Membranes total flux through

In order to interpret the physicochemical steps of retinal transduction as well as membrane excitability, we analyze macroscopic properties of membranes within biological components. Such membranes separate two aqueous ionic phases the chemical compositions of which are kept constant separately. The total flux through the membrane is directly deduced from the counterbalance quantities in order to maintain the involved thermodynamical affinities constant. From such measurement, we calculate the dynamical membrane permeability. This permeability depends not only on membrane structure but also on internal chemical reactions. 

Having said this, the bulk of the pervaporation literature continues to report membrane performance in terms of the total flux through the membrane and a separation factor, /3pervap, defined for a two-component fluid as the ratio of the two components on the permeate side of the membrane divided by the ratio of the two components on the feed side of the membrane. The term /3pervap can be written in several ways. 

Flux through the Membrane. The total flux through the membrane can be divided in to three parts [134] ... 

The first term on the right-hand side is the diffusive flux relative to the volume average velocity. The second term represents a contribution due to bulk flow. It should be emphasized here that the separation of the total flux into two contributions is always possible regardless of the actual transport mechanism through the membrane. In other words, Eq. (7) is purely phenomenological and does not require any specific transport model. 

In the absence of suspended solutes or colloids, the pure solvent flux through an ultrafiltration membrane is directly proportional to the applied pressure difference and inversely proportional to the viscosity of the solvent and the membrane thickness. Transport within the pores occurs in the creeping flow regime, since kinematic viscosities of liquids are sufficient to make Re < C 1 for practical pore sizes. In the simplest case, the membrane can be considered to be a packed array of straight, equal diameter nonintersecting capillary tubes. The observed volumetric flux, nAvA (cc/sec cm2), equals the product of the mass flux of solvent based on the total membrane area, nA... 

The above model has been refined based on the dusty gas model [Mason and Malinauskas, 1983] for transport through the gas phase in the pores and the surface diffusion model [Sloot, 1991] for transport due to surface flow. Instead of Equation (10-101), the following equation gives the total molar flux through the membrane pores which are assumed to be cylindrically shaped... 

In another study by Nishiyama et al. [53], the Vapour-phase Transport method was applied on alumina supports. No permeation of 1,3,5-triisopropylbenzene (kinetic diameter 0.85 nm) could be observed through the 10 pm thick membrane. Mordenite has parallel channels with an elliptical pore dimension of 0.65 x 0.7 nm. Pervaporation of benzene-p-xylene (molar ratio 0.86) at 22°C resulted in a separation factor of 164 (total flux 1.19 10" mol.m s ). The theoretical value based on the gas-liquid equilibrium amounts to 11.3. Apparently, the mordenite-based membrane shows high selectivity for aromatic hydrocarbons. 

The temperature dependence of the methane permeation through a silicalite membrane, showing a maximum and a minimum as a function of temperature (Fig. 3 [14]), can not be predicted by using the Maxwell-Stefan description for surface diffusion only. Such a maximum and minimum in the permeation as a function of temperature can be predicted only when the total flux is described by a combination of surface diffusion and activated-gas translational diffusion (Fig. 15). 

The models above may be useful for predicting mass fluxes in MD however, each of these models has its limitations. The Knudsen and Poiseuille model require knowledge of r, 8, and e, which in general can be estimated by applying the models to experimental gas fluxes through the given membrane. The molecular diffusion model is inadequate at low-partial pressures of air, as it predicts infinite flux since, in totally deaerated membrane 7 tends to zero. 

The permeation of gases in membranes due to surface diffusion and capillary condensation has been discussed in Section 9.2.3.S. together with some illustrative data. The total flux of a single gas is usually calculated as the sum of the flux by surface diffusion and the flux through the gas phase. As shown the surface flux can contribute considerably to the total flux (increased by factor 2-3 of gas diffusional flux), especially with smaller and uniform pore sizes (compare Eqs. (9.9a) and (9.15). With decreasing pore size the flux through the bulk gas decreases while the surface diffusional flux increases. With very small pore diameter (< 2-3 nm) the effective diameter for bulk gas transport is less than the geometric pore diameter due to the thickness of the absorbed layer which... 

