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

Abstract

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 latter 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 systems 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.

Dynamics of first-order phase transitions in multicomponent systems: a new theoretical approach

“…This statement is confirmed by a variety of computer simulations or density functional calculations proving a strong change of the bulk properties of critical clusters in dependence on the size of the critical clusters or, equivalently, the supersaturation in the system [21][22][23][24]. In this way, one is led to the conclusion that not only some kind of curvature dependence of the specific surface energy has to be incorporated into the description of nucleation, but a size dependence of the thermodynamic driving force of the transformation as well.…”

“…This mechanism was studied earlier in application to segregation processes in solutions [25][26][27]. Alternatively or simultaneously, variations in the density of the critical clusters as compared with the macroscopic values (similarly to condensation of vapors [28] or bubble formation in liquids [24,29]) and, in application to crystallite formation, deviations in the structural properties could occur.…”

“…A generalization of Gibbs' classical approach, fulfilling the above requirements, has been developed in recent years and applied to the description of the properties of critical clusters [22][23][24][25][27][28][29][33][34][35]. It leads to reference states for the critical clusters, which deviate from Gibbs' predictions.…”

Columnar modelling of nucleation burst evolution in the convective boundary layer – first results from a feasibility study Part I: Modelling approach

“…However, this formula is not applicable to very intensive nucleation bursts, to potential nucleation events associated with cloud outflows or to nucleation occurring in plumes, which undergo strong mixing with ambient air. Based on a critical analysis of the advantages and shortcomings of the classical Gibbs approach to determine the parameters of the critical cluster and the work of critical cluster formation in heterogeneous systems, a generalised Gibbs approach has been proposed and applied to describe phase formation processes in multicomponent solutions by Schmelzer et al (1999Schmelzer et al ( , 2002Schmelzer et al ( , 2003Schmelzer et al ( , 2004aSchmelzer et al ( ,b, 2005, Schmelzer and Schmelzer Jr. (2002) and Schmelzer and Abyzov (2005). This approach delivers a theoretically wellfounded description not only of thermodynamic equilibrium but also of thermodynamic non-equilibrium states of a cluster or ensembles of clusters of arbitrary sizes and composi-4186 O. Hellmuth: Burst modelling tions.…”

Comment on “Minimum free-energy pathway of nucleation” [J. Chem. Phys. 135, 134508 (2011)]

“…Near to the spinodal curve it is by this reason kinetically more favorable to pass the ridge forming relatively small ridge clusters instead of large critical clusters corresponding to the saddle point of the thermodynamic potential surface. In contrast, employing the classical Gibbs method of determination of critical clusters sizes (utilizing instead of the capillarity approximation suitable methods for the determination of the work of critical cluster formation), the critical cluster size tends to zero near the spinodal curve [3][4][5][6][7] (for metastable initial states) or cannot be determined at all (for unstable ini-tial states). By this reason, the sketched here mechanism does not work in such theoretical treatment.…”