Effect of the surface-stimulated mode on the kinetics of homogeneous crystal nucleation in droplets

A kinetic theory of homogeneous crystal nucleation in unary droplets is presented taking into account that a crystal nucleus can form not only in the volume-based mode (with all its facets within the droplet) but also in the surface-stimulated one (with one of its facets at the droplet surface). The previously developed thermodynamics of surface-stimulated crystal nucleation rigorously showed that if at least one of the facets of the crystal is only partially wettable by its melt, then it is thermodynamically more favorable for the nucleus to form with that facet at the droplet surface rather than within the droplet. So far, however, the kinetic aspects of this phenomenon had not been studied at all. The theory proposed in the present paper advocates that even in the surface-stimulated mode crystal nuclei initially emerge (as sub-critical clusters) homogeneously in the sub-surface layer, not "pseudo-heterogeneously" at the surface. A homogeneously emerged sub-critical crystal can become a surface-stimulated nucleus due to density and structure fluctuations. This effect contributes to the total rate of crystal nucleation (as the volume-based mode does). An explicit expression for the total per-particle rate of crystal nucleation is derived. Numerical evaluations for water droplets suggest that the surface-stimulated mode can significantly enhance the per-particle rate of crystal nucleation in droplets as large as 10 microns in radius. Possible experimental verification of the proposed theory is discussed.Comment: 33 pages, 3 figure

Cinétique de la nucléation binaire non-isotherme et de la condensation binaire aux conditions dynamiques

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal

Histogram analysis as a method for determining the line tension by Monte-Carlo simulations

A method is proposed for determining the line tension, which is the main physical characteristic of a three-phase contact region, by Monte-Carlo (MC) simulations. The key idea of the proposed method is that if a three-phase equilibrium involves a three-phase contact region, the probability distribution of states of a system as a function of two order parameters depends not only on the surface tension, but also on the line tension. This probability distribution can be obtained as a normalized histogram by appropriate MC simulations, so one can use the combination of histogram analysis and finite-size scaling to study the properties of a three phase contact region. Every histogram and results extracted therefrom will depend on the size of the simulated system. Carrying out MC simulations for a series of system sizes and extrapolating the results, obtained from the corresponding series of histograms, to infinite size, one can determine the line tension of the three phase contact region and the interfacial tensions of all three interfaces (and hence the contact angles) in an infinite system. To illustrate the proposed method, it is applied to the three-dimensional ternary fluid mixture, in which molecular pairs of like species do not interact whereas those of unlike species interact as hard spheres. The simulated results are in agreement with expectations