Micro/nanoparticle melting with spherical symmetry and surface tension

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dc.contributor.authorMcCue, S.
dc.contributor.authorWu, B.
dc.contributor.authorHill, J.
dc.date.issued2009
dc.description.abstractThe 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.
dc.description.statementofresponsibilityScott W. McCue, Bisheng Wu and James M. Hill
dc.identifier.citationIMA Journal of Applied Mathematics, 2009; 74(3):439-457
dc.identifier.doi10.1093/imamat/hxn038
dc.identifier.issn0272-4960
dc.identifier.issn1464-3634
dc.identifier.urihttp://hdl.handle.net/2440/64165
dc.language.isoen
dc.publisherOxford Univ Press
dc.rights© The Author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
dc.source.urihttps://doi.org/10.1093/imamat/hxn038
dc.subjecttwo-phase Stefan problem
dc.subjectsize-dependent melting
dc.subjectsurface tension
dc.subjectfinite-time blow-up
dc.subjectsuperheating.
dc.titleMicro/nanoparticle melting with spherical symmetry and surface tension
dc.typeJournal article
pubs.publication-statusPublished

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