New Non-Stationary Gradient Model of Heat-Mass-Electric Charge Transfer in Thin Porous Media

Abstract

The well-known complicated system of non-equilibrium balance equations for a continuous fluid (f) medium needs the new non-Gibbsian model of f-phase to be applicable for description of the heterogeneous porous media (PMs). It should be supplemented by the respective coupled thermal and caloric equations of state (EOS) developed specially for PMs to become adequate and solvable for the irreversible transport f-processes. The set of standard assumptions adopted by the linear (or quasi-linear) non-equilibrium thermodynamics are based on the empirical gradient-caused correlations between flows and forces. It leads, in particular, to the oversimplified stationary solutions for PMs. The most questionable but typical modeling suppositions of the stationary gradient (SG) theory are: 1) the assumption of incompressibility accepted, as a rule, for f-flows; 2) the ignorance of distinctions between the hydrophilic and hydrophobic influence of a porous matrix on the properties; 3) the omission of effects arising due to the concomitant phase intra-porous transitions between the neighboring f-fragments with the sharp differences in densities; 4) the use of exclusively Gibbsian (i.e. homogeneous and everywhere differentiable) description of any f-phase in PM; 5) the very restrictive reduction of the mechanical velocity field to its specific potential form in the balance equation of f-motion as well as of the heat velocity field in the balance equation of internal energy; 6) the neglect of the new specific peculiarities arising due to the study of any non-equilibrium PM in the meso- and nano-scales of a finite-size macroscopic (N,V)-system of discrete particles. This work is an attempt to develop the alternative non-stationary gradient (NSG) model of real irreversible processes in PM. Another aim is to apply it without the above restrictions 1)-6) to the description of f-flows through the obviously non-Gibbsian thin porous medium (TPM). We will suppose that it is composed by two inter-penetrable fractal sf-structures of f-phase (formed by the “mixture” of g- and l-phases termed, in total, interphase) and solid (s) porous matrix termed below s-phase. The permanent influence of humidity and the respective increase of the moisture content in TPM including the unavoidable phenomenon of capillary condensation are the main factors to occur the non-stationary transport f-flows through its texture.