Diffusion Models Implied by the Theory of Mixtures

  • Ray M. Bowen

Abstract

In this appendix the essential features of five models of diffusion will be summarized. The starting place for this discussion is the Theory of Mixtures as presented in Lecture 5. For brevity, none of the models discussed here will include the effects of chemical reactions. Chemical reaction within the framework of the Theory of Mixtures is discussed in Lecture 6 of the book here republished and in reference [1] of this appendix. The discussion in Lecture 6 is based, in part, on my article [2], which omits the effects of diffusion. Reference [1] shows how diffusion and chemical reactions can be included in a common framework.

Keywords

Entropy Porosity Incompressibility 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R. M. Bowen, “Thermochemistry of a reacting mixture of elastic materials with diffusion”, Archive for Rational Mechanics and Analysis 34 (1969): 97–127.MathSciNetADSMATHCrossRefGoogle Scholar
  2. [2]
    R. M. Bowen, “Thermochemistry of reacting materials”, Journal of Chemical Physics 49 (1968): 1625–1637, 50 (1969): 4601–4602.Google Scholar
  3. [3]
    R. M. Bowen, “Theory of mixtures”, in Continuum Physics, Volume III, edited by A. C. Eringen, New York, Academic Press, 1976.Google Scholar
  4. [4]
    R. M. Bowen & J. C. Wiese, “Diffusion in mixtures of elastic materials”, International Journal of Engineering Science 7 (1969): 689–722.MATHCrossRefGoogle Scholar
  5. [5]
    R.M. Bowen & T.W. Wright, “On the growth and decay of wave fronts in a mixture of linear elastic materials”, Rendiconti del Circolo Matematico di Palermo (2) 21 (1972): 209–234.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    R.M. Bowen & M.L. Doria, “Effect of diffusion on the growth and decay of acceleration waves in gases ”, Journal of the Acoustical Society of America 53 (1973): 75–82.ADSCrossRefGoogle Scholar
  7. [7]
    R.M. Bowen & P.J. Chen, “Shock waves in a mixture of linear elastic materials”, Rendiconti del Circolo Matematico di Palermo (2) 21 (1972):267–283.MathSciNetMATHCrossRefGoogle Scholar
  8. [8]
    J. C. Podstrigac, “Differential equations of the problem of thermodiffusion in isotropic deformable solids”, Dopovidi Academii Nauk URSR 2 (1961): 169–172.Google Scholar
  9. [9]
    W. Nowacki, “Certain problems of thermodiffusion in solids”, Archivum Mechanicum 23 (1971): 731–755.MathSciNetMATHGoogle Scholar
  10. [10]
    W. Nowacki, “Dynamic problems of diffusion in solids”, Engineering Fracture Mechanics 8 (1976): 261–266.CrossRefGoogle Scholar
  11. [11]
    M. A. Biot, “General theory of three-dimensional consolidation”, Journal of Applied Physics 12 (1941): 155–164.ADSCrossRefGoogle Scholar
  12. [12]
    M. A. Biot, “Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range”, Journal of the Acoustical Society of America 28 (1956): 168–178.MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    T. B. Anderson & R. Jackson, “A fluid mechanical description of fluidized beds”, Industrial and Engineering Chemistry (Fundamentals) 6 (1967): 527–538.Google Scholar
  14. D. Drew, L. Cheng & RT. Lahey, Jr.., “The analysis of virtual mass effects in two-phase flow”, International Journal of Multiphase Flow 5 (1979): 232–242.Google Scholar
  15. [15]
    D. S. Drumheller & A. Bedford, “A thermomechanical theory for reacting immiscible mixtures”, Archive for Rational Mechanics and Analysis 73 (1980): 257–284.MathSciNetADSMATHCrossRefGoogle Scholar
  16. [16]
    R. M. Bowen, “A note on a symmetry relation of the Onsager type valid in certain theories of mixtures”, Acta Mechanica 20 (1974): 209–216.MathSciNetMATHCrossRefGoogle Scholar
  17. [17]
    J. E. Adkins, “Non-linear diffusion, II. Constitutive equations for mixtures of isotropic fluids”, Philosophical Transactions of the Royal Society (London) A 255 (1963): 635–648.ADSCrossRefGoogle Scholar
  18. [18]
    R. M. Bowen & D. J. Garcia, “On the thermodynamics of mixtures with several temperatures”, International Journal of Engineering Science 8 (1970): 63–83.CrossRefGoogle Scholar
  19. [19]
    R. M. Bowen & P. J. Chen, “Waves in a binary mixture of linear elastic materials”, Journal de Mecanique 14 (1975): 237–266.MathSciNetMATHGoogle Scholar
  20. [20]
    R. M. Bowen & K. M. Reinicke, “Plane progressive waves in a binary mixture of linear elastic materials”, Journal of Applied Mechanics 45 (1978): 493–499.ADSMATHCrossRefGoogle Scholar
  21. [21]
    R. M. Bowen & R. L. Rankin, “Acceleration waves in ideal fluid mixtures with several temperatures”, Archive for Rational Mechanics and Analysis 51 (1973): 261–277.MathSciNetADSMATHGoogle Scholar
  22. [22]
    R. M. Bowen & P. J. Chen, “Shock waves in ideal fluid mixtures with several temperatures”, Archive for Rational Mechanics and Analysis 53 (1974): 277–294.MathSciNetADSMATHCrossRefGoogle Scholar
  23. [23]
    R. M. Bowen & P. J. Chen, “Some properties of curved shock waves in ideal fluid mixtures with multiple temperatures”, Acta Mechanica 33 (1979): 265–280.MathSciNetADSMATHCrossRefGoogle Scholar
  24. [24]
    R. M. Bowen, “Compressible porous media models by use of the theory of mixtures”, International Journal of Engineering Science 20 (1982): 697–736.MATHCrossRefGoogle Scholar
  25. [25]
    R. M. Bowen, “Incompressible porous media models by use of the theory of mixtures”, International Journal of Engineering Science 18 (1980): 1129–1148.MATHCrossRefGoogle Scholar
  26. [26]
    R. M. Bowen, “Plane progressive waves in a heat conducting fluid saturated porous material with relaxing porosity”, Acta Mechanica 46 (1983): 189–206.MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc 1984

Authors and Affiliations

  • Ray M. Bowen

There are no affiliations available

Personalised recommendations