ABSTRACT
The weight concentration ratio (WCR) is expressed in the same manner, except with weights rather than volume. VCR and WCR are also frequently referred to in the literature as “concentration factor” (X). Sometimes the data is also presented in terms of percent volume reduction or percent water removed, where
where VP is volume of permeate. Assuming the size of the potential measure ment error is proportional to the size of the observation and the probability is constant throughout UF and subsequent diafiltration processes, the following expression was derived (Cheryan 1986):
Equation (7.4) shows that the concentration of a solute at any time or stage of membrane processing is a function of both the volume reduction and the value of R, where R is expressed by Equation (7.1). In other words, if the probability that a solute will go through the membrane is 1, then it implies it is a freely permeable solute that will not be rejected by the membrane, and its concentration on either side of the membrane will be equal. Or from Equation (7.1), CP = Cp , and it has a rejection of zero. Similarly, if the probability is zero, the solute will not go through the membrane, and we will measure a rejection R = 1. 7.A.I.EXAMPLE
Typical data from the fractionation of cheese whey is given in Table 7.1. The first row is VCR (or X ) — 1, showing the composition of the cheese whey used as feed. A sample calculation for VCR = 20 is given below, using Equation (7.4):
• for protein, R = 1, CR = 0.4(20) 1 = 8.0% • for lactose, R = 0, CR = 5(20)° = 5.0% ® for NPN, R = 0, CR = 0.2(20)° = 0.2% • for ash, R = 0.2, CR = 0.68(20)° 2 = 1.24% Figure 7.1 shows the behavior of cheese whey during UF. Straight lines
should be obtained when plotting data as C versus VCR, if rejection is 0 or 1. Rectangular hyperbolas will be obtained for all other R values. Deviations from expected behavior will suggest the following could be occurring: (a) solute adsorption by the membrane; (b) change in rejection during UF, which is quite common, especially at higher retentate concentrations; or (c) volume exclusion effects of the solute becoming significant, which becomes important at high solute concentrations.
