A GENERAL MODEL FOR MULTIPHASE MIXTURES AND APPLICATIONS
DE MATTOS NETO, ANTONIO GOMES
Doctor of Philosophy
A general model for a multiphase mixture is developed within the framework of the theory of mixtures formulated by BOWEN. Each phase in the mixture is considered to be a mixture itself, composed of multiple substances with independent kinematic, chemical and thermal behaviors. The field equations for the substances in each phase, for the phases in the mixture and for the mixture as a whole are presented. A particular set of constitutive equations is adopted where the volume fractions of the phases in the mixture are treated as internal state variables and required to obey rate type constitutive equations. Certain types of ideal behavior of the mixture are investigated in the limit of a small ratio of the specific area to the volume fraction for a particular phase in the mixture. The concepts of pressure of a fluid phase and capillary pressure between two fluid phases are discussed. In particular, an attempt is made to interpret the capillary pressure defined here in the same manner as in the classical literature on porous media, i.e. as resulting from the surface tension effects in the mixture. A linear version of the general model is derived. Examples of use of the general model are worked in detail for three distinct applications, namely the drying of grains, capillary rise and soil mechanics. In the first application it is shown how equations of balance present in the literature on drying can be obtained from the general model. In the second application the saturation profile of a fluid phase in a porous medium is calculated when static equilibrium is reached in the problem of capillary rise. In particular, circumstances are presented which show that no capillary rise occurs if the jump of the pressure of a fluid phase across the boundaries of a porous medium is zero. The third application contains the derivation of equations of motion customarily used in soil mechanics. The results obtained in this derivation motivate a discussion about TERZAGHI's principle of effective stress, which is then shown to be derivable from the general model.