Polarization and Osmotic Pressure

Considering a concentration average of the pure solvent values and assuming no viscous selectivity and a Hnear pressure profile inside the membrane the following relation using these two pure solvent parameters is obtained [34] to describe the total flux of a binary mixture 

A quaternary ammonium salt, tetraoctylammonium bromide (TOABr) and doco-sane were used as solutes and toluene was used as the solvent. The membrane used in this study was again the solvent-resistant polyimide membrane, STAR-MEM 122. A dual-cell crossflow filtration rig, similar to the one described in Section 4.3.1 was used in all the experiments with an effective membrane area of 78 cm. The stage cut was between 0.01 and 0.3% over the whole concentration and pressure range. Ideal mixing is assumed throughout the system. 

Two sets of experiments were performed. One set of experiments with toluene solutions of TOABr was performed to study the influence of the feed flow rate (crossflow velocity) on the permeate flux at a constant pressure of 30 bar. 

The other set studied the influence of solute concentration and applied pressure on the permeate flux and solute rejection. A wide range of experiments was performed using toluene solutions of docosane (MW=310 Da) and TOABr (MW=546 Da) using a range of pressures 0-50 bar, and concentrations 0-20 wt% (0-0.35 M, 0-0.04 mole fraction) for TOABr in toluene and 0-20 wt% (0-0.67 M, 0-0.09 mole fraction) for docosane in toluene. The construction of the crossflow rig made it difficult for exactly the same flow rate to be maintained through the cells at different pressures, however, it was always kept in the range of 40-80 L h in one of the cells, 120-150 L h in the other. 

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Both the concentration polarization and osmotic pressure descriptions can be applied to polymer solutions that form well-defined gels at high concentrations. In a gel the thermodynamic osmotic pressure results from the solvent-mediated interactions between the randomly moving gel monomers, and this pressure tends to swell the gel. Both descriptions have been calculated in some detail for gelling macromolecular solutions and shown to produce similar behaviors (Probstein et al. 1979, Trettin and Doshi 1981). Actually a relatively simple argument shows that the two approaches are equivalent if the diffusion... 

Almost all reported OSN data have been obtained at the lab scale and with dilute solutions (<1 wt% solute in solvent), whereas in actual appHcations, solutes will be more concentrated (>5 wt%). Under these conditions, concentration polarization and osmotic pressure may contribute to the solvent flux, as they do in well-studied aqueous systems. There are several studies on concentration polarization in aqueous systems, mainly concerning ultrafiltration [38-42]. We as-... 

L.G. Peeva, E. Gibbins, S.S. Luthra, L.S. White, R.P. Stateva, A.G. Livingston, Effect of concentration polarization and osmotic pressure on flux in organic solvent nanofiltration, J. Memhr. 

The effect of feed concentration on flux and rejection is depicted in Fig. 4.17. As expected, a rise in the feed concentration resulted in a decrease in flux and percentage of impurity rejection. This is due to increase in concentration polarization and osmotic pressure at the membrane surface. Higher solute concentrations at the feed side induce an osmotic pressure gradient, which... 

Equation (20-80) requires a mass transfer coefficient k to calculate Cu, and a relation between protein concentration and osmotic pressure. Pure water flux obtained from a plot of flux versus pressure is used to calculate membrane resistance (t ically small). The LMH/psi slope is referred to as the NWP (normal water permeability). The membrane plus fouling resistances are determined after removing the reversible polarization layer through a buffer flush. To illustrate the components of the osmotic flux model. Fig. 20-63 shows flux versus TMP curves corresponding to just the membrane in buffer (Rfouimg = 0, = 0),... 

Danckwerts P.V., Significance of liquid film coefficients in gas absorption. Industrial Engineering and Chemistry 43 1951 460-1470. Denisov C.A., Theory of concentration polarization in cross-flow ultrafiltration Cel-layer model and osmotic-pressure model. Journal of Membrane Science 91 1994 173-187. 

Gel polarized ultrafiltration was recently analyzed for cross flow and unstirred batch cell systems by Trettin and Doshi (1980 a,b). We have shown in these papers that the widely used film theory does not predict the limiting flux accurately. The objective of this paper is to derive an expression for the permeate flux when the pressure independent ultrafiltration of macro-molecular solutions is osmotic pressure limited. We will also attempt to distinguish between gel and osmotic pressure limited ultrafiltration of macromolecular solutions. 

It is theoretically shown for the unstirred batch cell that, in limiting cases, the assumption of constant wall (membrane) concentration with respect to time may be made even in the absence of gel formation. Although the assumption of constant wall concentration is similar in both gel and osmotic pressure limited ultrafiltration, it is important to recognize that in gel polarized ultrafiltration, wall concentration is also pressure independent since it corresponds to the solute solubility limit. This is not the case in osmotic pressure limited ultrafiltration... 

A number of solution properties differ from the properties of pure solvent. Ionic or highly polar solutes that dissociate in solution result in solutions that conduct electricity. Colligative solution properties depend on the concentration of solute particles in the solution and include vapor pressure, boiling point, freezing point, and osmotic pressure. 

As a consequence of the passage of solvent, say, water through the membrane, the solute is carried out to the membrane surface. Hence, the concentration at the membrane surface tends to be higher than in the bulk of the liquid. This phenomenon is called concentration polarization. Due to the concentration polarization, the osmotic pressure increases because of the increase in solute concentration. Hence, the solvent flux is decreased because the effective driving pressure is reduced based on equation (4.136). Another effect is the increase in the solute concentration in the product side for leaky membranes as the flux of the solute across the membrane is proportional to the difference in solute concentration of both sides. Therefore, the concentration distribution of the solute inside the reverse osmosis channel, that is, concentration polarization, influences its performance and has been discussed in the following section. 

In accordance with observed data, this model shows that water flux increases linearly with applied pressure AP, decreases with higher salt concentration through its impact on osmotic pressure Jt, increases with a smaller membrane thickness I, and increases with temperature through the temperature dependence of the water permeability P . The model also demonstrates that the solute or salt flux J, increases linearly with applied pressure AP, increases with higher salt concentration c , increases with a smaller membrane thickness I, and increases with temperature through the temperature dependence of the solute permeability Pj. Polarization, as described early in this section, causes the wall concentration c to exceed the bulk concentration ci,. 

A phenomenon that is particularly important in the design of reverse osmosis units is that of concentration polarization. This occurs on the feed-side (concentrated side) of the reverse osmosis membrane. Because the solute cannot permeate through the membrane, the concentration of the solute in the liquid adjacent to the surface of the membrane is greater than that in the bulk of the fluid. This difference causes mass transfer of solute by diffusion from the membrane surface back to the bulk liquid. The rate of diffusion back into the bulk fluid depends on the mass transfer coefficient for the boundary layer on feed-side. Concentration polarization is the ratio of the solute concentration at the membrane surface to the solute concentration in the bulk stream. Concentration polarization causes the flux of solvent to decrease since the osmotic pressure increases as the boundary layer concentration increases and the overall driving force (AP - An) decreases. 

As a result of Internal concentration polarization, the effective osmotic pressure difference across the membrane can be significantly below the osmotic pressure difference between the bulk solutions. The effective osmotic pressure can be calculated from the salt permeation coefficient and the salt diffusion resistance in the porous membrane substrate. The highest power output for a membrane is obtained at an operating pressure equal to about one half of the effective osmotic pressure. 

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