Mathematical modelling of phase change at the nanoscale *

Standard mathematical models for phase change at the nanoscale involve an implicit assumption that the latent heat is released at the bulk phase change temperature. They also assume the latent heat to be constant (while the melt temperature decreases with decreasing size). There is clear experimental evidence that this is not the case. In this paper, we examine the formulation of the Stefan problem at the nanoscale and present a new form of Stefan condition which correctly reflects the latent heat release, including both melt temperature and latent heat depression. We go on to show that the standard formulation can lead to melt rates up to three times slower than in reality.