench Scale Studies of CaS04 Desupersaturation Kinetics, ... 

The final data the designer hopes for are pilot plant data from tests he has conducted. It is here that the designer determines what level of supersaturationthe solution can support, the crystal surface area required for desupersaturation, the effect of secondary nucleation, and the residence time required for growth to desired size. Some of these values are measured directly while others are implied by indirect measurements. 

Forced oxidation is achieved by air sparging of the slurry in an oxidation tank, either on the bleed stream to the solids dewatering system or on the recirculated slurry within the scrubber slurry loop. For a one-scrubber-loop forced oxidation system, the slurry effluent from all scrubbers in the system (e.g., the venturi scrubber and spray tower at Shawnee constitute a two-scrubber system, and the spray tower alone or TCA, a one-scrubber system) are sent to a single effluent hold tank, which is the oxidation tank. For a two-loop forced oxidation system, there are two scrubbers in series (e.g., venturi and spray tower at Shawnee) with effluent from each scrubber going to a separate tank the effluent hold tank for the upstream scrubber (with respect to gas flow) is the oxidation tank. For either one-loop or two-loop forced oxidation systems, the oxidation tank may be followed by a second tank, in series, to provide further limestone dissolution and gypsum desupersaturation time prior to recycle to the scrubber. 

The second tank offers extra time for gypsum desupersaturation and precipitation... 

The areas which were found to be particularly important are absorption surface selection, control of reagent desupersaturation, reagent pH profiles, and closed-loop water balance. 

The reagent stream must be controlled to permit calcium salt desupersaturation external to the scrubber and absorber while maintaining adequate concentration levels for good absorption efficiency. In order to do this a reagent stream containing 8-15% solids is circulated. The solid portion is composed of some fly ash components but mainly calcium carbonate, sulfite, and sulfate. Sulfur dioxide removal efficiency dictates the carbonate level. Sulfite crystals enhance and control desupersaturation of calcium sulfate while providing nucleation sites for crystal growth... 

In the absorber tank, time for external desupersaturation is provided and fresh reagent is added to raise the pH and thereby promote desupersaturation of the spent reagent stream. The delay tank provides contact time for crystal growth and sulfite and sulfate salt precipitation. 

All of the direct measurement techniques are time consuming and require a significant number of experiments to obtain sufficient data to obtain kinetic parameters. This has led a number of investigators (Garside et al. 1982 Tavare and Garside 1986 Qiu and Rasmussen 1990 Witkowski et al. 1990) to look at indirect methods for the estimation of both growth and nucleation kinetics. Most of the indirect methods are based on the measurement of the solution concentration versus time in a seeded isothermal batch experiment. This is often called the desupersaturation curve since the concentration and the solubility can be used to calculate the supersaturation of the system versus time. 

A number of methods can be used to estimate growth kinetics from the desupersaturation curve obtained during batch-seeded isothermal experiments. The simplest of these methods was developed by Garside et al. (1982) and involves using the derivatives of the desupersaturation curve at time zero. It is assumed in this method that the concentration change is due only to crystal growth... 

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