Concentration boundary layer,

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. 

It is possible to derive a simple particle dissolution model where diffu-sional film thickness is not explicitly required. However, the boundary layer concentration profile derived from this model will extend for distances which cover an order of magnitude of the initial particle radius. 

At quasi-steady state, the two fluxes, Eqs. 1 and 2, have to be equal. This allows us to calculate the boundary layer concentration Cf ... 

Andreae et al. (22) found a similar profile over the Northeast Pacific ocean, but with lower boundary layer concentrations of less than 30 ppt. These low values were apparently related to low sea surface DMS concentrations in the open ocean (0.8 nM) during that study. 

Diffusion to and from the bulk gas to the external catalyst surface, represented as an external mass-transfer process across a film or boundary layer concentration gradient. For nonporous catalyst this is the only mass-transfer step. 

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

The osmotic pressure difference can usually be neglected in MF and UF, since the rejected solutes are large and their osmotic pressure small. However, even polymeric solutes can develop a significant osmotic pressure at boundary layer concentrations (Ho and Sirkar (1992)). This naturally implies that the resistance in series model (equation (3.4)) would be more appropriate in MF, while the osmotic pressure model (equation (3.6)) may be more useful in NF and RO. Both models have been applied to UF. 

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 ... 

The boundary-layer concentration profiles of CO, CO2, and O2 were measured by using a chemical ionization mass spectrometer (Airsense... 

Figure 25.24 See (i) Cooper, A.R. and Kingery, W.D. (1964) Dissolution in ceramic systems I. Molecular diffusion, natural convection, and forced convection studies of sapphire dissolution in calcium aluminum silicate, /. Am. Ceram. Soc. 47,37. (ii) Samaddar, B.N., Kingery, W.D., and Cooper, A.R. (1964) Dissolution in ceramic systems II. Dissolution of alumina, mullite, anorthite, and silica in a calcium-aluminum-silicate slag, J. Am. Ceram. Soc. 47, 249. (iii) Oishi, Y., Cooper, A.R., and Kingery, W.D. (1964) Dissolution in ceramic systems III. Boundary layer concentration gradients, J. Am. Ceram. Soc. 48,88. (A classic series of papers all on-line for ACerS members.)...

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