Membrane flux concentration

Salt flux across a membrane is due to effects coupled to water transport, usually negligible, and diffusion across the membrane. Eq. (22-60) describes the basic diffusion equation for solute passage. It is independent of pressure, so as AP — AH 0, rejection 0. This important factor is due to the kinetic nature of the separation. Salt passage through the membrane is concentration dependent. Water passage is dependent on P — H. Therefore, when the membrane is operating near the osmotic pressure of the feed, the salt passage is not diluted by much permeate water. 

That is, below this concentration the membrane flux is 0.04 m/h. 

Flux Decline Plugging, Fouling, Polarization Membranes operated in NFF mode tend to show a steady flux decline while those operated in TFF mode tend to show a more stable flux after a short initial decline. Irreversible flux decline can occur by membrane compression or retentate channel spacers blinding off the membrane. Flux decline by fouling mechanisms (molecular adsorption, precipitation on the membrane surface, entrapment within the membrane structure) are amenable to chemical cleaning between batches. Flux decline amenable to mechanical disturbance (such as TFF operation) includes the formation of a secondary structure on the membrane surface such as a static cake or a fluid region of high component concentration called a polarization layer. 

Flux depends on the product of membrane permeability of the solute times the concentration of the solute (summed over all charge state forms) at the water side of the donor surface of the membrane. This concentration ideally may be equal to the dose of the drug, unless the dose exceeds the solubility limit at the pH considered, in... 

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. 

Figure 3 Diffusion across a membrane. The solute molecules diffuse from the well-mixed higher concentration cY to the well-mixed lower concentration c2. Equilibrium is assumed at the interfaces of membrane and solutions. The concentrations on both sides of the membrane are kept constant. At steady state, the concentrations cm remain constant at all points in the membrane. The concentration profile inside the membrane is linear, and the flux is constant.

Permeabilities measured for pure gases can serve as a rough guide for selection of membrane materials. For design, data must be obtained on gas mixtures, where selectivities are often found to be much lower than those calculated from pure-component measurements. This effect is often due to plasticisation of the membrane by sorption of the most soluble component of the gas. This allows easier penetration by the less-permeable components. The problem of concentration polarisation, which is often encountered in small-scale flow tests, may also be responsible. Concentration polarisation results when the retention time of the gas in contact with the membrane is long. This allows substantial depletion of the most permeable component on the feed side of the membrane. The membrane-surface concentration of that component, and therefore its flux through the membrane, decreases. 

Figure 8.8. Dependence of membrane flux J on (a) Applied pressure difference AP, (b) Feed solute concentration Cf, (c) Cross-flow velocity (u) for ultrafiltration...

In trials at different feedwater concentrations, the FT-30 membrane showed single-pass seawater desalting capabilities at up to 6.0 percent synthetic seawater. Basically, any combination of pressure and brine concentration at room temperature that gave a membrane flux of 15 gfd also resulted in a 99 percent level of salt rejection. 

Fig. 2.1. Zero-current ion fluxes in the ion-selective membrane. Left (A) Concentrated inner solution induces coextraction of electrolyte into the membrane increasing the primary ion-ionophore concentration within the membrane. Consequently, primary ions leach into the sample increasing the activity of primary ions at the membrane/sample phase boundary. (B) Diluted inner solution and ion exchange at the inner solution side decreases the concentration of the complex within the membrane. Primary ions are siphoned-off from the sample, and their activity at the membrane/sample phase boundary is significantly decreased. (C) Ideal case of perfectly symmetric sample and inner solution resulting in no membrane fluxes. Note that fluxes of other species (counterions or interfering ions) are not shown for clarity. Right potential responses for each case. Ideal LOD is defined by the Nikolskii-Eisenman equation (Y Kj°jaj) and is obtained only in the ideal case (C). Fluxes in either direction significantly affect the LOD.

