Question

A microfiltration membrane was tested in the laboratory and found to have a clean-water flux of 6500 L/ m2*h at 23°C and 0.69 bar.
a) Calculate the specific flux at 20 °C.
b) Calculate the membrane resistance coefficient (you can assume dynamic viscosity as 10-3 kg/m*s).
c) Does membrane resistance depend on pressure and temperature used for the tests in lab? Please explain your reasoning.

Please show step by step solution. Thank you.

Answer 1

Ans a) We know,

Specific flux = J e-0.031(T-20)/ P

where, J = Flux = 6500 L /m2 h

T = Temperature = 23 C

P = Pressure = 0.69 bar or 69000 Pa

Putting values,

Specific flux = 6500 e-0.031(23 - 20) / 69000

=> Specific flux = 0.0958 L/m2 h / Pa

Ans b) We know,

Membrane resistance coefficient, RH = P / J

J = Flux = 6500 L/m^2 h or 6.5 m^3/h m^2 or 0.0018 m^3 / m^2 s

Putting values,

RH = 69000 / 0.001 x 0.0018

=> RH = 3.83 x 10^10 / m   

Ans c) Yes, membrane resistance depends on temperature and pressure used for test because as we can see from above formula that membrane resistance will depend on dynamic viscosity of water. Since, viscosity changes with change in temperature and pressure so membrance resistance also change with change in temperature and pressure