Species Movement and Transfer in a Porous Medium

Frequently we define a porous medium as a solid material that contains voids and pores. The notion of pore requires some observations for an accurate description and characterization. If we consider the connection between two faces of a porous body we can have opened and closed or blind pores between these two faces we can have pores which are not interconnected or with simple or multiple connections with respect to other pores placed in their neighborhood. In terms of manufacturing a porous solid, certain pores can be obtained without special preparation of the raw materials whereas designed pores require special material synthesis and processing technology. We frequently characterize a porous structure by simplified models (Darcy s law model for example) where parameters such as volumetric pore fraction, mean pore size or distribution of pore radius are obtained experimentally. Some porous synthetic structures such as zeolites have an apparently random internal arrangement where we can easily identify one or more cavities the connection between these cavities gives a trajectory for the flow inside the porous body (see Fig. 4.30). 

The diameter or the radius of the pores is one of the most important geometric characteristic of porous solids. In terms of lUPAC nomenclature, we can have macropores (mean pore size greater than 5 x 10 m), mesopores (between 5 x 10 and 2 x 10 m) and micropores (less than 2 x 10 m). The analysis of species transport inside the porous structure is very important for the detailed description of many unit operations or applications among them we can mention suspension filtration, solid drying and humidification, membrane processes (dialysis, osmosis, gaseous permeation. ), flow in catalytic beds, ion exchange, adsorp- 

The most used methods for the characterization of flow and species transport inside a porous body include the identification of the characteristics of the pores of the porous structure and the particularisation of classic transport equations to this case. These equations are generally associated with equations describing the solid-fluid interaction, adsorption, capillary condensation and flow due to the capillary forces etc. Concerning the species displacement (flow) problem inside a porous structure, we can consider the following classification  

Porous solids generally have a pores size distribution and in many cases this results in a complicated transport mechanism which is a combination of the different mechanisms described above. This is also the case when the pores size are ranged near the boundaries between these different mechanisms. 

All these different mechanisms of mass transport through a porous medium can be studied experimentally and theoretically through classical models (Darcy s law, Knudsen diffusion, molecular dynamics, Stefan-Maxwell equations, dusty-gas model etc.) which can be coupled or not with the interactions or even reactions between the solid structure and the fluid elements. Another method for the analysis of the species motion inside a porous structure can be based on the observation that the motion occurs as a result of two or more elementary evolutions that are randomly connected. This is the stochastic way for the analysis of species motion inside a porous body. Some examples that will be analysed here by the stochastic method are the result of the particularisations of the cases presented with the development of stochastic models in Sections 4.4 and 4.5. 

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