University of Cambridge > > Isaac Newton Institute Seminar Series > Stefan problem for spheres: surface tension, blow-up, and regularisation

Stefan problem for spheres: surface tension, blow-up, and regularisation

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Co-authors: Julian Back (Queensland University of Technology), Timothy Moroney (Queensland University of Technology)

The mathematical problem of melting a sphere seems simple enough to formulate as a classical Stefan problem, but happens to display an interesting and rather complicated asymptotic structure in the limit of complete melting. For the application of melting nanoscaled metal particles, the formulation needs a slight modification, as the melting temperature of very small particles is known to be size-dependent. The appropriate boundary condition should include a surface tension term (via the Gibbs-Thomson law), which acts to reduce the melting temperature as the radius of the particle decreases. For this model, the solution exhibits a form of blow-up at a finite particle radius. I will discuss this behaviour, and how the phenomenon of abrupt melting is driven by a counter-intuitive heat flux {m from} the particle into the solid-melt interface. This process seems closely related to the ill-posed problem of melting a superheated solid, even without the effects of surface ten sion. Regularisation of this blow-up via kinetic undercooling will also be discussed.

This talk is part of the Isaac Newton Institute Seminar Series series.

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