Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix

Physica D: Nonlinear Phenomena

Volumn 109, Issue 3-4, 1997, Pages 242-256

  Elliott, Charles M ^a   Garcke, Harald ^b  

^a UNIVERSITY OF SUSSEX   (United Kingdom)

^b UNIVERSITY OF BONN   (Germany)

Author keywords

Cahn Hilliard equation; Degenerate parabolic systems; Multicomponent diffusion; Phase separation

Indexed keywords

DIFFUSION; MATHEMATICAL MODELS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; PHASE TRANSITIONS;

CAHN-HILLIARD EQUATION; CONCENTRATION DEPENDENCE; DEGENERATE PARABOLIC SYSTEM; MOBILITY MATRIX; MULTICOMPONENT DIFFUSION; MULTICOMPONENT SYSTEM;

PHASE SEPARATION;

EID: 0031274570     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(97)00066-3     Document Type: Article

References (28)

1. H.W. Alt and I. Pawlow, Models of non-isothermal phase transitions in multicomponent systems. Part I: Theory, SFB256 University Bonn, Preprint 222 (1992).
2. E. Beretta, M. Bertsch and R. Dal Passo, Non-negative solutions of a fourth-order nonlinear degenerate parabolic equation, Archive Rational Mech. Anal. 129 (2) (1995) 175-200.
3. J.F. Blowey, M.I.M. Copetti and C.M. Elliott, Numerical analysis of a model for phase separation of a multi-component alloy, IMA J. Numer. Anal. 16 (1995) 111-139.
4. J.W. Cahn, On spinodal decomposition, Acta Metallurgica 9 (1961) 795-801.
5. J.W. Cahn, C.M. Elliott and A. Novick-Cohen, The Cahn-Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvature, Eur. J. Appl. Math. 7 (1996) 287-301.
6. J.W. Cahn and J.E. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys. 28 (1958) 258-267.
7. J.W. Cahn and J.E. Taylor, Surface motion by surface diffusion, Acta Metallurgica 42 (1994) 1045-1063.
8. J.W. Cahn and J.E. Taylor, Linking anisotropic and diffusive surface motion laws via gradient flows, J. Statist. Phys. 77 (1/2) (1994) 183-197.
9. D. De Fontaine, An analysis of clustering and ordering in multicomponent solid solutions - I. Stability criteria, J. Phys. Chem. Solids 33 (1972) 287-310.
10. D. De Fontaine, An analysis of clustering and ordering in multicomponent solid solutions - II. Fluctuations and kinetics, J. Phys. Chem. Solids 34 (1973) 1285-1304.
11. P.G. de Gennes, Dynamics of fluctuations and spinodal decomposition in polymer blends, J. Chem. Phys. 72 (1980) 4756-4763.
12. S.R. De Groot and P. Mazur, Non-equilibrium thermodynamics (North-Holland, Amsterdam, 1962).
13. C.M. Elliott and H. Garcke, On the Cahn-Hilliard Equation with degenerate mobility, SIAM J. Math. Anal. 27 (2) (1996) 404-423.
14. C.M. Elliott and S. Luckhaus, A generalized diffusion equation for phase separation of a multi-component mixture with interfacial free energy, SFB256 University Bonn, Preprint 195 (1991).
15. D.J. Eyre, Systems of Cahn-Hilliard equations, SIAM J. Appl. Math. 53 (6) (1993) 1686-1712.
16. D.D. Fitts, Non-equilibrium Thermodynamics (McGraw-Hill, New York, 1962).
17. M.E. Gurtin, On a non-equilibrium thermodynamics of capillarity and phase, Quart. Appl. Math. 47 (1989) 129-145.
18. J.E. Hilliard, Spinodal decomposition, in: Phase Transformations, American Society for Metals (Cleveland, 1970) 497-560.
19. J.J. Hoyt, Spinodal decomposition in ternary alloys, Acta Metallurgica 37 (1989) 2489-2497.
20. J.J. Hoyt, Linear spinodal decomposition in a regular ternary alloy, Acta Metallurgica 38 (1990) 227-231.
21. J.J Hoyt, The continuum theory of nucleation in multicomponent systems, Acta Metallurgica 38 (1990) 1405-1412.
22. J.S. Kirkaldy and D.J. Young, Diffusion in the condensed state, The Institute of Metals, London (1987).
23. J.S. Langer, N. Bar-On and H.D. Miller, New computational method in the theory of spinodal decomposition, Phys. Rev. A 11 (1975) 1417.
24. J.E. Morral and J.W. Cahn, Spinodal decomposition in ternary alloys, Acta Metallurgica 19 (1971) 1037-1045.
25. L. Onsager, Reciprocal relations in irreversible processes I, Phys. Rev. 37 (1931) 405-426.
26. L. Onsager, Reciprocal relations in irreversible processes II, Phys. Rev. 38 (1931) 2265-2279.
27. M. Takenaka and T. Hashimoto, Computer simulations of the spinodal decomposition for a polydisperse polymer mixture, Phys. Rev. E 48 (1993) 647-650.
28. A. Ziya Akcasu and M. Tombakoglu, Dynamics of copolymer and homopolymer mixtures in bulk and in solution via the random phase approximation, Macromolecules 23 (1990) 607-612.