Kinetics of boiling in binary liquid-gas solutions: Comparison of different approaches

摘要

A comparative analysis of the results of determination of the work of critical cluster formation in nucleation theory for three different methods of evaluation-Gibbs' method (employing the capillarity approximation), the van der Waals-Cahn and Hilliard and a newly developed modified GIbbs' approach-is given in application to phase formation in multicomponent systems. As an example, processes of boiling in binary liquid-gas solutions, in particular, in nitrogen-helium mixtures are investigated. In addition to the work of critical cluster formation, the bulk properties of the critical bubbles, their characteristic sizes and the values of the surface tension are determined in dependence on the initial supersaturation in the system or, equivalently, on the size of the critical clusters. It is shown that later two mentioned methods (the van der Waals-Cahn and Hilliard and the modified Gibbs' approach) lead, in the determination of the work of critical cluster formation, to qualitatively and widely even quantitatively equivalent results. As one of the more general consequences from the present analysis, it has been proven that the modified Gibbs' approach represents a highly effective tool for the determination of the work of formation of clusters or bubbles of critical sizes not only for one-component and quasibinary systems, discussed earlier, but for phase formation in multicomponent system of, in general, arbitrary numbers of components as well. It is shown that the modified Gibbs' approach is preferable as compared with Gibbs' original treatment not only due to its advantages with respect to an appropriate determination of the properties of clusters of critical sizes, but also from general theoretical considerations. In the limit of large sizes of the critical clusters, both approaches-Gibbs' original treatment and the modified or generalized Gibbs' approach-lead to equivalent results.