Permeation through porous membranes

Solute Permeability of erythrocyte membranes (cm/s) Permeability of lipid vesicles (cm/s) 

Permeability of doxorubicin in model membrane bilayers. From [7]. Permeability was measured in artificial unilamellar vesicles of known composition. Permeability varies with the addition of cholesterol (squares). Permeability also varies with change in phospholipid composition. 

The driving force for particle movement through the pore, the gradient of chemical potential, is balanced by the drag force acting on the particle  

Assuming that the activity coefficient is unity, so the chemical potential can be expressed in terms of the local solute concentration c, and considering only the axial gradient, Equation 5-5 becomes 

With these assumptions, the drag force on the particle can be written  

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It is obvious from the above discussion that porous and dense membranes form two different cases, each with its own advantages and disadvantages. Dense membranes, (permeable only to one component) operating at optimum conditions, can be used to obtain complete conversions. However, because the permeation rate is low, the reaction rate has also to be kept low. Porous membranes (permeable to all components but at different permselectivities) are limited under optimum conditions to a maximum conversion (which is not 100%) due to the permeation of all the components. The permeation rates through porous membranes are, however, much higher than those through dense membranes and consequently higher reaction rates or smaller reactor volumes are possible. 

For relatively porous nanofiltration membranes, simple pore flow models based on convective flow will be adapted to incorporate the influence of the parameters mentioned above. The Hagen-Poiseuille model and the Jonsson and Boesen model, which are commonly used for aqueous systems permeating through porous media, such as microfiltration and ultrafiltration membranes, take no interaction parameters into account, and the viscosity as the only solvent parameter. It is expected that these equations will be insufficient to describe the performance of solvent resistant nanofiltration membranes. Machado et al. [62] developed a resistance-in-series model based on convective transport of the solvent for the permeation of pure solvents and solvent mixtures ... 

As pointed out in Section A9.3.2.1, most of the CMRs for gas-phase applications require selective permeation through the membrane. The aim of this section is to briefly describe the different gas transport processes through a porous membrane. 

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. 

Membranes can be classified [2] according to the driving force (concentration or pressure difference) that causes the flow of the permeate through the membrane, or to the material(s) they consist of (organic polymers or inorganic materials). For both type of materials the membrane can be dense or porous. 

Most commercial systems like Mustang from Pall and Sartobind from Sartorius make use of functionalized microporous membranes. The fibrils reinforced membranes are (pleated) layered around a porous core. The feed is forced to permeate through the membranes in radial direction. This approach results in high area to volume ratio. The 3M and Mosaic Systems approach is different. Instead of functionalization of a porous support they make use of already functionalized beads, which are embedded in a porous support. In this approach, the beads are responsible for the capacity and selectivity where the porous matrix controls the hydrodynamics. The 3M modules consist of stacked flat sheet or pleated membranes, while Mosaic Systems makes use of porous fibers in which the active particles are embedded (Figure 3.23). 

This paper provides discussions on the hydrogen permeation through Pd membranes, methods of the formation of thin Pd and Pd/alloy films on porous supports with special emphasis on electroless plating, porous metallic supports, formation of intermetallic diffusion barrier and long term membrane stability at high temperatures. 

The permeation of binary mixtnre of ethanol/n-hexane showed that transport throngh dense membranes (solvent stable) occurs by couple diffusion, while for porous membranes transport has a convective natnre. It was shown that permeation through dense membranes is more affected by mutual affinities of membrane and solvent, whereas viscosity is the major transport parameter for porons membranes [33]. 

Knudsen mechanism occurs when the average pore diameter is similar to the average free path of fluid moleeules. In this ease, the collisions of the molecules with the porous wall are very frequent and the flux of the component permeating through the membrane is ealeulated by means of the following equation [12] ... 

The equipment for reverse osmosis is quite similar to that for gas permeation membrane processes described in Section 13.3C. In the plate-and-frame type unit, thin plastic support plates with thin grooves are covered on both sides with membranes as in a filter press. Pressurized feed solution flows between the closely spaced membranes (LI). Solvent permeates through the membrane and flows in the grooves to an outlet. In the tubular-type unit, membranes in the form of tubes are inserted inside porous-tube casings, which serve as a pressure vessel. These tubes are then arranged in bundles like a heat exchanger. 

Concerning non-porous membranes, these are categorized as dense ceramic electrolytes such as yttria-stabilized zirconia (YSZ) and perovskite membranes [16], which allow only the permeation of ionic oxygen. Permeation through metal membranes such as palladium and a palladium alloy is based on the selective dissolution of hydrogen and diffusion through the metal membrane. 

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. 

Here, we only consider the basic equations describing the flux through porous membranes used for filtration and water treatment, and permeation through a... 

The permeation of gases through polymer membranes depends upon whether the membrane is porous or dense. If the membrane is porous, the gas flow is predominantly controlled by the mean free path of the gas molecules and the pore size. The mechanism of flow through porous membranes has been discussed elsewhere. In short, the gas flow regime is contributed to by Poiseuille flow and Knudsen flow, the amount of each contribution being defined by pore size, pressure, viscosity and the molecular weight of the gas involved. However, microporous membranes exhibit low gas selectivity, as shown earlier in the resistance model approach. 

However, in a series of publications Ito et al. [7,23,24,26] have shown that polymer brush-decorated membranes offer a much faster response while depending on the mechanical properties of the porous membrane, they can be more mechanically robust. In these publications it was also demonstrated that different types of external stimuli, such as variation of pH, temperature, solvent quality, and ultraviolet irradiation, might be used for the control of solvent permeation through the membranes. 

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. 

Park, Y.S., Ito, Y, and Imanishi, Y. (1998) Permeation control through porous membranes immobilized with... 

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. 

We have seen in Section 3.4.2.1.1 that the volatile species permeating through the membrane in the pervaporation process is driven by its concentration gradient in the non-porous membrane. The concentration of this species in the membrane at the feed liquid-membrane interface, C , is related to the feed liquid-phase concentration at this interface, Cjj, by a partition coefficient... 

Gas permeation through the porous membranes may be driven by pressure or concentration gradient. Under a pressure or concentration gradient, gas will permeate through the membrane in a convective or a diffusive flow, respectively. In general, the pressure-driven convective fluxes are much higher than the concentration-driven diffusion fluxes. 

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