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Mathematical modelling of Tyndall star initiation

Published online by Cambridge University Press:  12 August 2015

A. A. LACEY ,
M. G. HENNESSY ,
P. HARVEY  and
R. F. KATZ
A. A. LACEY
Affiliation:
Maxwell Institute for Mathematical Sciences and Department of Mathematics, School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK email: A.A.Lacey@hw.ac.uk
M. G. HENNESSY
Affiliation:
Department of Chemical Engineering, Imperial College, London, SW7 2AZ, UK email: m.hennessy@imperial.ac.uk
P. HARVEY
Affiliation:
Department of Physics & Astronomy, University College London, Gower Street, London, WC1E 6BT, UK email: peter.harvey.11@alumni.ucl.ac.uk
R. F. KATZ
Affiliation:
Department of Earth Sciences, University of Oxford, South Parks Road, Oxford, OX1 3AN, UK email: richard.katz@earth.ox.ac.uk
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Abstract

The superheating that usually occurs when a solid is melted by volumetric heating can produce irregular solid–liquid interfaces. Such interfaces can be visualised in ice, where they are sometimes known as Tyndall stars. This paper describes some of the experimental observations of Tyndall stars and a mathematical model for the early stages of their evolution. The modelling is complicated by the strong crystalline anisotropy, which results in an anisotropic kinetic undercooling at the interface; it leads to an interesting class of free boundary problems that treat the melt region as infinitesimally thin.

Keywords

Free boundary problemskinetic Wulff shapesanisotropic kinetic undercoolingco-dimension-two problems
Type
Papers
Information
European Journal of Applied Mathematics , Volume 26 , Special Anniversay Issue 5: Celebrating 75 years , October 2015 , pp. 615 - 645
Copyright
Copyright © Cambridge University Press 2015 

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