Effect of fiber lumen radius on the permeate flux of hollow fiber membrane modules

Microfiltration of rigid spherical particle suspension in a hollow fiber module operating with inside–out flow, at a constant module inlet flow rate, was simulated using the shear-induced hydrodynamic diffusion model of Mondor and Moresoli, with consideration of the axial variation of the pressure drop through the cake layer and the membrane. The influence of the particle size and of the lumen radius, on the length-averaged permeate flux, was investigated for two typical membrane resistances. The results show that different patterns can be observed: A situation where there is negligible or no cake layer formation, a situation where the cake layer resistance is the main resistance to the permeate flux and finally a situation where both cake layer and membrane resistances are similar in magnitude. For the first situation, the length-averaged permeate flux increases with an increasing lumen radius, for the second situation the length-averaged permeate flux decreases with an increasing lumen radius and for the third situation, there exists an optimal lumen radius corresponding to a maximum length-averaged permeate flux. Finally, the current approach was compared with a similar analysis that has been performed for crossflow microfiltration by Arora and Davis.