Fluid Flow And Pressure Effects In Phase-field
Models For Solidification
Author(s)
M. Conti
Abstract
We present an extension of the classic phase-field model to incorporate
hydrodynamic effects and compressible fluid flow. The methods of the extended
irreversible thermodynamics are used to derive the dynamic equations for the
solidification process. We present also some numerical solutions of the model,
which show to what extent the crystal growth deviates from the pure diffusive
description of the process.
1 Introduction
The growth of a crystal from the melt is a complex phenomenon which
involves many physical effects. The rejection of the latent heat (and solute,
for alloy solidification), away from the solid-liquid interface is accompanied
by the formation of thermal and solute boundary layers which strongly affect
the morphological instability of the interface. Moreover across the interface the
density changes, (the solid is generally denser than the liquid); the change ranges
from a few percent for simple metals to more than 20% for some eutectic
mixtures. The shrinking, or in some cases the dilatation, of the system causes an
advection flow in the liquid phase. Then, even in absence of gravity, the purely
diffusive picture for the conserved fields in the bulk phases should be extended, to
incorporate hydrodynamic effects.
Flow effects in solidification may be treated through an extension of the
phase-field model [1]. In the classic formulation of the model, a non-conserved
order parameter φ(x, t) characterizes the phase of the system at each point.
A suitable free energy (or entropy) functional is then constructed, that depends
on the order parameter as well as on the associate fields and their gradients.
Keywords
Related Book
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