Membranes solute rejection coefficient

Under the influence of pressure, the membrane permits specific components to pass through (or permeate). The membrane also inhibits transport of some components. This selective transport forms the basis of the membrane separation process. Rejection is a bulk separation capability of the membrane. The observed solute rejection coefficient II for a given species i is given by... 

The selection ofthe membrane to be used in enzymatic membrane reactors should take into account the size of the (bio)catalyst, substrates, and products as well as the chemical species ofthe species in solution and ofthe membrane itself. An important parameter to be used in this selection is the solute-rejection coefficient, which should... 

Solute rejection coefficient of membrane Translation coefficients for translation of a spheroid parallel to its semiaxes, Eqs. (5.1.6), (5.1.7), also any body parallel to its principal axes, Eq. (5.1.10a)... 

Here, 6 is the solute permeability coefficient, Ac is the difference in solute concentrations immediately adjacent to the membrane (wall) on the feed and product sides, is the concentration on the feed side, and is the solute rejection coefficient, which is usually taken to be constant. 

The terminology for characterizing dialysis membranes is somewhat unique to the dialysis field. Instead of being characterized in terms of hydrauhc penneabUity, diffusive membrane permeabihties, and solute rejection coefficients, dialyzers arc generally characterized in terms of an ultrafiltration coefficient (Kuf), solute clearances, and the product of the mass transfer coefficient times the surface area (KoA). 

The pressure difference between the high and low pressure sides of the membrane is denoted as AP the osmotic pressure difference across the membrane is defined as Att the net driving force for water transport across the membrane is AP — (tAtt, where O is the Staverman reflection coefficient and a = 1 means 100% solute rejection. The standardized terminology recommended for use to describe pressure-driven membrane processes, including that for reverse osmosis, has been reviewed (24). 

The thermodynamic approach does not make explicit the effects of concentration at the membrane. A good deal of the analysis of concentration polarisation given for ultrafiltration also applies to reverse osmosis. The control of the boundary layer is just as important. The main effects of concentration polarisation in this case are, however, a reduced value of solvent permeation rate as a result of an increased osmotic pressure at the membrane surface given in equation 8.37, and a decrease in solute rejection given in equation 8.38. In many applications it is usual to pretreat feeds in order to remove colloidal material before reverse osmosis. The components which must then be retained by reverse osmosis have higher diffusion coefficients than those encountered in ultrafiltration. Hence, the polarisation modulus given in equation 8.14 is lower, and the concentration of solutes at the membrane seldom results in the formation of a gel. For the case of turbulent flow the Dittus-Boelter correlation may be used, as was the case for ultrafiltration giving a polarisation modulus of ... 

Predictions of salt and water transport can be made from this application of the solution-diffusion model to reverse osmosis (first derived by Merten and coworkers) [12,13], According to Equation (2.43), the water flux through a reverse osmosis membrane remains small up to the osmotic pressure of the salt solution and then increases with applied pressure, whereas according to Equation (2.46), the salt flux is essentially independent of pressure. Some typical results are shown in Figure 2.9. Also shown in this figure is a term called the rejection coefficient, R, which is defined as... 

The rejection coefficient is a measure of the ability of the membrane to separate salt from the feed solution. 

Figure 5.5 Water permeability as a function of sodium chloride permeability for membranes made from cellulose acetate of various degrees of acetylation. The expected rejection coefficients for these membranes, calculated for dilute salt solutions using Equation (5.6),...

Negative rejection coefficients, that is, a higher concentration of solute in the permeate than in the feed are occasionally observed, for example, for phenol and benzene with cellulose acetate membranes [48],... 

When the rejection coefficient equals one, Equation (6.6) reduces to Equation (6.5). A plot of the concentration ratio of retained solute as a function of the volume reduction for membranes with varying rejection coefficients is shown in Figure 6.18. This figure illustrates the effect of partially retentive membranes on loss of solute. 

Ds is the diffusivity of the solute in the membrane Cj is the solute concentration in the reject side ks is the solute distribution coefficient C2 is the solute concentration in the permeate side... 

C over 24 h. Initial pH was adjusted with HCl (5 N) and NaOH (5 N) solution. Batch ultrafiltration was performed in a stirred cell (Amicon model 52, feed volume 50 ml, effective membrane area 12.5 cm ), usually at 3 bars, with membrane YM5 (Amicon, mw cut off 5,000 Dalton). The first 10 ml of permeate were discarded. The next two consecutive 10 ml were analysed to determine the mercury concentration with an atomic absorption spectrophotometer. The rejection coefficient (R) defined as below, was calculated from the feed and permeate concentration of mercury. 

Rejection of the solute (or dispersed colloid) is, together with permeate flux, one of the two key performance parameters of any ultrafiltration membrane. The values of rejection coefficients are of crucial Importance in many applications of ultrafiltration. The objective of this contribution is to consider and analyze the individual factors affecting rejection of polymer solutes by ultrafiltration membranes. The factors that will be considered include, sterlc rejection (sieving), solute velocity lag and solute-membrane Interaction. 

It is seen that the effect is most pronounced below X = 0.7 and its magnitude depends on the value of the respective Hamaker constant. The rejection coefficient is increased by the attractive forces between the solute and the membrane. 

Typical results of an ultrafiltration experiment also reflect the presence of concentration polarization. This phenomenon, l.e. accumulation of solute in front of the membrane, was described in great detail by others (Refs. 3, 4). A consequence of concentration polarization is a strong dependence of measured rejection coefficients on transmembrane fluxes. An illustration of the effect is presented in Figure 9, which shows the measured "apparent" rejection coefficients (Rg) as a function of transmembrane flux for two water-soluble polymers (Tetronic 707 and Carbowax 4000). It is clear from Figure 9 that if we want to minimize the effects of concentration polarization, we have to conduct experiments at very low values of transmembrane flux. 

The typical ultrafiltration results will reflect effects of the respective size distributions of both the solute and the membrane pores, as well as of concentration polarization. All of these effects should be expected to lower the membrane rejection coefficient. 

The salt content on the downstream side of the membrane is determined by the relative salt and water fluxes through the membrane. A combination of results from the solution-diffusion model outlined earlier with the definition of the rejection coefficient gives... 

The nominal pore size of the NF membrane is typically about 1 nm. NF can retain molecules which have size of 100-1000 nm which ranges between ultrafiltration and reverse osmosis. The relative molecular weight of Mal-/3-CD is 342. The NF membrane (NE-1812) with molecular weight cut off (MWCO) of 200-400 can be used to initially concentrate the dilute solution of crude Mal-jS-CD. There are two important indicators membrane flux and rejection coefficient of maltose in the crude Mal-/3-CD. 

The hydraulic or water permeability coefficient (L ) can be determined from a simple permeation experiment Assume for a given membrane a Lp value of 5 lO m/hr. bar. The membrane has a rejection coefficient of 95% for NaCl and of 99.8% for NajSO< at 40 bar and 10000 ppm salt Calculate the solute permeability coefficient for both salts. 

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