Pore flow membranes

Reverse osmosis models can be divided into three types irreversible thermodynamics models, such as Kedem-Katchalsky and Spiegler-Kedem models nonporous or homogeneous membrane models, such as the solution—diffusion (SD), solution—diffusion—imperfection, and extended solution—diffusion models and pore models, such as the finely porous, preferential sorption—capillary flow, and surface force—pore flow models. Charged RO membrane theories can be used to describe nanofiltration membranes, which are often negatively charged. Models such as Dorman exclusion and the... 

Equation 7 shows that as AP — oo, P — 1. The principal advantage of the solution—diffusion (SD) model is that only two parameters are needed to characterize the membrane system. As a result, this model has been widely appHed to both inorganic salt and organic solute systems. However, it has been indicated (26) that the SD model is limited to membranes having low water content. Also, for many RO membranes and solutes, particularly organics, the SD model does not adequately describe water or solute flux (27). Possible causes for these deviations include imperfections in the membrane barrier layer, pore flow (convection effects), and solute—solvent—membrane interactions. 

Ultrafiltration separations range from ca 1 to 100 nm. Above ca 50 nm, the process is often known as microfiltration. Transport through ultrafiltration and microfiltration membranes is described by pore-flow models. Below ca 2 nm, interactions between the membrane material and the solute and solvent become significant. That process, called reverse osmosis or hyperfiltration, is best described by solution—diffusion mechanisms. 

Cake layer formation builds on the membrane surface and extends outward into the feed channel. The constituents of the foulant layer may be smaller than the pores of the membrane. A gel layer can result from denaturation of some proteins. Internal pore fouling occurs inside the membrane. The size of the pore is reduced and pore flow is constricted. Internal pore fouling is usually difficult to clean. 

It is well recognized that is an important regulatory element for many cellular processes, and that the major entry pathway for Ca in many cell types is via plasma membrane Ca channels. Ca channels are functional pores in membranes. They exist in plasma membranes, transverse tubule membranes and in intracellular membranes such as the sarcoplasmic and endoplasmic reticulum. Ca channels are normally closed when opened, Ca passively flows through the chan-... 

Chemical Phase Inversion Symmetrical phase-inversion membranes (Fig. 20-67) remain the most important commercial MF membranes produced. The process produces tortuous-flow membranes. It involves preparing a concentrated solution of a polymer in a solvent. The solution is spread into a thin film, then precipitated through the slow addition of a nonsolvent, usually water, sometimes from the vapor phase. The technique is impressively versatile, capable of producing fairly uniform membranes whose pore size may be varied within broad limits. 

Calculation of Solute Separation and Product Rate. Once the pore size distribution parameters R, ou R >,2, 02, and h2 are known for a membrane and the interfacial interaction force parameters B and D are known for a given system of membrane material-solute, solute separation f can be calculated by eq 6 for any combination of these parameters. Furthermore, because the PR-to-PWP ratio (PR/PWP) can also be calculated by the surface force-pore flow model (9), PR is obtained by multiplying experimental PWP data by this ratio. 

The interfacial force constants available in the literature for many organic solutes that constitute potential pollutants in water enable one to calculate the separation of such solutes at various operating conditions by a membrane of a given average pore size and pore size distribution on the basis of the surface force-pore flow model. The product rate of the permeate solution can also be calculated. Such data further allow us to calculate the processing capacity of a membrane to achieve a preset ratio of concentration in the concentrate to concentration of the initial feed solution. 

The ground-level air sampling was performed by filtering air through 5-/li pore size membrane filter papers at flow rates of 400-700 cu. ft./min. These membrane filters are essentially 100% efficient for the atmospheric aerosols on which airborne radionuclides are attached (8). The air is drawn through four 1-sq. ft. membrane filters which are mounted on the vertical sides of a cube-shaped air sampler (10). The air pumps... 

Annular Geometry DS Devices. The leakage problems associated with a 2- xm-pore PTFE membrane tube were solved by Tanner et al. (53) by adopting the annular geometry. Air flows through the annular space of... 

The difference between the solution-diffusion and pore-flow mechanisms lies in the relative size and permanence of the pores. For membranes in which transport is best described by the solution-diffusion model and Fick s law, the free-volume elements (pores) in the membrane are tiny spaces between polymer chains caused by thermal motion of the polymer molecules. These volume elements appear and disappear on about the same timescale as the motions of the permeants traversing the membrane. On the other hand, for a membrane in which transport is best described by a pore-flow model and Darcy s law, the free-volume elements (pores) are relatively large and fixed, do not fluctuate in position or volume on the timescale of permeant motion, and are connected to one another. The larger the individual free volume elements (pores), the more likely they are to be present long enough to produce pore-flow characteristics in the membrane. As a rough rule of thumb, the transition between transient (solution-diffusion) and permanent (pore-flow) pores is in the range 5-10 A diameter. 

Ultrafiltration, microfiltration and microporous Knudsen-flow gas separation membranes are all clearly microporous, and transport occurs by pore flow. 

Reactions in flow-through membrane systems ("pore flow-through reactors")... 

Because the mechanisms are based on pore flow and size exclusion (cf. Section 2.2), the polymer material itself does not have direct influence on flux and selectivity in U F. The U F membranes usually have an integrally asymmetric structure, obtained via the NIPS technique, and the porous selective barrier (pore size and thickness ranges are 2-50 nm and 0.1-1 (im, respectively) is located at the top (skin) surface supported by a macroporous sublayer (cf. Section 2.4.2). However, the pore-size distribution in that porous barrier is typically rather broad (Figure 2.6), resulting in limited size selectivity. 

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 ... 

A high electroosmotic flow through the stationary-phase particles may be created when the appropriate conditions are provided. This pore flow has important consequences for the chromatographic efficiency that may be obtained in CEC. From plate height theories on (pressure-driven) techniques such as perfusion and membrane chromatography, it is known that perfusive transport may strongly enhance the stationary-phase mass transfer kinetics [30-34], It is emphasised... 

Droplet sizes and important proeess parameters The properties of the membrane are very important in this process. The membrane should have a relatively narrow pore size distribution, just as with cross-flow membrane emulsification, and it should be wetted by the phase that should be the continuous phase. 

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