18 research outputs found
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
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