Abstract
We give an overview of contributions made to the computational phase-field modelling of alloy solidification from the University of Leeds as part of the LiME project (EPSRC Advanced Manufacturing Hub in Liquid Metal Engineering). The broader look at the more salient features from our research allows the individual contributions to be seen in a wider context than can be seen from each contribution separately. We begin with a general introduction to phase-field and then reference the numerical issues that arise from the solution of the model before outlining contributions to phase-field modelling that we found most interesting or significant. These range from controlling and developing interface-width independent modelling; controlling morphology in both single and multiphase settings; generalising from single to multiphase models; and creating a thermodynamically consistent framework for modelling entropy flow and thereby postulating a temperature field consistent with the concepts of, and applicable in, multiphase and density-dependent settings.
Highlights
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The principle difference between non-equilibrium and equilibrium thermodynamics is the existence of fields, such as temperature or concentration, that change in time
The principle behind much of the phase-field modelling is the principle of optimal free energy minimisation, which firmly establishes phase-field solidification as modelling dissipative phenomena
Summary
The process of solidification of metals and alloys can be modelled using non-equilibrium thermodynamics. Since the function, φ(x, t), is defined by all its values throughout the 2D (or 3D) domain, Equation (3) has infinite degrees of freedom. To understand this consider φ to be approximated by its value at N points, Φi, for i = 1 . Where the similarity with the component form of hill descent, Equation (2), is clear In this way, the specification of F, being the integral of the density, f , across the whole domain leads towards a field equation, which gives the evolution of φ at every point.
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