In a cross-flow ultrafiltration unit, a protein of MW = 3 x 10^5 da is separated from the fermentation broth by

In a cross-flow ultrafiltration unit, a protein of MW = 3 x 10^5 da is

separated from the fermentation broth by using a UF membrane. The flow rate of
liquid through a tube of diameter 2.5 cm and length 45 cm is 1.5 liter/min. The
flow regime is turbulent, f = 0.0005, and C4 = 2 [atm(s/cm)^2]. The inlet pressure is
Pi = 2.5 atm. Protein concentrations in the solution and on gel film are 25 mg/l
and 90 g/l, respectively.
a) Determine the exit pressure.
b) Determine the transmembrane pressure drop.
c) If the mass transfer coefficient for protein flux is 5.5 cm/s, determine the flux
of liquid through the UF membrane.
d) If the resistance of the filter medium is 0.0025 atm/cm2.s/cm3, determine the cake resistance.


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