Micro/nano particle melting with spherical symmetry and surface tension
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.
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