Micro/nanoparticle melting with spherical symmetry and surface tension

Abstract

The process of melting a small spherical particle is treated by setting up a two-phase Stefan problem. Surface tension is included through the Gibbs–Thomson condition, the effect of which is to decrease the melting temperature as the particle radius decreases. Analytical results are derived via a small-time expansion and also through large Stefan number asymptotics. Numerical solutions are computed with a front-fixing scheme, and these results suggest that the model exhibits finite-time blow-up, in the sense that both the interface speed and the temperature gradient in the solid phase (at the interface) will become unbounded at some time before complete melting. The near-blow-up behaviour appears to be similar to that encountered in the ill-posed problem of melting a superheated solid (without surface tension), and may help explain the onset of abrupt melting observed in some experiments with nanoscaled particles.