Single phase limit for melting nanoparticles
Wu, Bisheng, McCue, Scott W., Tillman, Pei, & Hill, James M. (2009) Single phase limit for melting nanoparticles. Applied Mathematical Modelling, 33( ), pp. 23492367.

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Abstract
The melting of a spherical or cylindrical nanoparticle is modelled as a Stefan problem by including the effects of surface tension through the GibbsThomson condition. A onephase moving boundary problem is derived from the general twophase formulation in the singular limit of slow conduction in the solid phase, and the resulting equations are studied analytically in the limit of small time and large Stefan number. Further analytical approximations for the temperature distribution and the position of the solidmelt interface are found by applying an integral formulation together with an iterative scheme. All these analytical results are compared with numerical solutions obtained using a frontfixing method, and are shown to provide good approximations in various regimes. The inclusion of surface tension, which acts to decrease the melting temperature as the particle melts, is shown to accelerate the melting process. Unlike the classical onephase Stefan problem without surface tension, the solidmelt interface exhibits blowup at some critical radius of the particle (which for metals is of the order of a few nanometres), a phenomenon that has been observed experimentally. An interesting feature of the model is the prediction that surface tension drives superheating in the solid particle before blowup occurs.
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