Porous membranes diffusion mechanisms

The main emphasis in this chapter is on the use of membranes for separations in liquid systems. As discussed by Koros and Chern(30) and Kesting and Fritzsche(31), gas mixtures may also be separated by membranes and both porous and non-porous membranes may be used. In the former case, Knudsen flow can result in separation, though the effect is relatively small. Much better separation is achieved with non-porous polymer membranes where the transport mechanism is based on sorption and diffusion. As for reverse osmosis and pervaporation, the transport equations for gas permeation through dense polymer membranes are based on Fick s Law, material transport being a function of the partial pressure difference across the membrane. 

First, porous membranes will be discussed. Gases can be separated due to differences in their molecular masses (Knudsen diffusion), due to interaction (surface diffusion, multilayer diffusion and capillary condensation) and due to their size (molecular sieving). All these mechanisms and their possibilities will be discussed. For the sake of simplicity, theoretical aspects are not covered in detail, but examples of separations in literature will be given. The next section deals with nonporous membranes. Here the separation mechanism is solution-diffusion, e.g. solution and diffusion of hydrogen through a platinum membrane. This section is followed by an outline of some new developments and conclusions. 

In dense membranes, no pore space is available for diffusion. Transport in these membranes is achieved by the solution diffusion mechanism. Gases are to a certain extent soluble in the membrane matrix and dissolve. Due to a concentration gradient the dissolved species diffuses through the matrix. Due to differences in solubility and diffusivity of gases in the membrane, separation occurs. The selectivities of these separations can be very high, but the permeability is typically quite low, in comparison to that in porous membranes, primarily due to the low values of diffusion coefficients in the solid membrane phase. 

Selective barrier structure. Transport through porous membranes is possible by viscous flow or diffusion, and the selectivity is based on size exclusion (sieving mechanism). This means that permeability and selectivity are mainly influenced by membrane pore size and the (effective) size of the components ofthe feed Molecules... 

The separation performance of membranes with nonporous barriers is - because of the transport via solution-diffusion (cf. Section 2.2) - predominantly influenced by the polymer material itself. Therefore, the material selection is directly related to the intrinsic (bulk) properties of the polymer, but - as for porous membranes - filmforming properties, mechanical and thermal stability form the basis of applicability (cf. Section 2.3.2.1). The following characteristics should be considered ... 

Microdialysis was achieved in a fused silica chip with in situ photopattemed porous membrane, as shown in Figure 5.13. Phase-separation polymerization of the membrane (7-50 pm thick) was formed between posts. The posts maximize the mechanical strength of the membrane so that it can withstand a pressure drop of 1 bar. Low MW cutoff (MWCO) membrane, which can be formed by using less organic solvent, 2-methoxyethanol, appears to be more transparent (see Figure 5.13). This low MWCO membrane can be used to dialyze away low MW molecules, such as rhodamine 560, but not fluorescently labeled proteins (insulin, BSA, anti-biotin, and lactalbumin). Fligh MWCO membrane, which was formed by more organic solvent, allows diffusion of lactalbumin [347]. 

In order to predict correctly the fluxes of multicomponent mixtures in porous membranes, simplified models based solely on Fields law should be used with care [28]. Often, combinations of several mechanisms control the fluxes, and more sophisticated models are required. A well-known example is the Dusty Gas Model which takes into account contributions of molecular diffusion, Knudsen diffusion, and permeation [29]. This model describes the coupled fluxes of N gaseous components, Ji, as a function of the pressure and total pressure gradients with the following equation ... 

The viscous diffusion mechanism is also valid for transport process in the liquid phase. Then, if we have a liquid filtration process through a porous (i.e., macroporous or mesoporous) membrane, the following form of the Carman-Kozeny equation can be used [9]... 

Transport in porous membranes occurs via diffusion of gaseous molecules within the porous framework this transport may involve different mechanisms (Section A9.3.2.4) which are more or less dependent on the nature of the gaseous molecules, and hence more or less efficient for the separation of a gas mixture. Porous membranes are therefore generally less permselective when compared to dense ones however, their permeability is higher (a conventional mesoporous y-Al2C>3 membrane has a permeability for hydrogen which is 10 to 100 times higher than a conventional Pd dense membrane. More detailed permeability data can be found in Ref. 9). 

