Transport in porous membranes

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). 

SECM-based methods provide unique experimental capabilities for imaging and quantifying molecular transport in porous membranes. No other experimental method or technique currently exists that provides a means to visu-... 

The aim of Chapter 5 by Thornton et al. was to give systematic consideration to different types of transport in porous membranes. They developed a new model that allows one to predict the separation outcome for a variety of membranes in which the pore shape, size and composition are known, and conversely to predict pore characteristics with known permeation rates. 

Considering only the extreme cases, it can be stated that transport in porous membranes occurs by convection and in nonporous ammbranesby diffusion. Howevei in going from porous to nonporous membranes, an intermediate region exists where both... 

Bath BD, Lee RD, White HS, Scott ER (1998) Imaging molecular transport in porous membranes. Observation and analysis of electroosmotic flow in individual pores using the scanning electrochemical microscope. Anal Qiem 70(6) 1047-1058. doi 10.1021/ac971213i... 

J. L. Anderson, D. M. Malone. Mechanisms of osmotic flow in porous membranes transport. Biophys 14 951, 1974. 

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. 

P.M. Bungay, Transport Principles-Porous Membranes, in Synthetic Membranes Science Engineering and Applications, P.M. Bungay, H.K. Lonsdale and M.N. dePintio (eds), D. Reidel, Dordrecht, pp. 109-154 (1986). 

Figure 6.21 shows the AC impedance spectra for the cathodic ORR of the cell electrodes prepared using the conventional method and the sputtering method. It can be seen that the spectra of electrodes 2 and 3 do not indicate mass transport limitation at either potentials. For electrode 1, a low-frequency arc develops, due to polarization caused by water transport in the membrane. It is also observable that the high-frequency arc for the porous electrode is significantly depressed from the typical semicircular shape. Nevertheless, the real-axis component of the arc roughly represents the effective charge-transfer resistance, which is a function of both the real surface area of the electrode and the surface concentrations of the species involved in the electrode reaction. 

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 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. 

Considering at first transport mechanisms in porous membranes, viscous flow (Fig. 9), also called Poiseuille flow, takes place when the mean pore diameter is larger than the mean free path of gas molecules (pore diameter higher than a few microns), so that collisions between different molecules are much more frequent than those between molecules and pore walls. In such conditions, no separation between different molecules can be attained [45]. 

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]. 

In summary, one can see that separation selectivity for gas and vapor molecules depends on the category of pores (mesopores, supermicropores, and ultramicropores) and on the related transport mechanisms. Either size effect or preferential adsorption effect (irrespective of molecular dimension) is involved in selective separation of multicomponent mixtures. The membrane separation selectivity for two gases is usually expressed either as the ratio between the two pure gas permeation fluxes (ideal selectivity) or between each gas permeation flux measured from the mixture of the two gases (real selectivity). More detailed information on gas and vapor transport in porous ceramic membranes can be found in Ref. [24]. 

An overview of the transport mechanisms in porous membranes is given in Table 9.1. 

P.M. Bungay, Transport principles — Porous membranes, in P.M. Bungay, H.K. Lonsdale, M.N. de Pinho (Eds), Synthetic Membranes Science, Engineering and Applications. NATO ASI Series, Series C Mathematical and Physical Sciences, Vol. 181,1986. p. 109. 

The capabilities of SECM make it a nearly ideal method for studying molecular transport across porous membrane samples. In a typical application, the SECM tip is rastered at constant height across the surface of a membrane mounted in a diffusion cell (Fig. 1). An electroactive species is... 

We gratefully acknowledge the contributions and insights of Dr. J. Bradley Phipps (ALZA Corp) to the development of the SECM methodology for imaging transport across porous membranes. Research on SECM imaging of porous membranes in the authors laboratory has been supported by ALZA Corp and the Office of Naval Research. 

Baltus, R.E. 1997. Characterization of the pore area distribution in porous membranes using transport measurements. J. Membrane Sci. 123 165-184. 

For porous membranes the mass transport mechanisms that prevail depend mainly on the membrane s mean pore size [1.1, 1.3], and the size and type of the diffusing molecules. For mesoporous and macroporous membranes molecular and Knudsen diffusion, and convective flow are the prevailing means of transport [1.15, 1.16]. The description of transport in such membranes has either utilized a Fickian description of diffusion [1.16] or more elaborate Dusty Gas Model (DGM) approaches [1.17]. For microporous membranes the interaction between the diffusing molecules and the membrane pore surface is of great importance to determine the transport characteristics. The description of transport through such membranes has either utilized the Stefan-Maxwell formulation [1.18, 1.19, 1.20] or more involved molecular dynamics simulation techniques [1.21]. 

Kimura and Sourirajan113 have offered a theory of preferential adsorption of materials at interfaces to describe liquid phase, selective transport processes in porous membranes. Lonsdale et al.,i4 have offered a simpler explanation of the transport behavior of asymmetric membranes which lack significant porosity in the dense surface layer. Their solution-diffusion model seems to adequately describe the cases for liquid transport considered to date. Similarly gas transport should be de-scribable in terms of a solution-diffusion model in cases where the thin dense membrane skin acts as the transport moderating element. 

The permeabilities of different components in a membrane depend on the mechanism by which the components are transported. For example, in homogeneous polymer membranes, the various chemical species are transported under a concentration or pressure gradient by diffusion. The permeability of these membranes is determined by the diffusivities and concentrations of the various components in the membrane matrix and the transport rates are, in general, relatively slow. In porous membrane structures, however, mass is transported under the driving force of a hydrostatic pressure difference via viscous flow and, in gen-... 

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

The importance of fluid flow in transporting drugs within the circulatory system is obvious. In the previous chapter, fluid flow was seen to be an important determinant of the overall rate of transport across porous membranes, as well. For some membranes, convection is more important than diffusion in determining the overall flux (recall Figure 5.24). This section illustrates other situa-... 

---