Growth and dissolution rates

A computer model has been generated which predicts the behaviour of a continuous well mixed gypsum crystallizer fed with a slurry of hemihydrate crystals. In the crystallizer, the hemihydrate dissolves as the gypsum grows. The solution operating calcium concentration must lie in the solubility gap. Growth and dissolution rates are therefore limited. 

The growth and dissolution rates depend on the driving forces within the solubility gap and are Interrelated by the material balance of relation 1 (In suitable form). 

The operating calcium concentration for a gypsum crystallizer fed with hemlhydrate crystals must lie In the solubility gap between the solubilities of the two species. This places severe limits on the range of growth and dissolution rates possible. 

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. 

Figure 4-6 Interface reaction rate as a function of temperature, pressure, and composition. The vertical dashed line indicates the equilibrium condition (growth rate is zero), (a) Diopside growth and melting in its own melt as a function of temperature with the following parameters Te= 1664K at 0.1 MPa, A5m-c = 82.76J mol K , E/R —30000 K, 4 = 12.8 ms K, and AV c l. l x 10 m /mol. The dots are experimental data on diopside melting (Kuo and Kirkpatrick, 1985). (b) Diopside growth and melting in its own melt as a function of pressure at 1810 K (Tg = 1810 K at 1 GPa from the equilibrium temperature at 0.1 MPa and the Clapeyron slope for diopside). (c) Calcite growth and dissolution rate in water at 25 °C as a function of Ca " and CO concentrations.

If mass transfer in the melt controls olivine growth and dissolution rate, explain why there may be dendritic growth but no dendritic dissolution. 

The processes of growth of a chemical compound layer at the solid-liquid interface and its dissolution into the liquid phase take place simultaneously. Depending on the sign of the difference of the growth and dissolution rates, the layer is formed (at a positive value of this difference) or is not formed (at a negative value) between the interacting substances. 

Growth and dissolution rates of crystals can be measured conveniently in the laboratory fluidized bed crystallizer described above Figure 6.20). Some typical results for potash alum are shown in Figure 6.31, where it can be seen that dissolution rates are very much greater than growth rates under equal driving forces (Ac). Similar results have been reported for potassium sulphate (Mullin... 

Garside, J. and Mullin, J.W. (1968) Crystallization of aluminium potassium sulphate a study in the assessment of crystallizer design data. Ill Growth and dissolution rates. Transactions of the Institution of Chemical Engineers, 46, 11-18. 

Baraboshkin AN, Esina N.O., Talanova M.l.(1988) The effect of oxychemical impurities on the growth and dissolution rates of monocrystalline molybdenum facets, Vysokochistye Veschestva 24, 206-207... 

Figure 6.9 Growth and dissolution rates of epsomite in the presence of NaCI. (a) Thermodynamic effect, (b) After correction of the supersaturation kinetic effect [22].

Figure 6.10 Growth and dissolution rates of NaCI in the presence of CuS04-5H20 [22]. 6.1.3...

As Fig. 6.13 illustrates growth and dissolution are not symmetric with respect to the saturation state. At very high undersaturation, the rate of dissolution becomes independent of S and converges to the value of the apparent rate constant. This is why studies of dissolution far from equilibrium allow to study the influence of inhibition/ catalysis on the apparent rate constant, independently from the effect of S. The same is not true for crystal growth. 

In carbonate diagenesis V we deal usually with a combination of low supersaturation and absence of mechanical agitation. Homogeneous nucleation will certainly not occur. The important factors to be investigated are heterogeneous nucleation and rates of growth and dissolution of crystals. 

The geochemical fate of most reactive substances (trace metals, pollutants) is controlled by the reaction of solutes with solid surfaces. Simple chemical models for the residence time of reactive elements in oceans, lakes, sediment, and soil systems are based on the partitioning of chemical species between the aqueous solution and the particle surface. The rates of processes involved in precipitation (heterogeneous nucleation, crystal growth) and dissolution of mineral phases, of importance in the weathering of rocks, in the formation of soils, and sediment diagenesis, are critically dependent on surface species and their structural identity. 

With regard to the attachment and detachment energies, the corners of a crystal or a rough interface that is constructed by kinks alone are sites where the process proceeds most quickly, whereas the low-index crystal faces, corresponding to smooth interfaces, represent the direction with the minimum rate of normal growth and dissolution. As a result, if a single crystalline sphere is dissolved in an isotropic environmental phase, a dissolution form bounded by both flat and curved crystal faces appears. This is called the dissolution form, which is not the same as the growth form. 

It should be emphasised that in following the rate of dissolution of solid A in liquid B by the mass loss of a solid specimen of substance A, measured by weighing the specimen before and after the experiment, errors may well arise, due to the formation of a chemical compound layer at the solid-liquid interface. On the one hand, dissolution of the solid phase A in the liquid phase B reduces the mass of the solid specimen. On the other, however, formation of the ApBq compound layer adhering to the surface of the solid specimen increases its mass (at k0 > b). Hence, the experimentally determined change in the mass of the solid specimen is a consequence of the two simultaneously occurring processes, namely, growth and dissolution of the ApBq layer. 

---