Coupled solvent and heat transport of a mixture of swelling porous particles and fluids: Single time-scale problem

A three-spatial scale, single time-scale model for both moisture and heat t ransport is developed for an unsaturated swelling porous media from first p rinciples within a mixture theoretic framework. On the smallest (micro) sca le, the system consists of macromolecules (clay particles, polymers, etc.) and a solvating liquid (vicinal fluid), each of which are viewed as individ ual phases or nonoverlapping continua occupying distinct regions of space a nd satisfying the classical field equations. These equations are homogenize d forming overlaying continua on the intermediate (meso) scale via hybrid m ixture theory (HMT). On the mesoscale the homogenized swelling particles co nsisting of the homogenized vicinal fluid and colloid are then mixed with t wo bulk phase fluids: the bulk solvent and its vapor. At this scale, there exists three nonoverlapping continua occupying distinct regions of space. O n the largest (macro) scale the saturated homogenized particles, bulk liqui d and vapor solvent, are again homogenized forming four overlaying continua : doubly homogenized vicinal fluid, doubly homogenized macromolecules, and singly homogenized bulk liquid and vapor phases. Two constitutive theories are developed, one at the mesoscale and the other at the macroscale. Both a re developed via the Coleman and Noll method of exploiting the entropy ineq uality coupled with linearization about equilibrium. The macroscale constit utive theory does not rely upon the mesoscale theory as is common in other upscaling methods. The energy equation on either the mesoscale or macroscal e generalizes de Vries classical theory of heat and moisture transport. The momentum balance allows for flow of fluid via volume fraction gradients, p ressure gradients, external force fields, and temperature gradients.