Thus, the total flux of i ion through the membrane is expressed as... 

Although the membranes used to extract hydrogen isotopes from plasmas meet the criterion for the definition of superpermeability, in that every atom of hydrogen incident upon the feed side surface of the membrane is transported through the dense membrane, it must be noted that superpermeability is achieved, in very large part, because of the relatively low flux of hydrogen incident upon the membranes. The plasma density in the quoted experiments was 5 x 10 cm-, and the total gas pressure was relatively low, 0.002-0.004 torr (0.3-0.6 Pa) [2]. 

The major output of interest is the solute flux through the liquid membrane. Often, this flux is described In a dimensionless fashion as a facilitation factor (F). F Is defined as the total solute flux with carrier present divided by the diffuslonal flux of solute alone. 

Analysis of hydrodynamic equations for the flow in the fuel cell channel shows that this flow is incompressible [13]. In other words, the variation of pressure (total molar concentration) along the channel is small. Consider first the case of zero water flux through the membrane. Each oxygen molecule in the cathode channel is replaced with two water molecules. Pressure is proportional to the number of molecules per unit volume. To support constant pressure, the flow velocity in the channel must increase. The growth of velocity provides expansion of elementary fluid volume the expansion keeps pressure in this volume constant. 

Stable pores are assumed to be present inside the membrane and the driving force for transport is the pressure gradient across the membrane. Assuming a system at constant temperature where there are no external forces except pressure, one can derive, from the Stefan-MaxweU equations [34], the following equations describing the total volumetric flux through a membrane ... 

Park et al. (2000) studied PV of pyridine-water mixture through a poly(acrylonitrile-co-monoacryloxyethyl phosphate) (PANPH) membrane for the dehydration of aqueous pyridine solution. All the PAN-based phosphoric acid-containing membranes were very selective toward water. The PV performance depended on the content of the phosphoric acid moiety in the membrane, operating temperature, and feed concentration. The PV performances of the water-pyridine mixture through the PANPH membrane showed good PV performance. PV performance at 75°C was such that the water concentration in the permeate was >99.8% and the total flux was about 120 g/m h. 

Zeolite Y clearly shows the most extreme results with an exceptionally high total flux, due entirely to the transport of water, leading to an extremely low enrichment factor. Among all other membranes, unfilled PDMS is one of the best. For the more hydrophobic fillers—US Y and silicalite—the enrichment factors are high due to the exclusion of water from the pores. Study of the influence of temperature revealed the importance of diffusion limitations on the transport of organics through the membranes. This effect was stronger when more zeolite was incorporated. 

Shah et al. (2000) used hydrophilic zeolite NaA membranes for the separation of alcohol-water, methanol-water, EtOH-water, IPA-water, and DMF-water mixtures. The total flux for EtOH-water mixture was found to vary from 2 to 0.05 kg/m h at 60°C as the feed solvent concentration was increased from 0 to 100 wt%. The total fluxes for methanol-water and IPA-water mixtures were observed to vary from 2 to 0.15 and 2 to 0.21 kg/m h, respectively, as the alcohol concentration was changed from 0 to 100 wt%. Both water-to-EtOH and water-to-IPA separation factors were observed to lie between 1000 and 5000 over a wide range of solvent concentrations. The water-to-methanol separation factor was found to lie in the range of 500-1000. It was observed that ionic Na+ sites in the NaA zeolite matrix play a very important role in the water transport through the membrane. These sites act both as water sorption and transport sites. 

Zhu and Chen (1998) prepared cross-linked PVA composite catalytic membranes on porous ceramic plate for PV separation and PV-esterification coupling. The composite catalytic membrane was evaluated through the PV and a model system of n-butyl alcohol esterification coupling with the PV. The conversion of n-butyl alcohol reached 95% when a cross-linked PVA catalytic manbrane was used. The order of permeation fluxes was water > acid > alcohol > acetate and the total flux was greater than 0.5 kg/m h during the reaction time. The order of the separation selectivities of membranes was water-acetate > water-alcohol > water-acid. The parameters such as temperature, initial molar ratio of acid to alcohol, and catalyst concentration could be changed in order to attain the optimum of the PV-esterification coupling operation. 

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