P

From Eqs. (12.25) and (12.11), considering the flow rate according to Eq. (12.27), we obtain:

and finally the result for the permeate concentration c2: Bco

For p0-p2 = An, no water is transported through the reverse osmosis membrane but the dissolved compound is transported, giving finally c2=c0.

At the membrane surface, some important effects may occur, e.g. concentration polarization and fouling processes that have to be taken into consideration (Section 12.3). In reverse osmosis and nanofiltration processes osmotic pressure is important, but even in ultrafiltration processes osmotic pressure can have an effect. At high fluxes and high retention values, the concentration of macromolecules at membrane surface becomes quite high (see Problem 12.1).

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