Concentration polarization velocity

Graphical solutions for concentration polarization. Uniform velocity through walls. 

This deviation may be attributable to concentration polarization caused by a decrease in the flow velocity of the feed water in the above conditions. 

When the voltage is critical, regime b), there is no concentration polarization because the electrophoretic transport is equal to the convective transport. Any build up of species on the membrane will be dissipated due to diffusion driven by the concentration difference. In this regime, increasing the tangential velocity is expected to have no influence on the flux because fluid shear can only improve the transport of particles down a concentration gradient. In this case, there is no concentration gradient. 

Equation 8.7 [6] was obtained to correlate the experimental data on membrane plasmapheresis, which is the MF of blood to separate the blood cells from the plasma. The filtrate flux is affected by the blood velocity along the membrane. Since, in plasmapheresis, all of the protein molecules and other solutes will pass into the filtrate, the concentration polarization of protein molecules is inconceivable. In fact, the hydraulic pressure difference in plasmapheresis is smaller than that in the UF of plasma. Thus, the concentration polarization of red blood cells was assumed in deriving Equation 8.7. The shape of the red blood cell is approximately discoid, with a concave area at the central portion, the cells being approximately 1-2.5 pm thick and 7-8.5 pm in diameter. Thus, a value of r (= 0.000257 cm), the radius of the sphere with a volume equal to that of a red blood cell, was used in Equation 8.7. 

Figure 4.2 Fluid flow velocity through the channel of a membrane module is nonuniform, being fastest in the middle and essentially zero adjacent to the membrane. In the film model of concentration polarization, concentration gradients formed due to transport through the membrane are assumed to be confined to the laminar boundary layer...

The effect of concentration polarization on specific membrane processes is discussed in the individual application chapters. However, a brief comparison of the magnitude of concentration polarization is given in Table 4.1 for processes involving liquid feed solutions. The key simplifying assumption is that the boundary layer thickness is 20 p.m for all processes. This boundary layer thickness is typical of values calculated for separation of solutions with spiral-wound modules in reverse osmosis, pervaporation, and ultrafiltration. Tubular, plate-and-ffame, and bore-side feed hollow fiber modules, because of their better flow velocities, generally have lower calculated boundary layer thicknesses. Hollow fiber modules with shell-side feed generally have larger calculated boundary layer thicknesses because of their poor fluid flow patterns. 

Concentration polarization plays a dominant role in the selection of membrane materials, operating conditions, and system design in the pervaporation of VOCs from water. Selection of the appropriate membrane thickness and permeate pressure is discussed in detail elsewhere [50], In general, concentration polarization effects are not a major problem for VOCs with separation factors less than 100-200. With solutions containing such VOCs, very high feed velocities through... 

For treating water containing VOCs with separation factors of more than 500, for which concentration polarization is a serious problem, feed-and-bleed systems similar to those described in the chapter on ultrafiltration can be used. For small feed volumes a batch process as illustrated in Figure 9.16 is more suitable. In a batch system, feed solution is accumulated in a surge tank. A portion of this solution is then transferred to the feed tank and circulated at high velocity through the pervaporation modules until the VOC concentration reaches the desired level. At this time, the treated water is removed from the feed tank, the tank is loaded with a new batch of untreated solution, and the cycle is repeated. 

The limiting current density is determined by concentration-polarization effects at the membrane surface in the diluate containing compartment that in turn is determined by the diluate concentration, the compartment design, and the feed-flow velocity. Concentration polarization in electrodialysis is also the result of differences in the transport number of ions in the solution and in the membrane. The transport number of a counterion in an ion-exchange membrane is generally close to 1 and that of the co ion close to 0, while in the solution the transport numbers of anion and cations are not very different. 

