llustrated below are general spatial variations in the concentration of solute (

Question

llustrated below are general spatial variations in the concentration of solute (Csolute) in a reverse osmosis membrane system, extending from the bulk of the feed solution where the solute concentration is fixed at a value of Cfeed to the bulk of the filtrate solution where the concentration is fixed at a value of Cfiütrate. The pressure of the feed solution (Pfeed) is adjusted with respect to that of the filtrate (Piütrate) in order to maintain a constant water (solvent) velocity of vwater C. polar solute feed Concentration polarization layer filtrate solute 7 water Ap olar membrane

Explanation / Answer

Robserved is the observed retention. This gives the qualitiative extent to the seperation a membrane can give with respect to the concentration in the feed.

Rtrue is the true retention. This refers to the partition of the solute just accross the membrane i.e. the membrane-solution interface and the permeate side. Hence, this gives the extent of seperation a membrane can give with respect to the solute concentration existing just at the interface.

In simple terms, the basis for Robserved is feed concentration and that for Rtrue is the interfacial concentration.

Since the definition of the true retention is not affected by any physical phenomena occuring in the path between the feed entry and the interface, true retention gives the true seperation effectiveness of the membrane alone.

Mathematically,

Robserved = (Cfeed - Cfiltrate) / Cfeed = 1 - Cfiltrate/Cfeed

Rtrue = (Cpolar - Cfiltrate)/ Cpolar = 1 - Cfiltrate / Cpolar

Since the concentration on the membrane interface is always greater than that in the feed, Cpolar > Cfeed

and Cfiltrate / Cpolar < Cfiltrate/Cfeed .

Thus, Rtrue > Robservedalways.

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