Concentration polarization force

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. 

The apparent resistance due to the reduction in driving force from concentration polarization is generally small in most reverse osmosis systems and is neglected. The resistance can also be written in terms of a characteristic thickness and permeability... 

If the flux is perpendicular to the membrane surface, solute tends to accumulate at the membrane surface up to the solute solubility limit. This phenomenon, called concentration polarization, often results in solute leakage and in reduced driving force owing to increased osmotic pressure. 

This effect, usually known as feed-side concentration polarization, may become particularly relevant for solutes with a high sorption affinity towards the membrane, which may lead to its depletion near the membrane interface if external mass-transfer conditions are not sufficiently good to guarantee their fast transport from the bulk feed to the interface [32, 36] (see Figure 11.3). As a consequence of their depletion near the interface the driving force for transport, and the resulting partial fluxes, become lower. 

Other important considerations in process bioseparations are fluid management and membrane rejuvenation methods. Crossflow, or flow tangential to the membrane surface, induces shear at the membrane surface and helps reduce concentration polarization. This flow pattern also creates lift forces that counteract the deposition of particulate matter on the membrane resulting from permeation flow normal to the membrane surface. (See Section I.A.)... 

An effective method of controlling concentration polarization and sustaining productivity involves inducing turbulent vortices on the membrane surface to counteract the forces of solute or particle deposition. The rotating... 

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Mobile phases in NP HPLC are based on nonpolar solvents (such as hexane, heptane, etc.) with the small addition of polar modiher (i.e., methanol, ethanol). Variation of the polar modifier concentration in the mobile phase allows for the control of the analyte retention in the column. Typical polar additives are alcohols (methanol, ethanol, or isopropanol) added to the mobile phase in relatively small amounts. Since polar forces are the dominant type of interactions employed and these forces are relatively strong, even only 1 v/v% variation of the polar modiher in the mobile phase usually results in a signihcant shift in the analyte retention. 

Thus a complicated interplay of forces and fluxes emerges diffusion, conduction and hydrodynamic flows. These will be treated in sec. 4.6, but in anticipation of this treatment we shall now emphasize on the (concentration-) polarization, mentioned under 1) and discuss some of Its consequences. From the outset it is Important to realize that quantities with different length scale Interact the double layer thickness is. and remains. 0(v ). but the polarization Jield, caused by the polarization of the particle, hcis a range 0(a). 

Relatively Important is the phenomenon of dijfusiophoresis and its counterpart plug or capillary osmosis. For both the driving force is a concentration gradient, either of an electrolyte or of a non-electrolyte. Consider for instance fig. 4.40. The presence of the gradient leads to at least an (osmotic) pressure gradient p(0) around the particle in the double layer. Moreover, by specific adsorption it can also lead to concentration polarization and x" may depend on 9. In this way driving forces are established to induce the particle to move. 

Permeate flux decreases with an increase in feed concentration. This phenomenon can be attributed to the reduction of the driving force due to decrease of the vapor pressure of the feed solution and exponential increase of viscosity of the feed with increasing concentration. The DCMD flux gradually increases with an increase in temperature difference between feed and cooling water. Lagana et al. [63] reported that the viscosity of apple juice at high concentration induces severe temperature polarization. It may be noted that temperamre polarization is more important than concentration polarization, which is located mainly on the feed side. 

In DCMD, increase in flow rate increases the permeate flux. The shear force generated at high-flow rate reduces concentration polarization. Banat [64] found that the flow rate of cooling water had minimal effect on the permeate flux. Ohta [65] has shown that an increase in coolant velocity from 0.02 to 0.08 m s resulted in 1.5-fold increase in the permeate flux. In the same study, it was found that an increase in velocity of hot feed increased the flux by twofold. 

The SGMD is a temperature driven process, and it involves (a) evaporation of water at the hot feed side, (b) transport of water vapor through the pores of hydrophobic membrane, (c) collection of the permeating water vapor into an inert cold sweeping gas, and (d) condensation outside the membrane module. A decrease in driving force has been observed due to polarization effects of both temperature and concentration [80,82]. To calculate both heat and mass transfer through microporous hydrophobic membrane as well as the temperature and concentration polarization layer, the theoretical model suggested by Khayet et al. [58] can be written as... 

Aimar et al. [19] noted that in the UF of complex liquids, such as cheese whey, which contains proteins, salts and casein fragments, concentration polarization, and adsorption and cake formation play a role in flux behavior during crossflow filtration. They may induce osmotic pressure in the retentate side since the chemical potential of the solute-rich polarized layer is lower than that of the permeate, and therefore at equilibrium, a positive osmotic pressure develops in the retentate to equal that of the permeate. The smaller the solute, the greater is its contribution to the osmotic pressure of the liquid, so that in milk, lactose and the minerals have the biggest contribution to osmotic pressure. In skim milk or whey, the osmotic pressure is around 7 bar (700 kPa) and this must be exceeded in RO to commence permeation in UF, only the proteins contribute to the osmotic pressure, which increases exponentially with protein concentration [56]. In any case, a TMP greater than the osmotic pressure is required for solvent to flow from the retentate side to the permeate side. This leads to the reduction in the effectiveness of applied TMP as driving force to permeation. 

Convection Reactants can also be transferred to or from an electrode by mechanical means. Forced convection, such as stirring or agitation, tends to decrease the thickness of the diffusion layer at the surface of an electrode and thus decrease concentration polarization. Natural convection resulting from temperature or density differences also contributes to the transport of molecules and ions to and from an electrode. 

Feed-side and strip-side concentration polarization result in a reduction in the driving force for mass transfer. There is a decrease in water activity at the feed-membrane interface and an increase at the strip-membrane interface. This results in a reduction in the water vapor pressure gradient across the membrane. The feed side and strip side mass transfer co-efficients, Kf and K, respectively, can be expressed in terms of the solute diffusion co-efficient in the boundary layer, D, ... 

At present, only the crude structural concept of Fprland (1954) and conclusions made by Lumsden (1964) have described the above listed conclusions on a semi-quantitative level. The recent molecular dynamics computer simulations made by Liska et al. (1995b) and Castiglione et al. (1999) for the system NaF-AlF3 resulted in a non-realistic dependence of structure on concentration. Obviously the polarization forces of atoms, which have not been taken into account, seem to be of great importance. 

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