Transport through porous membranes

Porous membranes are used in microfiluation and ulu-afiltration processes. These membranes consist of a polymeric matrix in which pores within the range of 2 nm to 10 jLm are present. A large variety of pore geomeoies is possible and figure V 5 gives a schematic representation of some of the characteristic structures found. Such structures exist over the whole membraite thickness in microfUtration membranes and here the resistance is determined by the total membrane thickness. On the other band, ultiafiltration membranes generally have an asymmetric structure, where the porous top-layer mainly determines the resistance to transport Here, the transpon length is only of the order of 1 fim or less. 

The existence of these different pore geometriesalso implies that different models have been developed to describe transport adequately. These transport models may be helpful in determining which structural parameters are important and how membrane performance can be improved by varying some specific parameters. 

The simplest representation is one in which the membrane is considered as a number of parallel cylindrical pores perpendicular or oblique to the membrane surface (see figure V -5a). The length of each of the cylindrical pores is equal or almost equal to the membrane thickness. The volume flux through these pores may be described by the Hagen-Poiseuille equation. Assuming that all the pores have the same radius, then we may write  

The Hagen-Poiseuille equation clearly shows the effect of membrane structure on transport. By comparing eq. V - 54 with the phenomenological eq. V - 43 (and writing in the latter case AP/Ax as driving force instead of AP), a physical meaning can be given to the 

The Hagen-Poiseutlle eq. V 54 gives a good description of transport through membranes consisting of a number of parallel pores. However, very few membranes posses such a structure in practice. 

---

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... 

Scott, E. R., White, H. S. and Phipps, J. B. lontophoretic transport through porous membranes using scanning electrochemical microscopy Application to in vitro studies of ion fluxes through skin. Anal. Chem. 65 1537-1545, 1993. 

The mass transfer through the membranes is achieved by application of an external driving force. The mass transport through porous membranes is enabled by a hydrostatic pressure difference (driving force) between the feed-side and the... 

Figure 5.8 Hindered transport through porous membranes. Schematic diagram of model for hindered transport of a spherical particle in a cylindrical pore.

Czaplewski, K.F., J.T. Hupp, and R.Q. Snurr (2001). Molecular squares as molecular sieves Size-selective transport through porous-membrane-supported thin-film materials. Adv. Mater. 13,1895-1897. 

Mass transport through porous membranes can be described with the pore model. In accordance with particle filtration, selectivity is determined solely by the pore size of the membrane and the particle or the molecular size of the mixture to be separated. This process is driven by the pressure difference between the feed and permeate sides [83]. The processes described by the pore model include microfiltration and ultrafiltration. Whereas membranes for microfiltration are characterized by their real pore size, membranes for ultrafiltration are defined according to the molar mass of the smallest components retained. 

The contribution of convective flow is the main term in any description of transport through porous membranes. In nonporous membranes, however, the convective flow term can be neglected and only diffusional flow contributes to transport.It can be shown by simple calculations that only convective flow contributes to transport in the case of porous membranes (microfiltration). Thus, for a membrane with a thickness of 100 pm, an average pore diameter of 0.1 pm, a tortuosity C of 1 (capillar) membrane) and a porosity e of 0.6, water flow at 1 bar pressure difference can be calculated from the Poisseuille equation (convective flow), i.e. 

Beyond these apphcations, SECM can also be used to probe diffusional transport in unusual samples because the UME can be placed precisely in the microenvironment of interest. For example, lateral proton diffusion in Langmuir monolayers (15), diffusional transport through porous membranes and dentin (16), and the contribution of diffusion to iontophoretic transport in skin (17) have been investigated using the SECM. 

McKelvey, K., M. E. Snowden, M. Peruffo, and P. R. Unwin, Quantitative visualization of molecular transport through porous membranes Enhanced resolution and contrast using intermittent contact-scanning electrochemical microscopy. Anal. Chem., Vol. 83, 2011 pp. 6447-6454. 

