Transport through nonporous membranes

Vk hen the sizes of molecules are in the same order of magnitude, as w ith oxygen and nitrogen or hexane and heptane, porous membranes cannot effect a separation. In this case nonporous membranes must be used. However, the term nonporous is rather ambiguous because pores are present on a molecular level in order to allow transport even in such membranes. The existence of these dynamic molecular pores can be adequately described in terms of free volume. 

Another difference between liquids and gases is that the gases in a mixture flow through a dense membrane in a quite independent manner whereas with liquid mixtures the transport of the components is influenced by flow coupling and thermodynamic interaction. This synergistic effect can have a very large influence on the ultimate separation, as will be shown later. 

Basically, the transport of a gas, vapour or liquid through a dense, nonporous membrane can be described in terms of a solution-diffusion mechanism, i.e. 

The solubility of gases in polymers is generally quite low ( 0.2% by volume) and it is assumed that the gas diffusion coefficient is constant. Such cases can be considered as 

Two separate cases must therefore be considered, ideal systems where both the di sivity and the solubility are constant, and concentradon dependent systems where the solubility and the diffusivity are functions of the concentradon.(Other cases can be distinguished where the solubility and the difiusivity are funedons of other parameters, such as dmeand place. These phenomena, oftm termed anomalous , can be observed in glassy polymers where relaxadon phenomena occur or in heterogeneous types of membranes. These cases will not be considered fiirtha here.) 

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Transport through nonporous membranes follows the solution-diffusion mechanism, and separation is achieved either by differences in solubility or diffusivity. Therefore,... 

Solution-diffusion model is the generally accepted mechanism of mass transport through nonporous membranes (Figure 9.3). According to this mechanism, PV consists of three consecutive steps ... 

Nonporous membranes are used to perform separations on a molecular level. However, rather than molecular weight or molecular size, the chemical nature and morphology of the polymeric membrane and the extent of interaction between the polymer and the permeants are the important factors to consider. Transport through nonporous membranes occurs by a solution-diffusion mechanism and separation is achieved ei er by differences in solubility and/or diffusivity. Hence such membranes cannot be characterised by the methods described in the previous section, where the techniques involved mainly characterised the pore size and pore size distribution in the membranes. The determination of the physical properties related to the chemical structure is now more important and in this respect the following methods will be described ... 

Figure V - 30 gives a representation of the process conditions necessary for describing transport through nonporous membranes, where the superscripts m and s refer to membrane and feed/permeate side, respectively. If it is assum that thermodynamic equilibrium exists at the membrane interfaces, i.e. that the chemical potential of a given component (liquid or gas) at the feed/membrane interface is equal in both the feed and the membrane, and furthermore, that the pressure inside the membrane is equal to the pressure...

Figure V - 30, Process conditions for transport through nonporous membranes.

Process Description Pervaporation is a separation process in which a liquid mixture contacts a nonporous permselective membrane. One component is transported through the membrane preferentially. It evaporates on the downstream side of the membrane leaving as a vapor. The name is a contraction of permeation and evaporation. Permeation is induced by lowering partial pressure of the permeating component, usually by vacuum or occasionally with a sweep gas. The permeate is then condensed or recovered. Thus, three steps are necessary Sorption of the permeating components into the membrane, diffusive transport across the nonporous membrane, then desorption into the permeate space, with a heat effect. Pervaporation membranes are chosen for high selectivity, and the permeate is often highly purified. 

The theories developed for transport in microporous membranes cannot be applied to nonporous gel membranes. The pore structure in microporous membranes is not analogous to the mesh of the nonporous gels. Thus a different set of theories had to be developed for the treatment of nonporous polymer gel membranes. These theories are based on the idea of the existence of free volume in the macromolecular mesh. As a result, diifusion through nonporous membranes is said to occur through the space in the polymer gel not occupied by polymer chains. 

The first theory of transport through nonporous gels was presented by Yasuda et al. [150] and was proposed as a result of previous experimental results [151, 152]. This theory relates the ratio of diffusion coefficient in the polymer membrane and diffusion coefficient in the pure solvent to the volume fraction of solvent in the gel membrane or in Yasuda s terminology, the degree of hydration of the membrane, H (g water/g swollen polymer). Yasuda et al. use the... 

