Physically representative model porous medium

The simplest models that can be constructed are based on the idea that the porous medium is like a bundle of capillaries. Early capillaric models have been discussed by a number of authors in the context of various physical problems (Kawakami, 1932 Smith, 1932 Rainard, 1947 Henderson, 1949 Purcell, 1949 Burdine et ai, 1950 Calhoun, 1953). There are a number of variants of this type of model, the simplest being the linear case representing a porous medium by a bundle of capillaries of uniform radius (see, for example, Scheidegger, 1953) this model is represented in Figure 6.1(a). It is easily shown that for such a model the porosity, (/>, permeability, /c, and pore radius, R, are related by ... 

At the present time there exist no flux relations wich a completely sound cheoretical basis, capable of describing transport in porous media over the whole range of pressures or pore sizes. All involve empiricism to a greater or less degree, or are based on a physically unrealistic representation of the structure of the porous medium. Existing models fall into two main classes in the first the medium is modeled as a network of interconnected capillaries, while in the second it is represented by an assembly of stationary obstacles dispersed in the gas on a molecular scale. The first type of model is closely related to the physical structure of the medium, but its development is hampered by the lack of a solution to the problem of transport in a capillary whose diameter is comparable to mean free path lengths in the gas mixture. The second type of model is more tenuously related to the real medium but more tractable theoretically. 

Within the alternative approach, the film is considered a porous medium [54, 94,114,119,121,122,127-129,148], Physically, it represents a porous membrane that includes a matrix formed by the conducting polymer and pores filled with an electrolyte. Mathematically, in this approach the film is modeled as a macroscop-ically homogeneous two-phase system consisting of an electronically conducting sohd phase and an ionically conducting electrolyte phase. Considering a planar geometry, each layer perpendicular to the electrode smface contains these two phases, and it can therefore be described at any point by two potentials that depend on the time and the spatial coordinates. 

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