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On diffusion in two-phase systems: the sharp interface versus the transition layer

I - Continuum Mechanics c - Fluids
Part of the Lecture Notes in Physics book series (LNP, volume 344)

Keywords

Spinodal Decomposition Outward Unit Interfacial Free Energy Nonequilibrium Thermodynamic Isothermal Diffusion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1878] Gibbs, J. W., On the equilibrium of heterogeneous substances, Trans. Connecticut Acad. 3. 108–248 (1876). Reprinted in: The Scientific Papers of J. Willard Gibbs, Vol. 1, Dover, New York (1961).Google Scholar
  2. [1893] van der Waals, J. D., The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density (in Dutch), Verhandel. Konink, Akad. Weten. Amsterdam (Sec. 1) Vol. 1, No. 8.Google Scholar
  3. [1901] Korteweg, D. J., Sur la forme que prennent les equations des mouvement des fluides si l'on tientcompte des forces capillaires par des variations de densite, Arch. Neerl. Sci. Exactes Nat. Ser. 11, 6. 1–24.Google Scholar
  4. [1951] Herring, C., Surface tension as a motivation for sintering, The Physics of Powder Metallurgy (ed. W. E. Kingston) McGraw-Hill, New York.Google Scholar
  5. [1958] Cahn, J. W. and J. E. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy, J. Chem. Phys. 28, 258–267.Google Scholar
  6. [1958] Frank, F. C., On the kinematic theory of crystal growth and dissolution processes, Growth and Perfection of Crystals (eds. R. H. Doremus, B. W. Roberts, D. Turnbull) John Wiley, New York.Google Scholar
  7. [1961] Cahn, J. W., On spinodal decomposition, Act. Metall. 9, 795–801.Google Scholar
  8. [1962] Cahn, J. W., On spinodal decomposition in cubic crystals, Act. Metall. 10, 179–183.Google Scholar
  9. [1963] Coleman, B. D. and W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal. 13, 167–178.Google Scholar
  10. [1963] Mullins, W. W. and R. F. Sekerka, Morphological stability of a particle growing by diffusion or heat flow, J. Appl. Phys. 34, 323–329.Google Scholar
  11. [1964] Mullins, W. W. and R. F. Sekerka, Stability of a planar interface during solidification of a dilute binary alloy, J. Appl. Phys. 35, 444–451.Google Scholar
  12. [1964] Voronkov, V. V., Conditions for formation of mosaic structure on a crystallization front [in Russian], Fizika Tverdogo Tela 6, 2984–2988. English Transl. Sov. Phys. Solid State 6, 2378–2381 (1965).Google Scholar
  13. [1971] Cahn, J. W. and J. E. Hilliard, Spinodal decomposition: a reprise, Act. Metall. 19, 151–161.Google Scholar
  14. [1972] Hoffman, D. W. and J. W. Cahn, A vector thermodynamics for anisotropic surfaces — 1. Fundamentals and applications to plane surface junctions, Surface Sci. 31, 368–388.Google Scholar
  15. [1974] Cahn, J. W. and D. W. Hoffman, A vector thermodynamics for anisotropic surfaces-2. curved and faceted surfaces, Act. Metall. 22, 1205–1214.Google Scholar
  16. [1984] Carr, J., Gurtin, M. E., and M. Slemrod, Structured phase transitions on a finite interval, Arch. Rational Mech. Anal. 86, 317–351.Google Scholar
  17. [1986] Gurtin, M. E., On the two-phase Stefan problem with interfacial energy and entropy, Arch. Rational Mech. Anal. 96, 199–241.Google Scholar
  18. [1988] Fonseca, I., Interfacial energy and the Maxwell rule, Arch. Rational Mech. Anal., forthcoming.Google Scholar
  19. [1988a] Gurtin, M. E., Toward a nonequilibrium thermodynamics of two phase materials, Arch. Rational Mech. Anal. 100, 275–312.Google Scholar
  20. [1988b] Gurtin, M. E., Multiphase thermomechanics with interfacial structure. 1. Heat conduction and the capillary balance law, Arch. Rational Mech. Anal., forthcoming.Google Scholar
  21. [1988c] Gurtin, M. E., on a nonequilibrium thermodynamics of capillarity and phase, Q. Appl. Math., forthcoming.Google Scholar
  22. [1988] Pego, R. L., Front migration in the nonlinear Cahn-Hilliard equation, forthcoming.Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  1. 1.Department of MathematicsCarnegie-Mellon UniversityPittsburgh

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