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Phase-field model for solidification of a monotectic alloy with convection

Phase-field model for solidification of a monotectic alloy with convection
Phase-field model for solidification of a monotectic alloy with convection
In this paper we discuss two phase-field models for solidification of monotectic alloys, a situation in which a liquid phase L1 may simultaneously transform into both a new liquid phase L2 and a solid phase S via the reaction L1?L2+S. The first model uses three different phase-fields to characterize the three phases in the system and, in addition, a concentration field. This construction restricts the validity of the model to describe phase transitions within the vicinity of the monotectic temperature. In contrast, the second model distinguishes the two liquid phases by their concentration using a Cahn–Hilliard type model and employs only one phase-field to characterize the system as solid or liquid. This formulation enables the second model to represent a wider temperature range of the phase diagram including the miscibility gap where the spinodal decomposition L?L1+L2 occurs. Both our models permit the interfaces to have temperature-dependent surface energies which may induce Marangoni convection at L1–L2 interfaces in non-isothermal systems. By deriving a generalized stress tensor including stresses associated with the capillary forces on the diffuse interface, we extend the two monotectic phase-field models to account for convection in both liquid phases. Together with a generalized set of Navier–Stokes equations, we give a complete set of dynamic field equations to describe monotectic systems with fluid flow. Finally, we present numerical simulations of lamellar monotectic growth structures which exhibit wetting phenomena as well as coarsening and particle pushing.
monotectic alloy, convection, phase-field model
0167-2789
133-154
Nestler, B.
0746e232-a39d-4784-916a-0cdeea4292e4
Wheeler, A.A.
eb831100-6e51-4674-878a-a2936ad04d73
Ratke, L.
c7b78a9e-2476-4257-8938-9e3e306b2940
Stöcker, C.
26676188-11cd-4a51-bbce-e8c18dc85ab5
Nestler, B.
0746e232-a39d-4784-916a-0cdeea4292e4
Wheeler, A.A.
eb831100-6e51-4674-878a-a2936ad04d73
Ratke, L.
c7b78a9e-2476-4257-8938-9e3e306b2940
Stöcker, C.
26676188-11cd-4a51-bbce-e8c18dc85ab5

Nestler, B., Wheeler, A.A., Ratke, L. and Stöcker, C. (2000) Phase-field model for solidification of a monotectic alloy with convection. Physica D, 141 (1-2), 133-154. (doi:10.1016/S0167-2789(00)00035-X).

Record type: Article

Abstract

In this paper we discuss two phase-field models for solidification of monotectic alloys, a situation in which a liquid phase L1 may simultaneously transform into both a new liquid phase L2 and a solid phase S via the reaction L1?L2+S. The first model uses three different phase-fields to characterize the three phases in the system and, in addition, a concentration field. This construction restricts the validity of the model to describe phase transitions within the vicinity of the monotectic temperature. In contrast, the second model distinguishes the two liquid phases by their concentration using a Cahn–Hilliard type model and employs only one phase-field to characterize the system as solid or liquid. This formulation enables the second model to represent a wider temperature range of the phase diagram including the miscibility gap where the spinodal decomposition L?L1+L2 occurs. Both our models permit the interfaces to have temperature-dependent surface energies which may induce Marangoni convection at L1–L2 interfaces in non-isothermal systems. By deriving a generalized stress tensor including stresses associated with the capillary forces on the diffuse interface, we extend the two monotectic phase-field models to account for convection in both liquid phases. Together with a generalized set of Navier–Stokes equations, we give a complete set of dynamic field equations to describe monotectic systems with fluid flow. Finally, we present numerical simulations of lamellar monotectic growth structures which exhibit wetting phenomena as well as coarsening and particle pushing.

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More information

Published date: 2000
Keywords: monotectic alloy, convection, phase-field model
Organisations: Applied Mathematics

Identifiers

Local EPrints ID: 29105
URI: http://eprints.soton.ac.uk/id/eprint/29105
ISSN: 0167-2789
PURE UUID: 24f2f86b-415c-4507-9f23-7296ea7efbe0

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Date deposited: 18 Jul 2006
Last modified: 08 Jan 2022 09:55

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Contributors

Author: B. Nestler
Author: A.A. Wheeler
Author: L. Ratke
Author: C. Stöcker

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