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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. 2349-2367.

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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 Gibbs-Thomson condition. A one-phase moving boundary problem is derived from the general two-phase 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 solid-melt 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 front-fixing 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 one-phase Stefan problem without surface tension, the solid-melt interface exhibits blow-up 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 blow-up occurs.

Impact and interest:

9 citations in Scopus
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8 citations in Web of Science®

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195 since deposited on 21 Jul 2008
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ID Code: 14114
Item Type: Journal Article
Keywords: Nanoparticle melting, one phase limit, Stefan problem, moving boundary, sphere, surface tension, Gibbs Thomson effect, finite time blow up, large Stefan number, small time behaviour
DOI: 10.1016/j.apm.2008.07.009
ISSN: 0307-904X
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > PURE MATHEMATICS (010100) > Pure Mathematics not elsewhere classified (010199)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical and Computational Mathematics not elsewhere classified (010399)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Applied Mathematics not elsewhere classified (010299)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Copyright Owner: Copyright 2008 Elsevier
Copyright Statement: Reproduced in accordance with the copyright policy of the publisher.
Deposited On: 21 Jul 2008
Last Modified: 29 Feb 2012 23:43

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