QUT ePrints

Micro/nano particle melting with spherical symmetry and surface tension

McCue, Scott W., Wu, Bisheng, & Hill, James M. (2009) Micro/nano particle melting with spherical symmetry and surface tension. IMA Journal of Applied Mathematics, 74, pp. 439-457.

View at publisher

Abstract

The 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.

Impact and interest:

7 citations in Scopus
Search Google Scholar™
6 citations in Web of Science®

Citation countsare sourced monthly from Scopus and Web of Science® citation databases.

These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.

Citations counts from the Google Scholar™ indexing service can be viewed at the linked Google Scholar™ search.

Full-text downloads:

231 since deposited on 27 Oct 2008
37 in the past twelve months

Full-text downloadsdisplays the total number of times this work’s files (e.g., a PDF) have been downloaded from QUT ePrints as well as the number of downloads in the previous 365 days. The count includes downloads for all files if a work has more than one.

ID Code: 15345
Item Type: Journal Article
Keywords: two phase Stefan problem, size dependent melting, surface tension, finite time blow up, superheating, free boundary problem, formal asymptotics
DOI: 10.1093/imamat/hxn038
ISSN: 1464-3634
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > OTHER MATHEMATICAL SCIENCES (019900) > Mathematical Sciences not elsewhere classified (019999)
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) > 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 Oxford University Press
Deposited On: 27 Oct 2008
Last Modified: 29 Feb 2012 23:47

Export: EndNote | Dublin Core | BibTeX

Repository Staff Only: item control page