Basic Equations All of the processes described in this section depend to some extent on the following background theory. Substances move through membranes by several mechanisms. For porous membranes, such as are used in microfiltration, viscous flow dominates the process. For electrodialytic membranes, the mass transfer is caused by an electrical potential resulting in ionic conduction. For all membranes, Fickian diffusion is of some importance, and it is of dom-... 

The water transport mechanism changes from the flow mechanism in porous membrane to the diffusive transport in nonporous homogeneous membrane due to the deposition of a homogeneous LCVD layer that fills the pore, i.e., water transport changes from bulk flow to diffusive flow when pores are covered by LCVD film. 

Ceramic membrane is the nanoporous membrane which has the comparatively higher permeability and lower separation fector. And in the case of mixed gases, separation mechanism is mainly concerned with the permeate velocity. The velocity properties of gas flow in nanoporous membranes depend on the ratio of the number of molecule-molecule collisions to that of the molecule-wall collision. The Knudsen number Kn Xydp is characteristic parameter defining different permeate mechanisms. The value of the mean free path depends on the length of the gas molecule and the characteristic pore diameter. The diffusion of inert and adsorbable gases through porous membrane is concerned with the contributions of gas phase diffusion and sur u e diffusion. 

Capillary condensation provides the possibility of blocking pores of a certain size with the liquid condensate simply by adjusting the vapor pressure. A permporometry lest usually begins at a relative pressure of 1, thus all pores filled and no unhindered gas transport. As the pressure is reduced, pores with a size corresponding to the vapor pressure applied become emptied and available for gas transport. The gas flow through the open mesopores is dominated by Knudsen diffusion as will be discussed in Section 4.3.2 under Transport Mechanisms of Porous Membranes. The flow rate of the noncondensable gas is measured as a function of the relative pressure of the vapor. Thus it is possible to express the membrane permeability as a function of the pore radius and construct the size distribution of the active pores. Although the adsorption procedure can be used instead of the above desorption procedure, the equilibrium of the adsorption process is not as easy to attain and therefore is not preferred. 

Laminar and turbulent flows, which occur in large pores where the mean pore diameter (say, larger than 1 )jun) is larger than the mean free paths of the fluid molecules involved, do not discriminate components in fluid mixtures. The same applies to molecular diffusion which occurs at relatively high pressures in large pores, llierefore, no separation is effected when only laminar or turbulent flow or bulk diffusion occurs in the pores. The permselectivity of a porous membrane will then have to rely on other transport mechanisms. 

Figure 4.17 Transport mechanisms for gaseous mixtures through porous membranes (a) viscous How (b) Knudsen diffusion (c) surface diffusion (d) multi-layer diffusion (e) capillary condensation and (0 molecular sieving [Saracco and Specchia, 1994]...

The inorganic membranes had until the late nineties received fairly little attention for applications in gas separation. This has mainly been due to their porous stmcmre, and therefore lack of ability to separate gas molecules. Within the group of inorganic membranes there are however the dense metallic membranes and the solid oxide electrolytes these are discussed separately in Section 4.3.5. With reference to Section 4.2, the possible transport mechanisms taking place in a porous membrane may be summarized as in Table 4.4 below, as well as the ability to separate gases (+) or not (—). Recent findings [29] have however documented that activated Knudsen diffusion may take place also in smaller pores than indicated in the table. 

Transfer mechanisms involved in SC CO2 permeation through such porous membranes can be convection (Poiseuille law), diffusion (Knudsen flow), and surface membrane interaction by adsorption, capillary condensation, etc. [11]. Mechanisms have been specifically investigated for nanofiltration and zeolite membranes. With a nanofilter presenting a pore diameter of about 1 nm, Sarrade [11] mentioned a Poiseuille flow associated with an irreversible CO2 adsorption on the micropore wall. Transfer... 

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