A protein with a MW of 15,000 in an aqueous solution (μ = 1 cP, ρ = 1 cm 3 s −1 ) is being filtered at 20°C through a microporous membrane within a 25 mm diameter stirred ultrafiltration cell. The...

A protein with a MW of 15,000 in an aqueous solution (μ = 1 cP, ρ = 1 cm³
s⁻¹) is being filtered at 20°C through a microporous membrane within a 25 mm diameter stirred ultrafiltration cell. The membrane has a NMWCO of 30,000. The stirring speed is 1000 RPM. Estimate the observed sieving coefficient, i.e., SO. The filtration flux, i.e., q = Q/S, is equal to 1.5 × 10⁻³
cm s⁻¹. For a stirred ultrafiltration cell, the following correlation can be used for the mass transfer coefficient:

where

r^cell is the radius of the stirred cell ultrafiltration chamber

ω is the stirring speed in radians per second