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A kinetic theory of homogeneous crystal nucleation in unary droplets ispresented taking into account that a crystal nucleus can form not only in thevolume-based mode (with all its facets within the droplet) but also in thesurface-stimulated one (with one of its facets at the droplet surface). Thepreviously developed thermodynamics of surface-stimulated crystal nucleationrigorously showed that if at least one of the facets of the crystal is onlypartially wettable by its melt, then it is thermodynamically more favorable forthe nucleus to form with that facet at the droplet surface rather than withinthe droplet. So far, however, the kinetic aspects of this phenomenon had notbeen studied at all. The theory proposed in the present paper advocates thateven in the surface-stimulated mode crystal nuclei initially emerge (assub-critical clusters) homogeneously in the sub-surface layer, not"pseudo-heterogeneously" at the surface. A homogeneously emerged sub-criticalcrystal can become a surface-stimulated nucleus due to density and structurefluctuations. This effect contributes to the total rate of crystal nucleation(as the volume-based mode does). An explicit expression for the totalper-particle rate of crystal nucleation is derived. Numerical evaluations forwater droplets suggest that the surface-stimulated mode can significantlyenhance the per-particle rate of crystal nucleation in droplets as large as 10microns in radius. Possible experimental verification of the proposed theory isdiscussed.

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