A protein feed solution is being ultrafiltered using a flat sheet membrane (1 m in width by 1 m in length). The feed flo

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A protein feed solution is being ultrafiltered using a flatsheet membrane (1 m in width by 1 m in length). The feed flowchannel is rectangular with 0.3 cm in height on top of themembrane. The feed flow rate is 200 L/min at 37degC. Assume: • gelpolarized (pressure independent) conditions at all times •rejection rate (R) of 99.5%, where R= 1- Cp/Cb; Cp is the proteinconcentration in the permeate • gel concentration Cg = 30 wt% •liquid density: 1000 kg/m3 • viscosity 0.002 Pa s (at 200C) and0.0015 Pa s (at 370C) • protein diffusivity of 2x10-11 m2/s (at200C) • feed bulk concentration (Cb) does not change over themembrane. For a feed solution of 10 wt% (Cb),
Calculate a) Concentration profile of the protein across themembrane
b) Reynold’s number in the feed solution Re: 4425
c) Diffusivity of protein at 37degC DAB: 2.8 10-11 m2 /s
d) Convective mass transfer coefficient for the protein in thefeed solution kc: 4.3 10-6 m/s
e) The permeate rate (L/h) N: 17 L/h