Gel-polarization model

A 1% by weight albumin (Mol weight 65000 g/mol) solution with a flow rate of 360 liter/hr must be concentrated to 10% by weight in a single-stage process. The gelation concentration of albumin is 200 kg/w . The membranes used do completely retain the albumin. Calculate the required membrane area at a cross-flow velocity of 0,5,1.0 and 5.0 m/s, respectively. The flux can be described by the gel polarization model while the mass transfer coefficient can be described as... 

It has been observed that particle flux expressions developed based on shear-induced particle diffusivity describe the observed solvent flux through a microflltration membrane much better than those based on Brownian diffusivity of a particle. For the following system properties, determine the ratio of the solvent fluxes based on shear-induced particle diffusivity and Brownian diffusivity. You should employ the particle volume fraction based solvent flux expression based on the gel polarization model used in ultrafiltration (equation (7.2.72)) ... 

The mechanism of such UF can be explained by the following concentration polarization model (cf. Figure 8.3) [3, 4]. In the early stages of UF, the thickness of the gel layer increases with time. However, after the steady state has been reached, the solute diffuses back from the gel layer surface to the bulk of solution this... 

As described above, the initial cause of membrane fouling is concentration polarization, which results in deposition of a layer of material on the membrane surface. The phenomenon of concentration polarization is described in detail in Chapter 4. In ultrafiltration, solvent and macromolecular or colloidal solutes are carried towards the membrane surface by the solution permeating the membrane. Solvent molecules permeate the membrane, but the larger solutes accumulate at the membrane surface. Because of their size, the rate at which the rejected solute molecules can diffuse from the membrane surface back to the bulk solution is relatively low. Thus their concentration at the membrane surface is typically 20-50 times higher than the feed solution concentration. These solutes become so concentrated at the membrane surface that a gel layer is formed and becomes a secondary barrier to flow through the membrane. The formation of this gel layer on the membrane surface is illustrated in Figure 6.6. The gel layer model was developed at the Amicon Corporation in the 1960s [8],... 

On the other hand, in support of the hypothesis that the polarization of water might play an important role in the hydration force between silica surfaces, one should note that the polarization model predicts an increase in the hydration force at higher ionic strength [30], which can be indeed observed in Fig. 5, by comparing the experiments at c =0.01 M (pH=3) with those at cE= 1 M. While both the gel-induced steric repulsion and the polarization model are consistent with the present experimental data, a final decision about the microscopic origin of the hydration force in the case of silica should be postponed until more accurate data or additional information regarding the nature of the silica surface will become available. 

A permeate flux declines in the presence of solute due to membrane fouling. A decrease in flux is a result of several phenomenons including adsorption of macromolecules to membrane surface involving pore blocking, concentration polarization, and formation of a gel-like cake layer within the membrane pores (50). Several models have been used to describe solute fouling, among them are hydraulic resistance, osmotic pressure, gel polarization, and film models (51,52). 

Blatt et al.(29) developed what has become known as the "gel polarization" theory for ultrafiltration, in which the amount of macromolecular material in the fouling layer is controlled by its back-diffusion rate into the feed stream. The gradual decline in flux observed in some practical systems was explained in terms of an irreversible consolidation of the gel layer with time, leading to a reduction in the layer s permeability. Kimura and Nakao (,1) used Blatt s approach to model the fouling of reverse osmosis... 

It was found that the gel layer concentration is not constant, but variable, which can be predicted by using the ordinary concentration polarization model with appropriate mass transfer coefficient. Also this concentration has a particular relation with the gel layer resistance. Using this relation the flux through the membrane can be calculated for the case of gel layer formation. 

The mechanism of such UF can be explained by the following concentration polarization model (cf. Figure 8.3) [3,4], In the early stages of UF, the thickness of the gel layer increases with time. However, after the steady state has been reached, the solute diffuses back from the gel layer surface to the bulk of solution this occurs due to the difference between the saturated solute concentration at the gel layer surface and the solute concentration in the bulk of solution. A dynamic balance is attained, when the rate of back-diffusion of the solute has become equal to the rate of solute carried by the bulk flow of solution towards the membrane. This rate should be equal to the filtrate flux, and consequently the thickness of the gel layer should become constant. Thus, the following dimensionally consistent equation should hold ... 

Denisov, G.A. 1994. Theory of concentration polarization in cross-flow ultrafiltration Gel-layer model and osmotic-pressure model. J Membr Sci. 91 173-187. 

The use of supercritical carbon dioxide for enzymatic reactions is limited by the difficulty of dissolving relatively polar substrates. To increase the solubility of polar compounds, Castillo et al. [84] complexed the substrate with phenylboronic acid or immobilized polar reactants on silica gel. As model reaction the esterification of oleic acid with... 

Polarization in the point dipole model occurs not at the surface of the particle but within it. If dipoles form in particles, an interaction between dipoles occurs more or less even if they are in a solid-like matrix [48], The interaction becomes strong as the dipoles come close to each other. When the particles contact each other along the applied electric field, the interaction reaches a maximum. A balance between the particle interaction and the elastic modulus of the solid matrix is important for the ER effect to transpire. If the elastic modulus of the solid-like matrix is larger than the sum of the interactions of the particles, the ER effect may not be observed macroscopically. Therefore, the matrix should be a soft material such as gels or elastomers to produce the ER effect. 

Table III describes the effect of solvent change on the lignin model compounds. None of the model compounds exhibited evidence of association all had unimodal elution in the different solvents. The Kp of the fully derivatized model compounds tended to increase as solvent polarity was increased, as had that of the polymer standards. As these are fully derivatized, relatively small molecules, the possibility for size change through interaction with the solvents is small. Increasing affinity for the column gel as the solvent polarity increased is the most probable explanation for their greater retention.

In recent years the Coal Research Laboratory has been investigating the kinetics and isotherm behavior of methanol sorption on coal (6, 7, 10) along with the sorption of other vapors on coal (6) and of polar vapors on swelling gels (9, 10). Methanol sorption was shown to be reversible on coal, and its sorption behavior supports the model of coal as a gel or mixture of gels in its physical structure. All indications (I, 6, 7) are that its interaction is with specific and a fixed number of sites for a particular coal sample. Although the sorption of methanol is reversible, coal exhibits sorption behavior which is interpreted in terms of an irreversible swelling of the coal gel upon initial exposure to methanol vapor. As a result of these studies, an isotherm and experimental rate equation for the sorption and desorption were derived that fit the observed data. The isotherm derived for methanol sorption on coal was ... 

The model described above of incorporation places the relatively polar carbonyl groups of 2-105 molecules at or near an aqueous interface, but allows the carbonyl groups of s-105 which are no longer than a KP or KS molecule to be buried in the hydrophobic portion of a gel layer. 

Figure 5 A schematic model of the formation of lipid gel phase by hydration of the polar groups in crystalline regions of emulsifiers, d = interplanar Bragg spacing d, = thickness of lipid bilayer dw = thickness of water iayer. Redrawn from reference 15, courtesy of Marcel Dekker Inc.

The combination of X-ray and DSC has also been used to explore the effects of pindolol on model membranes. Changes in thermodynamic and structural parameters were observed. Depending on the temperature pindolol induced either a interdigitat-ed gel phase or, at high temperature, a lamellar phase. The data would seem to indicate that the non-polar moiety of pindolol penetrates deep into the bilayer interior while the hydrocarbon chains have to adopt a different conformation [156],... 

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