Single phase limit for melting nanoparticles
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14114a.pdf. |
Description
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.
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ID Code: | 14114 | ||
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Item Type: | Contribution to Journal (Journal Article) | ||
Refereed: | Yes | ||
ORCID iD: |
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Measurements or Duration: | 19 pages | ||
Keywords: | Nanopartical Melting, One-Phase Limit, Stefan Problem, Surface Tension | ||
DOI: | 10.1016/j.apm.2008.07.009 | ||
ISSN: | 0307-904X | ||
Pure ID: | 31921918 | ||
Divisions: | Past > QUT Faculties & Divisions > Faculty of Science and Technology Past > QUT Faculties & Divisions > Science & Engineering Faculty Current > Research Centres > Australian Research Centre for Aerospace Automation |
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Copyright Owner: | Consult author(s) regarding copyright matters | ||
Copyright Statement: | This work is covered by copyright. Unless the document is being made available under a Creative Commons Licence, you must assume that re-use is limited to personal use and that permission from the copyright owner must be obtained for all other uses. If the document is available under a Creative Commons License (or other specified license) then refer to the Licence for details of permitted re-use. It is a condition of access that users recognise and abide by the legal requirements associated with these rights. If you believe that this work infringes copyright please provide details by email to qut.copyright@qut.edu.au | ||
Deposited On: | 21 Jul 2008 00:00 | ||
Last Modified: | 03 Mar 2024 13:46 |
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