Porous membranes permeation transport 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. 

Pervaporation is a membrane separation process in which a dense, non-porous membrane separates a liquid feed solution from a vapour permeate (Fig. 19.2c). The transport across the membrane barrier is therefore based, generally, on a solution-difliision mechanism with an intense solute-membrane interaction. It... 

In the fourth subtechnique, flow FFF (F/FFF), an external field, as such, is not used. Its place is taken by a slow transverse flow of the carrier liquid. In the usual case carrier permeates into the channel through the top wall (a layer of porous frit), moves slowly across the thin channel space, and seeps out of a membrane-frit bilayer constituting the bottom (accumulation) wall. This slow transverse flow is superimposed on the much faster down-channel flow. We emphasized in Section 7.4 that flow provides a transport mechanism much like that of an external field hence the substitution of transverse flow for a transverse (perpendicular) field is feasible. However this transverse flow—crossflow as we call it—is not by itself selective (see Section 7.4) different particle types are all transported toward the accumulation wall at the same rate. Nonetheless the thickness of the steady-state layer of particles formed at the accumulation wall is variable, determined by a combination of the crossflow transport which forms the layer and by diffusion which breaks it down. Since diffusion coefficients vary from species to species, exponential distributions of different thicknesses are formed, leading to normal FFF separation. 

The permeation of a simple permeant, e.g., O2, through a polymeric membrane could occur, in principle, by two different mechanisms. One is the transport through pores, and the other is the transport through the free volume of polymer solid. The size of pore and its distribution is the most crucial parameter in the former case (porous membrane), and the value of a is determined by the molecular sizes of permeants A and B. The values of Ps are in the reverse order of the size of permeant, i.e., Pn2 > -P02 > -Pco2, and P can be dealt as a kinetic parameter. 

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]. 

As a rule, permeability in glassy polymers (e.g. cellulose) is lower than in rubbery polymers (e.g. polydimethylsiloxane, PDMS) on the other hand, selectivity is dictated by the molecular dimensions of the permeating species [167]. The polymers used as membranes in analytical pervaporation are similar to those employed for gas separation and possess a dense, non-porous macroscopic structure. The difference between the two lies in the transport mechanism and arises mainly from a large affinity difference between the permeating molecules and the polymer membrane. 

It is understood that the economical success of any membrane process depends primarily on the quality of the membrane, specifically on flux, selectivity and service lifetime. Consideration of only the transport mechanisms in membranes, however, will in general, lead to an overestimation of the specific permeation rates in membrane processes. Formation of a concentration boundary layer in front of the membrane surface or within the porous support structure reduces the permeation rate and, in most cases, the product quality as well. For reverse osmosis. Figure 6.1 shows how a concentration boundary layer (concentration polarization) forms as a result of membrane selectivity. At steady state conditions, the retained components must be transported back into the bulk of the liquid. As laminar flow is present near the membrane surface, this backflow is of diffusive nature, i.e., is based on a concentration gradient. At steady state conditions, the concentration profile is calculated from a mass balance as... 

Vapor permeation and pervaporation are membrane separation processes that employ dense, non-porous membranes for the selective separation of dilute solutes from a vapor or liquid bulk, respectively, into a solute-enriched vapor phase. The separation concept of vapor permeation and pervaporation is based on the molecular interaction between the feed components and the dense membrane, unlike some pressure-driven membrane processes such as microfiltration, whose general separation mechanism is primarily based on size-exclusion. Hence, the membrane serves as a selective transport barrier during the permeation of solutes from the feed (upstream) phase to the downstream phase and, in this way, possesses an additional selectivity (permselectivity) compared to evaporative techniques, such as distillation (see Chapter 3.1). This is an advantage when, for example, a feed stream consists of an azeotrope that, by definition, caimot be further separated by distillation. Introducing a permselective membrane barrier through which separation is controlled by solute-membrane interactions rather than those dominating the vapor-liquid equilibrium, such an evaporative separation problem can be overcome without the need for external aids such as entrainers. The most common example for such an application is the dehydration of ethanol. 

The flux also depends on the physical make-up of the membrane and the pore size. The pure water flux vs. hydrauhc pressure difference curve is linear. Liquid flux for membrane processes is shown in F ure 1.5. The data show how the permeation rate varies with the size of the species and pore size (implicit in type of membrane). The ordinate represents the flux of water per unit pressure gradient. Since the pore radius of an RO membrane is 0.6 nm, water molecules whose radius is about 0.1 nm can pass through the membrane freely while dissolved ions and organic solutes (e.g., sucrose) cannot. These solutes are either rejected at the membrane surface, or are more strongly attracted to the solvent water phase than to the membrane surface. The preferential sorption of water molecules at the solvent—membrane interface, which is caused by the interaction force working between the membrane, solvent, and solute responsible for the separation [8]. As the pore size decreases and tends toward a non-porous skin structure, the transport mecharusm changes from convective flow through pores to SD in the membrane polymer. The latter is the transport mechanism in GS and PV. 

Concerning the gas transport mechanisms, for dense membranes the permeation of a gas takes place through the bulk of its material and the transport can be described by a solution/diffusion mechanism. Otherwise, in the case of porous membranes, it takes place through its porous stmcture and the gas transport can be described by... 

In porous membranes, the permeation happens through their pores and then the transport mechanisms (sieving mechanism and/or Knudsen diffusion) depend on the pore size. In dense membranes, the mass transport takes place by the so-called solu-tion/diffusion mechanism. 

Often the single-stage design does not result in the desired product quality and for this reason the retentate or permeate stream must be treated in a second stage. A combination of stages is called a cascade. A well-known example of a cascade operation occurs in die enrichment of uranium hexafluoride (235U) with porous membranes. In this process transport through the membrane proceeds by a Knudsen mechanism and the selectivity is very low. 

Integration of a H2 PSA process with an adsorbent membrane can meet this goal [23, 24]. A nano-porous carbon adsorbent membrane called Selective Surface Flow (SSF) membrane which selectively permeates CO2, CO and CH4 from their mixtures with H2 by an adsorption- surface diffusion-desorption transport mechanism may be employed for this purpose. The SSF membrane can produce an enriched H2 gas stream from a H2 PSA waste gas, which can then be recycled as feed to the PSA process for increasing the over-all H2 recovery. The membrane is prepared by controlled carbonization of poly-vinyledene chloride supported on a macro-porous alumina tube. The membrane pore diameters are between 6 -7 A, and its thickness is - 1-2 pm [25]. 

All these methods lead to a set of parameters (membrane thickness, pore volmne, hydraulic radius) which are related to the working (macroscopic) permselective membrane properties. In the case of liquid permeation in a porous membrane, macro- and mesoporous structures are more concerned with viscous flow described by the Hagen-Poiseuille and Carman-Kozeny equations whereas the extended Nernst-Plank equation must be considered for microporous membranes in which diffusion and electrical charge phenomena can occur (Mulder, 1991). For gas and vapor transport, different permeation mechanisms have been described depending on pore sizes ranging from viscous flow for macropores to different diffusion regimes as the pore size is decreased to micro and ultra-micropores (Burggraaf, 1996). 

The permeation of gas mixtures through porous membranes provides more stringent test of the transport mechanism than the single gas permeation. If the transport occurs by the Knudsen diffusion, the selectivity based on the single gas experiments and that for the gas mixture should be equal. 

It is well known that the pore network of real porous membranes is very complicated, and geometrical effects play an important role in gas permeation. Different transport mechanisms may take place in the individual pores with different radius. 

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