On Gibbs stability in the classical theory of fluid mixtures

  • Scott J. Spector
Original Papers


We prove that Gibbs' criterion for stability is a necessary condition for the dynamic stability of a classical (non-linear) inviscid fluid mixture.


Mathematical Method Classical Theory Dynamic Stability Fluid Mixture Fluid Inviscides 
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.


On démontre que le critère de Gibbs pour la stabilité est une condition nécessaire pour la stabilité dynamique d'une mixture classique (non linéaire) des fluids inviscides.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. W. Gibbs,On the equilibrium of heterogeneous substandes, Trans. Conn. Acad.3, (1875–1878), 108–248, 343–524=The Collected Works of J. Williard Gibbs,1, 55–353, Yale University Press, New Haven 1948.Google Scholar
  2. [2]
    G. D. Coleman,On the stability of equilibrium states of general fluids, Arch. Rational Mech. Anal.36, 1–32 (1970).Google Scholar
  3. [3]
    B. D. Coleman and J. M. Greenberg,Thermodynamics and the stability of fluid motion, Arch. Rational Mech. Anal.25, 321–341 (1967).Google Scholar
  4. [4]
    J. E. Dunn and R. L. Fosdick,Lemmas in thermodynamic stability: a priori constitutive inequalities and induced global bounds on thermodynamic states, Arch. Rational Mech. Anal.67, 183–224 (1978).Google Scholar
  5. [5]
    J. E. Dunn and R. L. Fosdick,The morphology and stability of material phases, Arch. Rational Mech. Anal.74, 1–99 (1980).Google Scholar
  6. [6]
    O. D. Kellog,Foundations of Potential Theory, Springer-Verlag, Berlin 1929.Google Scholar
  7. [7]
    M. E. Gurtin and A. S. Vargas,On the classical theory of reacting fluid mixtures, Arch. Rational Mech. Anal.43, 179–197 (1971).Google Scholar
  8. [8]
    C. Eckart,The thermodynamics of irreversible processes, II. Fluid mixtures, Physical Rev.58, 269–275 (1940).Google Scholar
  9. [9]
    J. Meixner and H. G. Reik,Thermodynamic der irreversiblen Prozesse, Handbuch der Physik, II/2, Springer-Verlag, Berlin 1959.Google Scholar
  10. [10]
    M. E. Gurtin and P. Villaggio,On stability in the classical linear theory of fluid mixtures, Ann. Mate. Pura Appl. III, 57–67 (1976).Google Scholar
  11. [11]
    T. J. R. Hughes and J. E. Marsden,A Short Course in Fluid Mechanics, Publish or Perish, Boston 1976.Google Scholar
  12. [12]
    R. M. Bowen,The thermochemistry of a reacting mixture of elastic materials with diffusion, Arch. Rational Mech. Anal.34, 97–127 (1969).Google Scholar
  13. [13]
    C. Truesdell,Rational Thermodynamics: A Course of Lectures on Selected Topics. McGraw-Hill, New York 1969.Google Scholar
  14. [14]
    M. E. Gurtin and S. J. Spector,On the sign of the specific heat, Q. J. Mech. Appl. Math.29, 493–497 (1976).Google Scholar

Copyright information

© Birkhäuser Verlag 1981

Authors and Affiliations

  • Scott J. Spector
    • 1
  1. 1.Dept. of MathematicsUniversity of TennesseeKnoxvilleUSA

Personalised recommendations