Skip to main content

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

  • I - Continuum Mechanics
  • Conference paper
  • First Online:
PDEs and Continuum Models of Phase Transitions

Part of the book series: Lecture Notes in Physics ((LNP,volume 344))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • [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 

  • [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 

  • [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 

  • [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 

  • [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 

  • [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 

  • [1961] Cahn, J. W., On spinodal decomposition, Act. Metall. 9, 795–801.

    Google Scholar 

  • [1962] Cahn, J. W., On spinodal decomposition in cubic crystals, Act. Metall. 10, 179–183.

    Google Scholar 

  • [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 

  • [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 

  • [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 

  • [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 

  • [1971] Cahn, J. W. and J. E. Hilliard, Spinodal decomposition: a reprise, Act. Metall. 19, 151–161.

    Google Scholar 

  • [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 

  • [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 

  • [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 

  • [1986] Gurtin, M. E., On the two-phase Stefan problem with interfacial energy and entropy, Arch. Rational Mech. Anal. 96, 199–241.

    Google Scholar 

  • [1988] Fonseca, I., Interfacial energy and the Maxwell rule, Arch. Rational Mech. Anal., forthcoming.

    Google Scholar 

  • [1988a] Gurtin, M. E., Toward a nonequilibrium thermodynamics of two phase materials, Arch. Rational Mech. Anal. 100, 275–312.

    Google Scholar 

  • [1988b] Gurtin, M. E., Multiphase thermomechanics with interfacial structure. 1. Heat conduction and the capillary balance law, Arch. Rational Mech. Anal., forthcoming.

    Google Scholar 

  • [1988c] Gurtin, M. E., on a nonequilibrium thermodynamics of capillarity and phase, Q. Appl. Math., forthcoming.

    Google Scholar 

  • [1988] Pego, R. L., Front migration in the nonlinear Cahn-Hilliard equation, forthcoming.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

M. Rascle D. Serre M. Slemrod

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag

About this paper

Cite this paper

Gurtin, M.E. (1989). On diffusion in two-phase systems: the sharp interface versus the transition layer. In: Rascle, M., Serre, D., Slemrod, M. (eds) PDEs and Continuum Models of Phase Transitions. Lecture Notes in Physics, vol 344. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024937

Download citation

  • DOI: https://doi.org/10.1007/BFb0024937

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51617-0

  • Online ISBN: 978-3-540-46717-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics