Gas-liquid nucleation

The natural first question to ask is whether the crystal-liquid surface free energy can be measured experimentally by some method that is independent of nucleation kinetics. In gas-liquid nucleation studies, for example, it is routine to measure the surface tension of the liquid and to use its equality with the gas-liquid surface free energy to make predictions of nucleation rates and compare them with experiment. For the liquid-solid transition, the situation is quite different, however. This is true first because the surface tension and the surface free energy are no longer strictly equal due to the possible existence of strains in the crystal. The second reason is that measurements of liquid-solid free energies or interfacial tensions are by no means simple to devise or carry out, and so are available only in certain special cases. These limited experimental data are summarized in this section. 

Talanquer V, Oxtoby DW (1994) Dynamical density functional theory of gas-liquid nucleation. J Chem... 

The traditional method of studying gas-liquid nucleation involves the use of a cloud chamber. In such a chamber the saturation ratio S is changed until, at a given temperature,... 

The traditional method of studying gas-liquid nucleation involves the use of a cloud chamber. In such a chamber the saturation ratio 5 is changed until, at a given temperature, droplet formation is observable. Because once clusters reach the critical size for nucleation, subsequent droplet growth is rapid, the rate of formation of macroscopically observable droplets is assumed to be that of formation of critical nuclei. In such a device it is difficult to measure the actual rate of nucleation because the nucleation rate changes so rapidly with S. J is very small for S values below a critical saturation ratio 5, and very large for S > 5,. Thus what is actually measured is the value of 5, defined rather arbitrarily by the point where the rate of appearance of droplets is 1 cm s . ... 

Zeng, X.C., and Oxtoby, D.W. (1991) Gas-liquid nucleation in Lennard-jones fluids, J.Chem. Phys. 94,4772. 

In this article, we have discussed a newly developed theory of gas-liquid nucleation at large metastability. The theory is based on an extended set of order parameters... 

The size of crystals produced in the gas-liquid system varied from 10 to 100 pm by controlling the level of supersaturation, while the liquid-liquid system produced crystals of 5—30 pm. The wide variation of crystal size is due to the marked sensitivity of the nucleation rate on the level of supersaturation, while the impurity content is another variable that can affect the crystal formation. 

The overall set of partial differential equations that can be considered as a mathematical characterization of the processing system of gas-liquid dispersions should include such environmental parameters as composition, temperature, and velocity, in addition to the equations of bubble-size and residence-time distributions that describe the dependence of bubble nucleation and growth on the bubble environmental factors. A simultaneous solution of this set of differential equations with the appropriate initial and boundary conditions is needed to evaluate the behavior of the system. Subject to the Curie principle, this set of equations should include the possibilities of coupling effects among the various fluxes involved. In dispersions, the possibilities of couplings between fluxes that differ from each other by an odd tensorial rank exist. (An example is the coupling effect between diffusion of surfactants and the hydrodynamics of bubble velocity as treated in Section III.) As yet no analytical solution of the complete set of equations has been found because of the mathematical difficulties involved. To simplify matters, the pertinent transfer equation is usually solved independently, with some simplifying assumptions. 

If it slow, then nucleation is likely to be due solely to proximity. Model D is an example of volame nucleation idiere decomposition of a solid is involved whereas Model E is that involving gas or liquid nucleation of the solid. Note that if nucleation does not occur, the solid reacts uniformly throughout its whole volume (Model F). However, this mode is rare and the nucleation stages are more likely to occur. We wUl not dwell upon how these nucleation models were derived and will only present the results here. One is referred to Appendix I wherein one can study the mathematics used to obtain the net-result. 

Kosterin, S. I., 1949, Study of Influence of Tube Diameter and Position upon Hydraulic Resistance and Flow Structure of Gas-Liquid Mixtures, Izvestiza Akademii Nauk SSSR, Otdelema Tekhni-cheskikh No. 12, 1824, Translation 3085, Henry Brutcher Tech. Translation, Altadena, CA. (3) Kottowski, H., and G. Grass, 1970, Influence on Superheating by Suppression of Nucleation Cavities and Effect of Surface Microstructure on Nucleation Sites, Proc. Symp. LIM Heat Transfer and Fluid Dynamics, p. 108, ASME, New York. (2)... 

