The effect of fibre diameter on filtration and flux distribution — relevance to submerged hollow fibre modules

This paper examines the effect of fibre diameter on filtration and flux distribution with inter-fibre two-phase flow for conditions relevant to submerged bioreactors (SMBR). Hollow fibres of different diameters fixed in a specially designed holder providing shell-side feed were tested for a model biomass feed with pumping and submerged systems. The experimental results showed that the effect of the fibre diameter on filtration increased with the increase in turbulence around the fibres. For filtration with two-phase flow, the performance was sensitive to changes in fibre diameter and significantly lower flux declines were obtained with smaller fibres. On the other hand, a theoretical analysis of flux distribution along the fibre in a submerged system showed the smaller fibres to be disadvantaged. The theoretical model based on the simplified Navier–Stokes equations and filtration equations revealed that the flux distribution along the fibre depends on fibre inner diameter, length and fibre permeability. The effect of these factors can be related to a dimensionless coefficient ζ=4lRi−3/2Rm−1/2. Sensitivity analysis demonstrated that for ζ>2, the maximum flux along the fibre can be approximately estimated by Jmax=ζJmi. Although, the effect of high initial local flux on performance of filtration is still to be assessed, the flux distribution model is useful in design and operation of the SMBR system.