Supersaturated systems

Sometimes the calculation predicts that the fluid as initially constrained is supersaturated with respect to one or more minerals, and hence, is in a metastable equilibrium. If the supersaturated minerals are not suppressed, the model proceeds to calculate the equilibrium state, which it needs to find if it is to follow a reaction path. By allowing supersaturated minerals to precipitate, accounting for any minerals that dissolve as others precipitate, the model determines the stable mineral assemblage and corresponding fluid composition. The model output contains the calculated results for the supersaturated system as well as those for the system at equilibrium. 

Theofanous, T., Biasi, L., Isbin, H. S., and Fauske, H. (1969). A theoretical study on bubble growth in constant and time-dependent pressure fields. Chem. Eng. Sci. 24, 885. Trefetben, L. (1957). Nucleadon at a liquid-liquid interftice. J. Appl. Phys. 28,923. Volmer, M., and Weber, A. (1926). Nucleus formation in supersaturated systems. Z. Phys. Chem. 119, 277. 

We can apply classical germination laws to this supersaturated system thus, the Avrami-Mempel laws confirm the unidimensional growth of the solid-like gel network. Induction times can also be studied in this framework 11). Here, we are interested first by the different kinetic behaviors which are dependent upon the location in the phase diagram of the initial solution defined by its supersaturation degree. 

However, as experiment shows, supersaturated systems under pure conditions, in the absence of the phase with respect to which the system is unstable (bubbles, condensate drops, small crystals in the examples given), turn out in practice to be quite stable within a rather broad range. 

The formulation development strategies are similarto thatifoivo PK screening. It is common to use supersaturated solutions in the early phase studies. However, the physical and chemical stabilities of the supersaturation systems should be well understood as the information provided will help formulation scientists to decide if the formulation needs to be prepared daily, weekly or monthly. 

Although a supersaturated system may remain in this state for an appreciable length of time, it will eventually reach thermodynamic equilibrium through crystallization of excess solute. 

Over the last decade, solid-dispersions or solid solutions, a high-energy supersaturated system has been extensively studied and widely used to enable delivery of water-insoluble compounds [32-40],... 

Zel dovich theory — The theory determines the time dependence of the nucleation rate 7(f) = d N (f )/df and of the number N(t) of nuclei and derives a theoretical expression for the induction time T needed to establish a stationary state in the supersaturated system. The -> Zel dovich approach [i] (see also [ii]) consists in expressing the time dependence of the number Z(n,t) of the n-atomic clusters in the supersaturated parent phase by means of a partial differential equation ... 

Equations (16) and (17) were derived for the isotopic effects associated with condensation in the idealized limit of no re-evaporation of the condensed material. Such a situation can arise for highly supersaturated systems and then Equation (16) gives the isotopic fractionation of the gas and Equation (17) that of the condensate as a function of the amount condensed. The same result obtains if we consider evaporation when recondensation is negligible, and then Equation (16) applies to the evaporation residue and Equation (17) to the evaporated gas. The magnitude of fractionations given by Equations (16) and (17) are illustrated in Figure 4 in the specific case of magnesium isotopes. The key point is that for systems not in... 

Pellet, M., Raghavan, S.L., Hadgraft, J. and Davis, A.R (2003) The application of supersaturated systems to percutaneous drug delivery . In Guy, R.H. and Hadgraft, J., eds., Transdermal drug delivery. Marcel Dekker, Marcel Dekker, New York, pp. 305-326. 

The classic biological example of these systems is bile salt (BS)-lecithin (L)-cholesterol (Ch) micelles which have been studied in detail by QLS [239], In TC-L-Ch systems, particle size and polydispersity were studied as functions of Ch mole fraction (= 0-15%), L/TC molar ratio (0-1.6), temperature (5-85°C), and total lipid concentration (3 and 10 g/dl) in 0.15 M NaCl. For values below the established solubilization limits (A )> added Ch has little influence on the size of simple TC micelles, on the coexistence of simple and mixed TC-L micelles, or on the growth of mixed disk TC-L micelles. For supersaturated systems >1), 10 g/dl simple micellar systems (L/TC = 0) exist as metastable micellar solutions even at = 5.3. Metastability is decreased in coexisting systems... 

One should remember that the formula is used only to describe how fast after supersaturation is achieved one can expect precipitation, and not whether it will happen. The solubility product describes the supersaturated system thermod5mamically and predicts that precipitation will take place. The supersaturation ratio describes the supersaturated system kinetically by prediction of when it will take place. Also one should remember the role of impurities in nucleation. In the original determination of the critical supersaturation ratio of barium sulfate, solvent and reagents of the lower purity were used, giving a value of 21 instead of 32. 

At the present time there is no general agreement on nucleation nomenelat-ure so to avoid confusion the terminology to be used in this and subsequent chapters will be defined here. The term primary will be reserved for all eases of nueleation in systems that do not eontain erystalline matter. On the other hand, nuelei are often generated in the vicinity of crystals present in a supersaturated system this behaviour will be referred to as secondary nucleation. Thus we may consider a simple seheme ... 

The existence of an induction period in a supersaturated system is contrary to expectations from the classical theory of homogeneous nucleation (section 5.1.1), which assumes ideal steady-state conditions and predicts immediate nucleation once supersaturation is achieved. The induction period may therefore be considered as being made up of several parts. For example, a certain relaxation time , c, is required for this system to achieve a quasi-steady-state distribution of molecular clusters. Time is also required for the formation of a stable nucleus, and then for the nucleus to grow to a detectable size, tg. So the induction period, tmd, may be written. 

A common method for producing a precipitate is to mix two reactant solutions together as quickly as possible, but the analysis of this apparently simple operation can be exceedingly complex. Precipitation processes, almost by definition, involve the creation of highly supersaturated systems and the main practical difficulty is to maintain reasonably uniform conditions throughout the reaction vessel. The choice of the method of mixing the reactants is therefore very important and the aim should be to avoid any accidental development of zones of excessive supersaturation. The sequence of reactant mixing can... 

Till PH Jr (1957) The growth of single crystals of linear polyethylene. J Polym Sci 24 301-306 Turnbull D, Fisher JC (1949) Rate of nucleation in condensed systems. J Chem Phys 17 71-73 Vohner M, Weber A (1926) Nucleus formation in supersaturated systems. Z Phys Chem (Leipzig) 119 277-301... 

Raghavan SL, Schuessel K, Davis A, Hadgraft J (2003) Formation and stabilisation of triclosan colloidal suspensions using supersaturated systems. Int J Pharm 261 153-158... 

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