Membrane Boundary Layer Concentrations

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. 

Equation (4.9) shows the factors that determine the magnitude of concentration polarization, namely the boundary layer thickness S, the membrane enrichment E0, the volume flux through the membrane. / , and the diffusion coefficient of the solute in the boundary layer fluid >, The effect of changes in each of these parameters on the concentration gradients formed in the membrane boundary layer are illustrated graphically in Figure 4.5 and discussed briefly below. 

In Equation (4.9) the balance between convective transport and diffusive transport in the membrane boundary layer is characterized by the term JvS/Di. This dimensionless number represents the ratio of the convective transport Jv and diffusive transport Dj/8 and is commonly called the Peclet number. When the Peclet number is large (./ 5>> D,/S), the convective flux through the membrane cannot easily be balanced by diffusion in the boundary layer, and the concentration polarization modulus is large. When the Peclet number is small (Jv <5C D,/8), convection is easily balanced by diffusion in the boundary layer, and the concentration polarization modulus is close to unity. 

Enhancement of transmembrane flux has been shown in OMD of grape juice pretreated by UF [131]. The increase in flux has been attributed to a reduction in the viscosity of the concentrated juice-membrane boundary layer as the result of removal of high-molecular weight biopolymers present in juice. UF is a powerful method for removing natural polymers (polysaccharides, proteins) from fruit and vegetable juices. Lukanin et al. [12] have improved the concept of (UF + OMD), by enzymatic pretreatment of the apple juice prior to the UF step. Introduction of an additional enzymatic deproteinization step with the pectinase/amylase treatment of apple juice followed by UF has yielded minimal biopolymer content. Such a treatment is found to enhance transmembrane flux during concentration of clarified juice by MD. As in the case of grape juice this has been... 

Figure 7. Correlation of the pore-blocking factor, 1-(PF/PWF), and the boundary layer concentration of benzene, X 2, for six membranes of different pore sizes fsee Table I). Operating conditions are the same as in Figure 2 with operating pressures of 690 kPa (O), 1725 kPa (0), 3450...

It is understood that the economical success of any membrane process depends primarily on the quality of the membrane, specifically on flux, selectivity and service lifetime. Consideration of only the transport mechanisms in membranes, however, will in general, lead to an overestimation of the specific permeation rates in membrane processes. Formation of a concentration boundary layer in front of the membrane surface or within the porous support structure reduces the permeation rate and, in most cases, the product quality as well. For reverse osmosis. Figure 6.1 shows how a concentration boundary layer (concentration polarization) forms as a result of membrane selectivity. At steady state conditions, the retained components must be transported back into the bulk of the liquid. As laminar flow is present near the membrane surface, this backflow is of diffusive nature, i.e., is based on a concentration gradient. At steady state conditions, the concentration profile is calculated from a mass balance as... 

The calculated concentration profiles in a KC1 solution-anion exchange membrane boundary layer at different times after the start of a constant current of density 5 ma. per sq. cm. are plotted in Figure 5. The diffusion coefficient of KC1 in the solution was taken as 2.0 X 10—5 sq. cm. per second and the thickness of the diffusion layer as 0.03 cm. 

The solubility determines whether compounds precipitate on the membrane surface when the boundary layer concentration increases or the pH is adjusted to avoid inorganic precipitation... 

Apart from solute-solute interactions, the deposition of foulants on the membrane can alter rejection. Rejection can increase due to a lower porosity of the fouling layer or pore constriction, or decrease due to a higher concentration in the boundary layer (concentration polarisation effect). 

NF and RO pores are small and internal fouling by colloids is unlikely. The deposition of colloids on tight membranes may increase the boundary layer concentration, and give rise to an increased flux decline due to osmotic effects or cake resistance. 

Note that these initially estimated values are sUghtiy larger than those calculated in Table 7.20. The diffusivities arc likely to change in the boundary layer, and Bhattacharjee et aL (1999) predicted an increase in diffusivity with an increase of concentration. This means that backdiffusion would be enhanced and the estimated boundary layer concentration would be lower. It is evident from the results that modules with high mass transfer coefficients are important to avoid excessively high values of c vv. Alternatively, low flux operation (or larger membrane area) will also reduce c w. 