Fig. 9.4.1 Schematic diagram of a particle growth in the aerosol technique. Nucleation proceeds in between two substrates with high and low temperature, the difference of which is several thousands of kelvins, High-temperature substrate is a heating element and low-temperature substrate is a kind of coolant such as gas, liquid, or solid substrate, depending on the operation mode. (From Ref. 1,)...

With such low concentrations of components available to form critical nuclei, hydrate formation seems unlikely in the bulk phases. However, at an interface where higher concentrations exist through adsorption (particularly at the vapor-liquid interface where both phases appear in abundance) cluster growth to a supercritical size is a more likely event. High mixing rates may cause interfacial gas + liquid + crystal structures to be dispersed within the liquid, giving the appearance of bulk nucleation from a surface effect. 

Hydrate formation from free gas will likely initiate at a gas-liquid interface, as observed in the laboratory experiments of Chapter 6. As indicated in Chapter 3, either initial hydrate formation or a solid phase can serve as nucleation sites for additional formation from the gas and aqueous liquid phases. However, most geochemists (Claypool and Kaplan, 1974 Finley et al., 1987, etc.) suggest hydrates form from gas (either at equilibrium or supersaturated) dissolved in the liquid phase, without a free gas. 

In 1949, Turnbull and Fisher extended to the liquid-solid transition the earlier work of Becker and Doring on homogeneous nucleation of the gas-liquid transition. Their work presumed the existence in the liquid of a steady-state distribution of small crystallites which were taken to be approximately spherical in shape. The free energy of a crystallite containing i atoms was assumed to have the form... 

Thus, if a liquid contains suspended particles with complex microrelief, a vapor-gas nucleus often remains in small cracks in such particles. With poor wettability by the liquid, nucleation of a cavity under action of tensile acoustic stresses should always begin from the vapor-gas state in the entrance of the crack. 

The analysis of thermo-baric changes in the wet soil samples saturated with CO2 as a function of time under condition of cyclic cooling and heating permits to follow the kinetic and thermo-baric indicators of phase transitions within the pore space of the samples. On cooling of wet gas-saturated soils under gas pressures higher than the three-phase equilibrium line gas - water - CO2 hydrate , conditions for gas hydrates nucleation in pore space of soils are created. Pressure stabilization marks the end of the phase transition of water into hydrate. Upon further cooling below 0°C the remaining, untransformed liquid turns into ice. 

The nucleation barrier is easy to formulate considering that the created gas-liquid interface related to bubble nucleation increases the system energy by 27ir (r is the radius of the spherical bubble, and y is the liquid-vapour surface tension), while the formation of the most stable phase provides bulk energy (4/37ir AP, with AP = Pliquid - Pvapour) According to the CNT, the competition between these two opposite effects results in an energy barrier... 

The process of crystal nucleation and growth is equivalent to a phase transition. The initial phase might be a gas, liquid, solution or solid (e.g. glass or another crystal) and the final phase need not be a crystal as traditionally defined. It could be a liquid crystal, a quasi-crystal, a polytype or some other defect solid. The phase transition proceeds via a critical state, which is intermediate between the two phases of the transition and holds the key to the understanding of crystal growth. 

Model D is an example of the decomposition of a solid whereas Model E is that involving gas or liquid nucleation of the solid. Note that if nucleation does not occur (this mechanism is not usualfy the norm), the solid reacts uniformly throughout its whole volume (Model F). 

In theory it is possible to nucleate bubbles either in the bulk phase or at solid surfaces as a result of statistical density fluctuations. In practice, the theoretical and measured fracture pressures of pure liquids are far in excess of those corresponding to the superheats or supersaturations for vapor or gas bubble nucleation experimentally observed in engineering systems (F2, F7, Kl). On the other hand, conditions for homogeneous nucleation become favorable at extremely high superheats in the presence of ionizing radiation (G4, G5). The latter observation led to the introduction of the liquid-hydrogen bubble chamber. A simple explanation of this phenomenon is that the... 

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