The permeation flux expressions (3.4.76) and (3.4.81a) are valid for membranes whose properties do not vary across the thickness. Most practical gets separation membranes have an asymmetric or composite structure, in which the properties vary across the thickness in particular ways. Asymmetric membranes are made from a given material therefore the properties varying across Sm are pore sizes, porosity and pore tortuosity. Composite membranes are made from at least two different materials, each present in a separate layer. Not only does the intrinsic Qim of the material vary from layer to layer, but also the pore sizes, porosity and pore tortuosity vary across Sm- At least one layer (in composite membranes) or one section of the membrane (in asymmetric membranes) must be nonporous for efficient gas separation by gas permeation. The flux expressions for such structures can be developed only when the transport through porous membranes has been studied. 

The flux expressions for gas transport through porous membranes have been considered in Section 3.I.3.2.4. The steady state Knudsen diffusion flux expression (3.1.115a),... 

Figure 12.4 Schema of DCMD mechanism of transport through porous membranes (a) homogenous hydrophobic and (b) composite bydropbobic/hydiophilic. Tbe concentration profiles correspond to nonvolatile solutes. (Adapted liom Khayet et al., 2005b.)...

The diffusing flux through different membranes can be adequately described by Tick s law (Equation [8.4]), indicating that gas transport through porous membranes is driven by a cross membrane pressure gradient. Based on the differences in partial pressures, gas diffusivities, molecular sizes and shapes, gases can be separated when they flow through a membrane. 

This method is commonly used to obtain the diffusion coefficient through porous membranes. The schematic diagram illustrating the best technique for application of the time-lag method for determination of diffusion transport is shown in Fig. 4. As in the test setup shown in Fig. 4 a, the soil is contained between the source and collection reservoirs. Using this technique for diffusion coefficient determination of pollutants requires that the following conditions are satisfied ... 

The transport properties across an MIP membrane are controlled by both a sieving effect due to the membrane pore structure and a selective absorption effect due to the imprinted cavities [199, 200]. Therefore, different selective transport mechanisms across MIP membranes could be distinguished according to the porous structure of the polymeric material. Meso- and microporous imprinted membranes facilitate template transport through the membrane, in that preferential absorption of the template promotes its diffusion, whereas macroporous membranes act rather as membrane absorbers, in which selective template binding causes a diffusion delay. As a consequence, the separation performance depends not only on the efficiency of molecular recognition but also on the membrane morphology, especially on the barrier pore size and the thickness of the membrane. 

Synthetic membranes for molecular liquid separation can be classified according to their selective barrier, their structure and morphology and the membrane material. The selective barrier- porous, nonporous, charged or with special chemical affinity -dictates the mechanism of permeation and separation. In combination with the applied driving force for transport through the membrane, different types of membrane processes can be distinguished (Table 2.1). 

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]...

Separation of the polar gases such as carbon dioxide, hydrogen sulfide and sulfur dioxide behaves in many respects differently from other nonpolar gases. Their transport mechanisms through porous membranes are often different and therefore their separation performances can also be markedly different. This has been observed for separating carbon dioxide from other nonpolar, non-hydrocarbon gases. 

There are, however, evidences that other more effective separating mechanisms such as surface diffusion and capillary condensation can occur in finer pore membranes of some materials under certain temperature and pressure conditions. Carbon dioxide is known to transport through porous media by surface diffusion or capillary condensation. It is likely that some porous inorganic membranes may be effective for preferentially carrying carbon dioxide through them under the limited conditions where either transport mechanism dominates. 

A general model for transport through porous crystal membranes was described by Barter [35]. The model involves five steps (Fig. 7) ... 

Retention of ionic species modifies ionic concentrations in the feed and permeate liquids in such a way that osmotic pressure or electroosmotic phenomena cannot be neglected in mass transfer mechanisms. The reflexion coefficient, tr, in Equations 6.4 and 6.5 represents, respectively, the part of osmotic pressure force in the solvent flux and the diffusive part in solute transport through the membrane. One can see that when a is close or equal to zero the convective flux in the pores is dominant and mostly participates to solute transport in the membrane. On the contrary when diffusion phenomena are involved in species transport through the membrane, which means that the transmembrane pressure is exerted across an almost dense stmcture. Low UF and NF ceramic membranes stand in the former case due to their relatively high porous volume and pore sizes in the nanometer range. Recendy, relevant results have been published concerning the use of a computer simulation program able to predict solute retention and flux for ceramic and polymer nanofiltration membranes [21]. 

---