Tortuous pore network membrane pores

As discussed in the previous chapter, the network of the inter-connected membrane pores formed during preparation and fabrication may be tortuous or nearly straight depending on the synthesis and subsequent heat treatment methods and conditions. The microstructure of a membrane, particularly the type with tortuous pores, is too complicated to be described by a single parameter or a simple model. Due to the relatively poor knowledge of flow through porous media, an empirical term called " tortuosity" has been introduced and used by many researchers to reflect the relative random orientation of a pore network and is based on the Kozeny-Carmen equation for the membrane flux, J ... 

Systems used in practice have a spongy structure (porous glass or carbon) or have the structure common in ceramic membranes. The latter have an interconnected, tortuous and randomly oriented pore network with constrictions and dead ends (Fig. 9.1) and are formed by packing of particles. 

All current MF membranes may be classified as either "tortuous-pore" or "capillary-pore" membranes (see Figure 2.1). The "capillary-pore" structure is distinguished by its straight-through cylindrical capillaries, whereas the "tortu-ous-pore" structure resembles a sponge with a network of interconnecting tortuous pores. 

On the largest length scale, top picture of Fig. 2, the distribution of water in the membrane is depicted as a porous network. The latter is characterized by a pore size distribution (psd) and a tortuousity factor , which accounts for multiple interconnectivity and bending of pathways in the network. The distribution of pore radii translates into a distribution of pore conductivities. Via this correspondence, the distribution of water in the membrane finally determines its transport properties, namely, proton conductivity and water dif-fusivity. 

Shelekhin developed his model for a single wall (Vycor type) membrane with pore diameter of approximately 1.5 nm. The large pores in the tortuous network are interconnected by pore openings (windows) with a smaller diameter in the range 0.5-0.6 nm. 

The gas relative permeability, Pr, is defined as the permeability of a fluid through a porous medium partially blocked by a second fluid, normalized by the permeability through the same porous solid, when the pore space is free of this second fluid. In most cases, the gas relative permeability diminishes at the percolation threshold , at which a significant portion of the pores are still conducting but they don t form a continuous path through the membrane along the direction of flow. The tortuous capillary model fails to predict this the percolation threshold arises only when all pores are blocked by capillary condensation. In comparison, the network model can provide a satisfactory analysis of the percolation threshold problem, without, as noted earlier, increasing the number of the model parameters. 

---