Abstract
In this paper, I begin with the general formulation of mixture theory by Bowen and present the derivation of a minimal set of field equations, constitutive relations, and material parameters suitable for the solutions of meaningful diffusion problems. The specific results are for a single solid and two fluids, and they may be extended to any number of fluids. I allude to the results of three problems, viz. (1) the injection of a fluid into a geological formation saturated with another fluid, (2) the drainage of two dissimilar fluids from a geological formation due to in-situ fluid pore pressures, and (3) the process of squeezing a sponge dry, in order to illustrate the general applicability of the derived theory.
Similar content being viewed by others
References
C. Truesdell, Sulle basi della termomeccanica. Accademia Nazionale Lincei, Rendiconti della Classe di Scienze Fisiche, Matematiche e Naturadi (8) 22 (1957) 33–38, 158–166.
P.D. Kelly, A reacting continuum. International Journal of Engineering Science 2 (1964) 129–153.
A.E. Green and P.M. Naghdi, A dynamical theory of interacting continua. International Journal of Engineering Science 3 (1965) 231–241.
A.C. Eringen and J.D. Ingram, A continuum theory of chemically reacting media—I, International Journal of Engineering Science 3 (1965) 197–212.
R.M. Bowen, Toward a thermodynamics and mechanics of mixtures. Archive for Rational Mechanics and Analysis 24 (1967) 370–403.
I. Müller, A thermodynamic theory of mixtures of fluids. Archive for Rational Mechanics and Analysis 28 (1968) 1–39.
R.J. Atkin and R.E. Craine, Continuum theory of mixtures: Basic theory and historical development. Quarterly Journal of Mechanics and Applied Mathematics 29 (1976) 244–290.
C. Truesdell, Rational Thermodynamics, 2nd edition, Lecture 5, Springer-Verlag, New York (1984).
R.M. Bowen, Theory of Mixtures, in Continuum Physics, Vol. III, Academic Press, New York (1976).
R.M. Bowen, Compressible porous media models by use of the theory of mixtures. International Journal of Engineering Science 20 (1982) 697–735.
R. Hill, A self-consistent mechanics of composite materials. Journal of the Mechanics and Physics of Solids 13 (1965) 213–222.
B. Budiansky, On the elastic moduli of some heterogeneous materials. Journal of the Mechanics and Physics of Solids 13 (1965) 223–227.
Z. Hashin and S. Shtrikman, A variational approach to the theory of the elastic behaviour of multiphase materials. Journal of the Mechanics and Physics of Solids 11 (1963) 127–140.
S. Nemat-Nasser, T. Iwakuma and M. Hejazi, On composites with periodic structure. Mechanics of Materials 1 (1982) 239–267.
J.G. Berryman and P.A. Berge, Rock elastic properties: Dependence on microstructure, in Abstracts, MEET'N'93, First Joint ASCE/ASME/SES Meeting (1993).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chen, P.J. A coupled solid/fluids mixture theory that suffices for diffusion problems. J Elasticity 45, 117–134 (1996). https://doi.org/10.1007/BF00042486
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00042486