Rejection coefficient

It foUows from these two equations that the water flux is proportional to the appHed pressure, but the salt flux is iadependent of pressure. This means the membrane becomes more selective as the pressure increases. Selectivity can be measured ia a number of ways, but conventionally, it is measured as the salt rejection coefficient, R, defined ia equation 6. 

Eig. 16.9. Dependence of rejection coefficient on molecular weight for ultrafiltration membranes. 

The rejection coefficient R) was calculated according to the following equation / = In (Cr/C )/ln (VJVr). Cr or Vr represent the protein concentration in the retentate or the volume of the retentate Co is the concentration of the protein in the solution before filtration 1 is the initial volume of the feed. The pH value of each protein solution was immediately measured after dissolving the proteins in distilled water. 

The results are often presented in terms of the rejection coefficient which is a dimensionless number defined as... 

Alkalinity. The FAM solution was divided into several aliquots and the pH was adjusted with H2SO4 to a pH ranging from 8.5 to 13.8, each at a concentration of about 11 g/L. Each solution was individually ultrafil-tered and a permeate sample obtained. The pH 8.5 solution was titrated with 0.1M NaOH to several alkalinities and ultrafiltered. The permeate concentrations and rejection coefficients are presented in Table I, and the permeate molecular weight distributions are shown in Figure 1. 

Molecular Weight. The four KL solutions and 50 50 mixtures of the SAM, NASM and LAM with FAM were ultrafiltered at pH 13.8 and 8.5 to explore the effect of the parent solution molecular weight distribution on the association process. The results at pH 13.8 are presented as rejection coefficient distributions in Figure 2. The rejection coefficient distribution was... 

Figure 2. Rejection coefficient distribution on the XM300 membrane showing the association caused by an increase in the concentration of large molecules at constant total lignin concentration.

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. 

For a perfectly selective membrane the permeate salt concentration, cJe = 0 and R = 100%, and for a completely unselective membrane the permeate salt concentration is the same as the feed salt concentration, ck = cJo and R = 0%. The rejection coefficient increases with applied pressure as shown in Figure 2.9, because the water flux increases with pressure, but the salt flux does not. 

The effect of temperature on salt rejection and water flux illustrated in Figure 5.2(c) is more complex. Transport of both salt and water represented by Equations (5.1) and (5.3) is an activated process, and both increase exponentially with increasing temperature. As Figure 5.2(c) shows, the effect of temperature on the water flux of membranes is quite dramatic the water flux doubles as the temperature is increased by 30 °C. However, the effect of temperature on the salt flux is even more marked. This means that the salt rejection coefficient, proportional to the ratio B/A in Equation (5.6), actually declines slightly as the temperature increases. 

Some confusion can occur over the rejection coefficients quoted by membrane module manufacturers. The intrinsic rejection of good quality membranes measured in a laboratory test system might be in the range 99.5 to 99.7 %, whereas... 

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. 

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... 

Mitchell, B. C., and Deen, W. M. (1986). Effect of concentration on the rejection coefficients of rigid macromolecules in track-etch membranes, J. Coll. Inter. Sci. 113, 132. 

The mechanisms by which various components in a liquid or gaseous feed stream to the membrane system are transported through the membrane structure determine the sq>aiation properties of the membrane. These transport mechanisms are quite different in liquid and in gas or vapor phases. So are their effects on permeate flux (or permeability) and retention (or rejection) coefficient or separation factor in the case of gas separation. 

Figure 4.26 Rejection coefficient of bovine serum albumin (BSA) protein as a function of time for untreated titania membrane and two titania membranes treated with 0.1 M phosphoric acid at room temperature for 1 and 14 hours, respectively. (A) without phosphate buffer (B) with 0.01 M Na2HP04/NaH2P04 buffer [Randon el al.. 1995]...

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. 

The experiment was started with 3 I of mercury-MED complex solution and the rejection coefficient was determined at every 250 ml of permeate. The final volume of retentate was 500 ml. When a 50 ppm of mercury solution was ultrafiltered, loss of mercury was less than 6 ppm up to 2 1 of permeate. Above 2 1, it increased rapidly. 

To determine the relative degree of purification in a given UF process or to estimate the period of UF processing required to achieve a certain degree of separation or purification, the UF process must be mathematically modeled (29). The observed rejection coefficient at any point in the UF process is defined as... 

Membrane technology is used to remove oil particles from industrial wastewater. The initial feed tank volnme is 8640 m /d and after treatment the retained volume is required to be 50% of the initial volume entering to the basin. If the observe rejected coefficient is... 

---