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The melting temperature of a nanoscaled particle is known to decrease as the curvature of the solid-melt interface increases.  This relationship is most often modelled by a Gibbs--Thomson law, with the decrease in melting temperature proposed to be a product of the curvature of the solid-melt interface and the surface tension.  Such a law must break down for sufficiently small particles, since the curvature becomes singular in the limit that the particle radius vanishes.  Furthermore, the use of this law as a boundary condition for a Stefan-type continuum model is problematic because it leads to a physically unrealistic form of mathematical blow-up at a finite particle radius.  By numerical simulation, we show that the inclusion of nonequilibrium interface kinetics in the Gibbs--Thomson law regularises the continuum model, so that the mathematical blow up is suppressed.  As a result, the solution continues until complete melting, and the corresponding melting temperature remains finite for all time.  The results of the adjusted model are consistent with experimental findings of abrupt melting of nanoscaled particles.  This small-particle regime appears to be closely related to the problem of melting a superheated particle

Including nonequilibrium interface kinetics in a continuum model for melting nanoscaled particles