Straight cylindrical membrane pores

As the membrane pore widths dimmish, or the mean free path of the molecules rise, the permeating particles tend to collide more with the pore walls than among themselves [60,64], In this case, the Knudsen flow regime is established therefore, the molar gas flow, J, for the Knudsen flow, in a straight cylindrical mesopore of length, /, and trans-pore pressure, AP = Px - P2, is given by [64]... 

The most simple pore morphologies (Figs. 2.1A and B) are those of more or less straight cylindrical or conical-shaped pores. This type of pore is formed in so-called track etch and in "anopore" membranes. The latter is obtained by anodic oxidation of A1 metal foils and results in porous (amorphous) alumina (mesoporous) membranes. A detailed discussion is given by Burggraaf and Keizer in Ref. [1]. These types of membrane are useful for fundamental trans-... 

Fig. 2.1. Schematic picture of pore shapes. A and B are single wall, symmetric and asymmetric membranes respectively with straight cylindrical (a) or conical (b) pore shape (c) represents a ceramic asymmetric multilayered membrane with intercormected pores.

Fig. 9.2. Schematic representation of main types of pore structures and membrane architectures (A) straight cylindrical pores (B) straight as)onmetric pores (C) tortuous pore system.

Track-etched polymer membranes, which have straight cylindrical pores that are oriented normal to the plane of the membrane, provide a promising platform to design membranes with nano-domains with high aspect ratios oriented in the desired direction. Presently, track-etched membranes are commercially available in polyester and polycarbonate with various thicknesses (6 pm or above), pore sizes (10 nm to microns), and porosities ( 0.05% to... 

Okada and Matsuura (1991,1992) proposed a transport model applicable to PV based on a pore flow mechanism. It is assumed that there are a bundle of straight cylindrical pores at the membrane surface. The mass transport by the pore flow mechanism... 

Figure 2.2 Schematic representation of the main types of membrane pores (a) isolated (b) dead-end (c) straight cylindrical (d) constricted (e) conical.

The tortuosity factor, the measure of the deviation of the structure from straight cylindrical pores normal to the surface, should be small as it is inversely proportional to the MD membrane permeability. 

Mesoporous alumina membranes ( anodic aluminium oxide , or AAO) are prepared by anodic oxidation of aluminium metal [1,2]. The cylindrical pores, perpendicular to the membrane surface, form hexagonal arrays of straight non-intersecting channels with pore densities up to lO Vcm. Their diameters are controllable within the range 5 - 100 nm as a linear function of anodisation voltage. These membranes are used as molecular sieves, and have also found application as templates for metallic nanowires [3,4,5,6], metal elusters and colloids [7,8], and carbon nanotubes [9,10]. 

The resulting metal membrane has a structure similar to the bulk pores of the anodic alumina but without the dense "skin layer and has straight through-pores. Nickel and platinum membranes having pore diameters in the 15 to 200 nm range can be produced this way. One of the critical steps of this method is depositing palladium catalyst on the surface, but not inside the pores, of the anodic alumina. The catalyst is used to facilitate the deposition of metal from the bottom to the surface of the cylindrical pores. 

Other methods have also been adopted to produce inorganic membranes with essentially straight pores. Witte [1988] subjected a metal foil such as nickel to a two-step photolithographic procedure. The pore density of the final membrane exceeds 150,(X)0/cm and the pore sizes form fall under the microfiltration and ultrafiltration ranges. Although both flat and cylindrical shapes can be handled, the flat shape is preferred. 

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. 

The second hydrodynamic model is the Hagen-PoiseuiUe model. It is used to macroporous membranes with cylindrical straight pores of same diameter ... 

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