Spherically symmetric nanoparticle melting with a variable phase change temperature

Research Paper


In this paper, we analyse the melting of a spherically symmetric nanoparticle, using a continuum model which is valid down to a few nanometres. Melting point depression is accounted for by a generalised Gibbs–Thomson relation. The system of governing equations involves heat equations in the liquid and solid, a Stefan condition to determine the position of the melt boundary and the Gibbs-Thomson equation. This system is simplified systematically to a pair of first-order ordinary differential equations. Comparison with the solution of the full system shows excellent agreement. The reduced system highlights the effects that dominate the melting process and specifically that rapid melting is expected in the final stages, as the radius tends to zero. The results agree qualitatively with limited available experimental data.


Nanoparticle melting Mathematical model Phase change Gibbs–Thomson Numerical simulation 



The research of TGM was supported by a Marie Curie International Reintegration Grant Industrial applications of moving boundary problems Grant No. FP7-256417, and Ministerio de Ciencia e Innovación Grant MTM2011-23789. FF acknowledges the support of a Centre de Recerca Matemàtica PhD Grant.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Centre de Recerca Matemàtica, Campus de BellaterraBellaterraSpain
  2. 2.Departament de Matemàtica Aplicada IUniversitat Politècnica de CatalunyaBarcelonaSpain

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