The value of the concentration modulus depends on the convective velocity and the mass-transfer coefficient of the concentration boundary layer (D/ i) that means that on the membrane structure and the hydrodynamic conditions. If the retention coefficient is equal to 1, then c /ch = exp(Pe). The larger convective velocity (or smaller diffusion coefficient) causes higher concentration polarization on the membrane interface. 

The basic hydrodynamic equations are the Navier-Stokes equations [51]. These equations are listed in their general form in Appendix C. The combination of these equations, for example, with Darcy s law, the fluid flow in crossflow filtration in tubular or capillary membranes can be described [52]. In most cases of enzyme or microbial membrane reactors where enzymes are immobilized within the membrane matrix or in a thin layer at the matrix/shell interface or the live cells are inoculated into the shell, a cake layer is not formed on the membrane surface. The concentration-polarization layer can exist but this layer does not alter the value of the convective velocity. Several studies have modeled the convective-flow profiles in a hollow-fiber and/or flat-sheet membranes [11, 35, 44, 53-56]. Bruining [44] gives a general description of flows and pressures for enzyme membrane reactor. Three main modes... 

The transfer of reactants from the bulk solution to the electrode interface and in the reverse direction is an ordinary feature of all electrode reactions. As the oxidation-reduction reactions advance, the accessibility of the reactant species at the electrode/electrolyte interface changes. This is because of the concentration polarization effect, that is, r c, which arises due to the limited mass transport capabilities of the reactant species toward and from the electrode surface, to substitute the reacted material to sustain the reaction [6,8,10,66,124], This overpotential is usually established by the velocity of reactants flowing toward the electrolyte through the electrodes and the velocity of products flowing away from the electrolyte. The concentration overpotential, r c, due to mass transport restrictions, can be expressed as... 

Scaling is exacerbated by high membrane flux and low cross-flow velocity, in the same manner as membrane fouling is increased. Higher flux brings more solutes into the concentration polarization boundary layer quicker. If the concentration of the solutes in the boundary layer reaches saturation, these solutes will scale the membrane. Lower cross-flow velocity corresponds to a thicker boundary layer. This increases the residence time for solute within the boundary layer, increasing the chance that saturation will be achieved and scale will form. 

Advantages Minimal filtration pretreatment Easier membrane cleaning Higher surface area means more filtration area per fiber True cross flow velocity minimizes concentration polarization and membrane fouling When no air is utilized for backwashing the less fiber movement leads to breakage of fewer fibers Can be created with a variety of inside fiber diamters... 

J. Tubes and parallel plates, laminar RO Graphical solutions for concentration polarization. Uniform velocity through walls. [T] [137]... 

Recovery of catalyst from converted oil. Another way to process the residues is to add hydrogen to effect hydroconversion which avoids the formation of a large quantity of asphalt Solid catalyst is formed afterward by reaction. Membrane filtration is used to separate the converted oil from the catalyst This makes it possible to partially recycle the catalyst to the reactor. Alumina and zirconia membranes with pore diameters ranging from 30 to 600 nm have been tested for this application. The membrane with a pore diameter of 30 nm yields a stable flux and a catalyst retention better than 98% [Deschamps et al., 1989). Concentration polarization is significant and requires a high crossflow velocity and temperature to overcome it. 

The Re number accounts for both hydrodynamics and fluid characteristics, i.e., on the one hand cross-flow velocity, v, and hydraulic diameter, in the module on the other hand dynamic viscosity, tj, and mass density, p, of the fluid. Normally, Re > 2100 guarantees a turbulent flow in the module and a minimum thickness for the concentration polarization layer. A small value of coefficient a means that v has a weak influence on J, so that a weak fluid velocity or even a dead-end filtration mode can be used. On the contrary, when the value of a is high (>0.5), a cross-flow filtration mode with a high-fluid velocity is necessary. 

Benefit of bubbling becomes more significant when polarization is more serve, for example, at high TMP(or flux), a low liquid velocity, and a high feed concentration, due to the disruption effect of bubbling on concentration polarization. 

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. 

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