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). 

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. 

The last part of.Ais chapter will be devoted to a comparison of meiribr c processes v where transport occurs through nonporous membranes. A solution-diffusion model will be used where each component dissolves into the membrane and diffuses through the membrane independently [41]. A similar approach was recently followed by Wijmans[43]. As a result, simple equations will be obtained for the component fluxes involved in the various processes which allows to compare the processes in terms of transport parameters. 

The possibility of gas transport through nonporous polymeric membranes is one of the basic phenomena of polymer materials [1]. It is based on solution-diffusion concept. It means that the presence of mieroseopie open pores or capillaries is not necessary for mass transfer through polymerie films. On the other hand, closed porosity or the presence of free-volume elements within a polymer matrix is required for gas permeation in the polymers considered for use as materials for gas separation membranes. 

The mechanism of separation by non-porous membranes is different from that by porous membranes. The transport through nonporous polymeric membranes is usually described by a solution-diffusion mechanism (Figure 9.12a). The most current commercial polymeric membranes operate according to the solution-diffusion mechanism. The solution-diffusion mechanism has three steps (1) the absorption or adsorption at the... 

Transport through nonporous materials requires solute to be absorbed (solubilized) in the matrix material. Solute molecules are thus subject to thermodynamic equihbrium factors at the fluid-soHd interfaces, as weU as the nature of the fluid and soHd phases themselves. These include ion strength, degree of solute hydration, and other interactive forces. Once the solute is within the membrane, a simple Fickian... 

The solution-diffusion transport model was originally described by Lonsdale et al. This model assumes that the membrane is nonporous (without imperfections). The theory is that transport through the membrane occurs as the molecule of interest dissolves in the membrane and then diffuses through the membrane. This holds true for both the solvent and solute in solution. 

Ideally, it is necessary to use mass-transfer equations in the feed-gas phase and the product-gas phase along with the permeation equation (3.4.72). However, in general, the gas permeation rate through a nonporous membrane is so slow that mass-transfer equations in the feed-gas and product-gas phases are not needed. Note that, for species i transport through the membrane from the feed to the product gas, pif> pip, but fy need not be greater than Pp, although in practice it generally is. In such a case, flux expression (3.4.72) may also be expressed as... 

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. 

Gas transport through nonporous inorganic membranes falls into two categories. It is known that the conventional solution-diffusion permeation mechanism is valid for nonporous membranes of silica, zeolite and inorganic salts. It is no longer so when the membrane is metallic in nature (Hwang and Kammermeyer, 1975). Diatomic gases such as O2, H2 and N2 dissolve atomically in the metallic membrane (see (3.3.67)). While a conventional flux expression is valid for atomic species i dissolved in the membrane, Le. 

Most theoretical studies of osmosis and reverse osmosis have been carried out using macroscopic continuum hydrodynamics [5,8-13]. The models used include those that treat the wall as either nonporous or porous. In the nonporous models the membrane surface is assumed homogeneous and nonporous. Transport occurs by the molecules dissolving in the membrane phase and then diffusing through the membrane. Mass transfer across the membrane in these models is usually described using the solution-diffusion... 

As previously discussed, electron, light, and confocal microscopy techniques may be used to visualize the position of electron-dense precipitates, radioactive substances, and fluorescent probes, respectively, in the sample tissue. However, none of these techniques possess the capability both to visualize and to selectively measure the flux of a molecule across the skin. SECM, however, permits the measurement and subsequent imaging of the local flux of an electroactive species across biological membranes. Scott et al. [3] used SECM to investigate the effect of pretreatment of the penetration enhancer sodium dodecyl sulfate (SDS), on the ion transport rate and transport pathways of Fe(CN) across hairless mouse skin. Increasing the time of SDS exposure from 10 min to 30 min increased the overall (porous and nonporous) transport of Fe(CN) by 17-fold. More specifically, the SDS-induced increase in Fe(CN)g transport was found to be associated with nonporous (i.e., intercellular) transport routes, while transport via porous routes was significantly reduced. The fraction of Fe(CN)g transport through pores, as measured by... 

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