Mathematical Problems in Engineering
Volume 2005 (2005), Issue 3, Pages 309-324

Modelling of free boundary problems for phase change with diffuse interfaces

Dipayan Sanyal,1 P. Ramachandra Rao,2 and O. P. Gupta3

1Central Glass and Ceramic Research Institute, 196 Raja S. C. Mullick Road, Calcutta 700032, India
2Institute of Armament Technology, Girinagar, Pune 411025, India
3Department of Mechanical Engineering, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India

Received 29 May 2004; Revised 18 November 2004

Copyright © 2005 Dipayan Sanyal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a continuum thermodynamical framework for simulating multiphase Stefan problem. For alloy solidification, which is marked by a diffuse interface called the mushy zone, we present a phase filed like formalism which comprises a set of macroscopic conservation equations with an order parameter which can account for the solid, liquid, and the mushy zones with the help of a phase function defined on the basis of the liquid fraction, the Gibbs relation, and the phase diagram with local approximations. Using the above formalism for alloy solidification, the width of the diffuse interface (mushy zone) was computed rather accurately for iron-carbon and ammonium chloride-water binary alloys and validated against experimental data from literature.