Toward a Continuum Theory of Liquid-Gas Mixtures

Abstract

The terminology “micromorphic materials” is used by A.C. Eringen to denote media whose continuum behavior is dependent on its micro-structure. Anisotropic fluids such as liquid crystals, granular and porous solids, suspensions, etc, are but a few examples of materials which require special consideration regarding the local structure of the media. In this paper we present the basic ideas and some recent results of a properly invariant micromorphic continuum model, as opposed to statistical theories, of a mixture of liquid and non condensible gas, at equal temperature and no slip velocity between phases, in which the spherical growth of bubbles is taken into account. For the mixture as a whole, balance laws are constructed for mass, micro-inertia, momentum, moment of momentum, energy and the production of entropy. The general form of non-linear, isotropic constitutive equations is derived from continuum thermodynamics principles. As an illustration, for a linear simple mixture, constitutive relations are given explicitly and field equations are then obtained. Finally, physical considerations lead to an equation of state which allows for the complete description of such a medium. The effects of bubble growth and wave propagation are among the various problems which can be interpreted. It is believed that the present model may provide a sound basis for investigating problems associated with gas/liquid mixtures and that it can complement the partial results already obtained using statistical and phenomenological approaches. Comparison is needed with experimental results from a well defined physical situation in order to substantiate our results.