Concentration polarization layer

Dynamic membranes are concentration—polarization layers formed in situ from the ultrafiltration of coUoidal material analogous to a precoat in conventional filter operations. Hydrous zirconia has been thoroughly investigated other materials include bentonite, poly(acryhc acid), and films deposited from the materials to be separated (18). 

P. Dejmek, "PermeabiHty of the Concentration Polarization Layer in Ultrafiltration of Macro Molecules," Proceedings of the International Symposium, Separation Processes by Membranes, Paris, Mar. 13—14,1975. 

Thin concentration polarization layer. Short tubes, concentration profile not fully developed. Use arithmetic concentration difference. 

However, in the case of a concentration polarization layer, is not zero. 

Figure 14.4 Schematic of the membrane, cake (gel) and concentration-polarization layer with their parameters.

Figure 14.3 also shows the concentration-polarization layer that also forms during the filtration. Due to it, there is a backdiffusion of the retained compound that has higher concentration on the membrane surface. These phenomena can also decrease the efficiency ofthe filtration. This effect should also be taken into account during the mathematical modeling of the transport processes of the membrane bioreactor, as will be discussed later. 

The formation of a cake layer can be neglected (e.g., biocatalytic reaction without macromolecules) in this case the concentration-polarization layer can also exist ... 

Both the concentration-polarization layer and membrane fouling are present (filtration in presence of macromolecules, proteins, cells in the liquid phase). 

If one wants to take into account all three mass-transfer resistances, the mass-balance equation [Equation 14.16] should be given for every layer. From that one can obtain the solution for every layer (i = m for membrane layer, i = g for gel layer, the concentration-polarization layer has no index according to Figure 14.4) ... 

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... 

I. Tubes, laminar, RO systems er Use arithmetic concentration difference. Thin concentration polarization layer, not fully developed. Nr, < 2000, L = length tube. [40]... 

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. 

Physical displacement of the concentration polarization layer Gas slugs can penetrate into the concentration polarization layer and displace the upper part of it. 

In a key study, Nikolova and Islam [29] reported that the decisive factor in flux decline was the adsorption resistance. With the development of a concentration polarization layer, the adsorbed layer resistance at the membrane wall increased linearly as a function of the solute concentration at the wall. They described the flux by the following relationship ... 

Pope J.M., Yao S., and Fane A.G., Quantitative measurements of the concentration polarization layer thickness in membrane filtration of oil-water emulsions using NMR micro-imaging. Journal of Membrane Science 118 1996 247-257. 

Cowman, L.M. and Ethier, C.R., Concentration and concentration gradient measurements in an ultrafiltration concentration polarization layer. Part I A laser-based refractometric experimental technique. Journal of Membrane Science 131 1997 95-105. 

During TFF, species retained by the membrane form a concentrated boundary layer, called concentration polarization layer, on the surface of the membrane that creates a resistance to the filtrate flow and reduces flux [11], The effect of polarization is a flux—usually called limiting flux—that does not change with TMP above a critical pressure as shown in Figure 14.2. 

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... 

Gekas, V. and Hallstrom, B. Mass transfer in the membrane concentration polarization layer under turbulent cross flow I. Critical literature review and adaptation of existing Sherwood correlations to membrane operations, J. Membr. Sci., 30, 153, 1987. 

The concentration polarization model, which is based on the stagnant fihn theory, was developed to describe the back-diffusion phenomenon during filtration of macromolecules. In this model, the rejection of particles gives rise to a thin fouling layer on the membrane surface, overlaid by a concentration polarization layer in which particles diffuse away from the membrane surface, where solute concentration is high, to the bulk phase, where the solute concentration is low [158]. At steady state, convection of particles toward the membrane surface is balanced by diffusion away from the membrane. Thus, integrating the onedimensional convective-diffusion equation across the concentration polarization layer gives... 

Jo is the initial flux at f = 0, which is an indication of the resistance to solvent transport by the membrane as well as the concentration polarization layer formed on the membrane by the proteins b is the indicator of the rate of fouling during long-term operation, or the true fouling effects, due to specific membrane-solute interactions... 

Field et al. [157] introduced the concept of critical flux in membrane filtration. They proposed that upon start-up, there exists a flux below which a decline of flux with time does not occur. Although a concentration polarization layer is present, solid deposition on the membrane that gives rise to cake layer formation does not take place, so that a nonfoufing or cake-free operation is achieved. This flux is the critical flux and it may either be in strong form, in which flux is identical to the clean water flux at the same TMP, or in weak form, in which flux varies linearly with TMP but the slope of the fine differs from that of clean water [6,157,161]. 

Concentration polarization Concentration polarization is important for membrane operation and modeling. It represents increased concentrations of rejected solutes near the membrane surface. The concentration-polarization layer is described with the classic film model [19]. 

---