If solutes are rejected, their boundary layer concentration increases due to a balance between backdiffusion into the bulk and convection to the membrane with the feed (concentration polarisation ... 

Spedation calculations were carried out for the feed solutions. The issue of increased concentrations in the membrane boundary layer (where the precipitation is most likely to occur) was addressed in the NF Chapter (Chapter 7). It should be noted here that the local pH in the boundary layer is very likely to be different, due to the different mobility of H and OH . For this reason (the larger mobility of H" ) the pH of permeate is often lower. It is possible that the pH of the boundary layer will be larger than the bulk solution which could lead to higher precipitation. 

A similar device for membrane immobilization has been proposed by Michels [282], as a membrane-moderated immobilized cell bioreactor. A continuous-type bioreacior system is schematically shown in Figure 9.2. The feed solution is pumped into the reactor at a speed sufficient to produce fluid turbulence tti the proximity of the membrane boundary layer, so that the development of the concentrated boundary layer due to concentration polarization was prevented. After passing a bioreactor, the feed solution was recycled to the feed solution vessel. 

The phenomenon of concentration polarization, which is observed frequently in membrane separation processes, can be described in mathematical terms, as shown in Figure 30 (71). The usual model, which is weU founded in fluid hydrodynamics, assumes the bulk solution to be turbulent, but adjacent to the membrane surface there exists a stagnant laminar boundary layer of thickness (5) typically 50—200 p.m, in which there is no turbulent mixing. The concentration of the macromolecules in the bulk solution concentration is c,. and the concentration of macromolecules at the membrane surface is c. 

At any point within the boundary layer, the convective flux of the macromolecule solute to the membrane surface is given by the volume flux,/ of the solution multipfled by the concentration of retained solute, c. At steady state, this convective flux within the laminar boundary layer is balanced by the diffusive flux of retained solute in the opposite direction. This balance can be expressed by equation 1 ... 

The concentration boundary layer forms because of the convective transport of solutes toward the membrane due to the viscous drag exerted by the flux. A diffusive back-transport is produced by the concentration gradient between the membranes surface and the bulk. At equiUbrium the two transport mechanisms are equal to each other. Solving the equations leads to an expression of the flux ... 

Fig. 1. General dialysis is a process by which dissolved solutes move through a membrane in response to a difference in concentration and in the absence of differences in pressure, temperature, and electrical potential. The rate of mass transport or solute flux, ( ), is directly proportional to the difference in concentration at the membrane surfaces (eq. 1). Boundary layer effects, the difference between local and wall concentrations, are important in most...

With eveiy change in ion concentration, there is an electrical effect generated by an electrochemical cell. The anion membrane shown in the middle has three cells associated with it, two caused by the concentration differences in the boundaiy layers, and one resulting from the concentration difference across the membrane. In addition, there are ohmic resistances for each step, resulting from the E/I resistance through the solution, boundary layers, and the membrane. In solution, current is carried by ions, and their movement produces a fric tion effect manifested as a resistance. In practical applications, I R losses are more important than the power required to move ions to a compartment wim a higher concentration. 

FIG. 22-58 Concentration profile of electrolyte across an operating ED cell. Ion passage through the membrane is much faster than in solution, so ions are enriched or depleted at the cell-solution interface, d is the concentration boundary layer. The cell gap, A should he small. The ion concentration in the membrane proper will he much higher than shown. (Couttesij Elsevier.)... 

There are several drawbacks to the RDC that need to be emphasized. First, the fact that the interface must be supported adds a considerable resistance to the transport of species, which is in addition to that from the concentration boundary layers on both sides of the membrane. This limits the range of kinetics that can be studied. Second, in practical applications, blocking of the membrane can be problematic for some reactions. Third, measurements are generally made in the bulk of the solution and not at the interface although, as mentioned above, for certain processes it is possible to measure fluxes via a ring or an arc electrode. 

---