Supersaturation coefficient

Crystal Formation There are obviously two steps involved in the preparation of ciystal matter from a solution. The ciystals must first Form and then grow. The formation of a new sohd phase either on an inert particle in the solution or in the solution itself is called nucle-ation. The increase in size of this nucleus with a layer-by-layer addition of solute is called growth. Both nucleation and ciystal growth have supersaturation as a common driving force. Unless a solution is supersaturated, ciystals can neither form nor grow. Supersaturation refers to the quantity of solute present in solution compared with the quantity which would be present if the solution were kept for a veiy long period of time with solid phase in contac t with the solution. The latter value is the equilibrium solubility at the temperature and pressure under consideration. The supersaturation coefficient can be expressed... 

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. 

Sasaki, N. and Minato, M. (1983) Effect of the degree of supersaturation upon apparent partition coefficients of lead and strontium ions between BaSOa and aqueous solution. Miner. J., 11, 365-381. 

The activity product Q ave corresponding to the averaged analysis (ignoring variation in activity coefficients) equals the equilibrium constant K only when fluids A and B are identical otherwise Qmc exceeds K and anhydrite is reported to be supersaturated. To demonstrate this inequality, we can assume arbitrary values for aCa++ and so4 that satisfy Equations 6.4—6.5 and substitute them into Equation 6.6. 

The model calculated in this manner predicts that two minerals, alunite [KA13(0H)6(S04)2] and anhydrite (CaSC>4), are supersaturated in the fluid at 175 °C, although neither mineral is observed in the district. This result is not surprising, given that the fluid s salinity exceeds the correlation limit for the activity coefficient model (Chapter 8). The observed composition in this case (Table 22.1), furthermore, actually represents the average of fluids from many inclusions and hence a mixture of hydrothermal fluids present over a range of time. As noted in Chapter 6, mixtures of fluids tend to be supersaturated, even if the individual fluids are not. 

Whilst the fundamental driving force for crystallisation, the true thermodynamic supersaturation, is the difference in chemical potential, in practice supersaturation is generally expressed in terms of solution concentrations as given in equations 15.1-15.3. Mullin and Sohnel(19) has presented a method of determining the relationship between concentration-based and activity-based supersaturation by using concentration-dependent activity-coefficients. 

How can this be No additional gas was added to the water. The answer lies in the nonlinear temperature effect on the Bunsen solubility coefficient (Figure 6.1). Because of the concave nature of the curves relating the Bunsen solubility coefficient to temperature, the result of this type of postequilibration temperature change is always supersaturation. 

The values of k were 0.18, 1.98 and 1.16 x 10 (moldm s basis) for Soils A, B and C in Figure 3.15, respectively. These values are more than four times k for the solution system. The values of the inhibition coefficients-a = —1686, = 6.13, c = 3854—were smaller than in the solution system. As a result the concentrations of P and DOC required to halve the rate of precipitation were 10 times those in the solution system. Also the interaction between [Pl] and [Cl] was negligible in the solution system but important in the soils. Figure 3.16 shows plots of Equation (3.54) for different valnes of [Pl] and [Cl] and w = 0.75 gdm. For the values used, which are realistic for submerged-soil solutions, the combined inhibitory effect of P and DOC was snch that an order of magnitude greater degree of supersaturation [(Ca +)(C03 )/A sp] is necessary to produce the same rate of precipitation as in the absence of inhibitors. 

Growth of particles by accumulation on existing particles can be classed as two broad processes. If the precursor is supersaturated, growth will occur at a rate limited by vapor diffusion, which depends on the supersaturation, the temperature, the particle size, and the accommodation coefficient at the surface. The proportionality of particle size changes with the ratio of particle diameter to mean free path of the suspending... 

The membrane and diffusion-media modeling equations apply to the same variables in the same phase in the catalyst layer. The rate of evaporation or condensation, eq 39, relates the water concentration in the gas and liquid phases. For the water content and chemical potential in the membrane, various approaches can be used, as discussed in section 4.2. If liquid water exists, a supersaturated isotherm can be used, or the liquid pressure can be assumed to be either continuous or related through a mass-transfer coefficient. If there is only water vapor, an isotherm is used. To relate the reactant and product concentrations, potentials, and currents in the phases within the catalyst layer, kinetic expressions (eqs 12 and 13) are used along with zero values for the divergence of the total current (eq 27). 

Employing experimental supersaturated solution diffusion coefficient data and the cluster di sion theory of Cussler (22), Myerson and Lo (27 attempted to estimate the average cluster size in supersaturated glycine solutions. They estimated an average cluster size on the order of two molecules. Their calculations indicated that while the average cluster size was small, large clusters of hundreds of molecules existed, only there were very few of them. Most of the molecular association was in the form of dimers and trimers. 

The level of impurity uptake can be considered to depend on the thermodynamics of the system as well as on the kinetics of crystal growth and incorporation of units in the growing crystal. The kinetics are mainly affected by the residence time which determines the supersaturation, by the stoichiometry (calcium over sulfate concentration ratio) and by growth retarding impurities. The thermodynamics are related to activity coefficients in the solution and the solid phase, complexation constants, solubility products and dimensions of the foreign ions compared to those of the ions of the host lattice [2,3,4]. 

Geochemical kinetics is stiU in its infancy, and much research is necessary. One task is the accumulation of kinetic data, such as experimental determination of reaction rate laws and rate coefficients for homogeneous reactions, diffusion coefficients of various components in various phases under various conditions (temperature, pressure, fluid compositions, and phase compositions), interface reaction rates as a function of supersaturation, crystal growth and dissolution rates, and bubble growth and dissolution rates. These data are critical to geological applications of kinetics. Data collection requires increasingly more sophisticated experimental apparatus and analytical instruments, and often new progresses arise from new instrumentation or methods. 

The relationship between the number concentration (AO of CCN and the supersaturation (S) is often expressed in the form N = CSk, where C and k are empirical coefficients characteristic of the particular air mass (Pruppacher and Klett, 1997). However, alternate forms such as... 

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