Second order sharp-interface and thin-interface asymptotic analyses and error minimization for phase-field descriptions of two-sided dilute binary alloy solidification

Journal of Crystal Growth

Volumn 291, Issue 1, 2006, Pages 272-289

  Gopinath, Arvind ^a   Armstrong, Robert C ^b   Brown, Robert A ^b  

^a HARVARD UNIVERSITY   (United States)

^b Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

A1. Anti trapping solutal flux; A1. Directional solidification; A2. Phase field models; A3. Two sided model; B1. Dilute binary alloys

Indexed keywords

ASYMPTOTIC STABILITY; DIFFUSION; INTERPOLATION; SOLIDIFICATION; THICKNESS MEASUREMENT;

ANTI-TRAPPING SOLUTAL FLUXES; DILUTE BINARY ALLOYS; PHASE-FIELD MODELS; TWO SIDED SOLUTAL MODEL (TSM);

BINARY ALLOYS;

EID: 33749414426     PISSN: 00220248     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcrysgro.2006.03.001     Document Type: Article

References (12)

1. Beckermann C., Diepers H.J., Steinech I., Karma A., and Tong X. Phase-field model with convection. J. Comput. Phys. 154 (1999) 468
2. Karma A. Phase-field formulation for quantitative modeling of alloy solidification. Phys. Rev. Lett. 87 11 (2001) 115701
3. Almgren R.F. Second-order phase-field asymptotics for unequal conductivities. SIAM J. Appl. Math. 59 6 (1999) 2086
4. Boettinger W.J., Warren J.A., Beckermann C., and Karma A. Phase-field simulation of solidification. Ann. Rev. Mater. Res. 32 (2002) 163
5. Ramirez J.C., Beckermann C., Karma A., and Diepers H.-J. Phase-field modeling of binary alloy solidification with coupled heat and solute diffusion. Phys. Rev. E. 69 (2004) 051607
6. Lan C.W., and Shih C.J. Efficient phase-field simulation of a binary dendritic growth in a forced flow. Phys. Rev. E. 69 (2004) 031601
7. Ungar L.H., Ramprasad N., and Brown R.A. Finite element methods for unsteady solidification problems arising in prediction of morphological structure. J. Sci. Comput. 3 1 (1988) 77
8. B. Echebarria, R. Folch, A. Karma, M. Plapp, 2004. Quantitative phase-field model of alloy solidification, in 〈http://cul.arxiv.org/abs/cond-mat/0404164 〉, 2004.
9. Tiaden J., Nestler B., Diepers H.J., and Steinbech. The multiphase-field model with an integrated concept for modelling solute diffusion. Physica D 115 (1998) 73
10. The Steinbech model which is derived using mixture principles rather than from the sharp interface equations yields equations almost identical to the Beckermann model. Thus, the asymptotic analysis presented here is more generally applicable.
11. ′*. Comparison of this formulation to the analogous equation from the Beckermann model indicates that even in near equilibrium conditions, the last term is not small and varies significantly over the phase boundary. This term contributes to an effective flux that influences the form of the Gibbs-Thompson condition.
12. Mullins W.W., and Sekerka R.F. Stability of a planar interface during solidification of a dilute binary alloy. J. Appl. Phys. 35 (1964) 444