Figure 2.3 depicts comparison of the theoretical predictions and experimental observations of the potential response of a silver-selective electrode based on o-xylylenebis(/V,/V-diisobutyldithiocarbamate. Figure 2.3A demonstrates the potential response of an electrode that utilizes a classical experimental setup, i.e. concentrated inner solution (open circles) compared with theoretical prediction based on Eq. (2.2) (full line). The experimentally observed LOD of 10 7M corresponds poorly with the optimistic theoretical prediction of 4 x 10 15M. On the other hand, after optimization of the inner solution [19], the potential response is extended (Fig. 2.3B closed circles) and the detection limit is improved by almost three orders of magnitude to 3 x 10 10M. At the same time, an excellent correspondence between experimental observation and theoretical prediction was achieved by employing the extended Nikolskii-Eisenman equation (Eq. (2.4)—full line). This demonstrates the essential role of membrane fluxes in the potential response of ion-selective electrodes. (For all experimental and calculations parameters see the figure caption.)... 

In these experiments, the measured helium flux through the membrane was less than the flux predicted on the basis of the average bulk concentrations. Consequently, the helium permeability coefficients calculated from observed membrane flux and the bulk partial pressures are lower than the pure gas values obtained by the membrane supplier or independently by us. At the same time, observed nitrogen coefficients are higher than predicted. 

The concentration terms in Equations (2.67) and (2.72) can be substituted into Equation (2.13) (Fick s law) to obtain an expression for the membrane flux. 

Figure 4.5 The effect of changes in boundary layer thickness S, membrane enrichment E0, membrane flux Jv, and solute diffusion D, on concentration gradients in the stagnant boundary layer...

The final parameter in Equation (4.9) that determines the value of the concentration polarization modulus is the diffusion coefficient A of the solute away from the membrane surface. The size of the solute diffusion coefficient explains why concentration polarization is a greater factor in ultrafiltration than in reverse osmosis. Ultrafiltration membrane fluxes are usually higher than reverse osmosis fluxes, but the difference between the values of the diffusion coefficients of the retained solutes is more important. In reverse osmosis the solutes are dissolved salts, whereas in ultrafiltration the solutes are colloids and macromolecules. The diffusion coefficients of these high-molecular-weight components are about 100 times smaller than those of salts. 

The salt concentration on the permeate side of the membrane can be related to the membrane fluxes by the expression... 

Studies of concentration polarization such as those illustrated in Figures 6.8-6.10 are usually performed during the first few hours of the membrane use. Compaction of the secondary membrane layer has then only just begun, and membrane fluxes are often high. Fluxes obtained in industrial processes, which must operate for days or weeks without cleaning, are usually much lower. 

The most important effect of concentration polarization is to reduce the membrane flux, but it also affects the retention of macromolecules. Retention data obtained with dextran polysaccharides at various pressures are shown in Figure 6.12 [17]. Because these are stirred batch cell data, the effect of increased concentration polarization with increased applied pressure is particularly marked. A similar drop of retention with pressure is observed with flow-through cells, but the effect is less because concentration polarization is better controlled in such cells. With macromolecular solutions, the concentration of retained macromolecules at the membrane surface increases with increased pressure, so permeation of the macromolecules also increases, lowering rejection. The effect is particularly noticeable at low pressures, under which conditions increasing the applied pressure produces the largest increase in flux, and hence concentration polarization, at the membrane surface. At high pressure, the change in flux with... 

Carrier facilitated transport involves a combination of chemical reaction and diffusion. One way to model the process is to calculate the equilibrium between the various species in the membrane phase and to link them by the appropriate rate expressions to the species in adjacent feed and permeate solutions. An expression for the concentration gradient of each species across the membrane is then calculated and can be solved to give the membrane flux in terms of the diffusion coefficients, the distribution coefficients, and the rate constants for all the species involved in the process [41,42], Unfortunately, the resulting expressions are too complex to be widely used. 

A second characteristic of coupled transport membranes is that the membrane flux usually increases with increasing metal concentration in the feed solution, but is usually independent of the metal concentration in the product solution. This behavior follows from the flux Equations (11.6) and (11.8). In typical coupled... 

Membrane distillation offers a number of advantages over alternative pressure-driven processes such as reverse osmosis. Because the process is driven by temperature gradients, low-grade waste heat can be used and expensive high-pressure pumps are not required. Membrane fluxes are comparable to reverse osmosis fluxes, so membrane areas are not excessive. Finally, the process is still effective with slightly reduced fluxes even for very concentrated solutions. This is an advantage over reverse osmosis, in which the feed solution osmotic pressure places a practical limit on the concentration of a salt in the feed solution to be processed. 

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