Modelling ultrafiltration performance by integrating local (critical) fluxes along the membrane length

Despite the vast number of studies on the understanding and estimation of the permeate flux in ultrafiltration, most of them base their estimations on either one or another mechanism, without pointing out a clear ‘bridge’ between them. The aim of this paper is to assess these mechanisms on the determination of the permeate flux, using as feed a multicomponent mixture of BSA, NaCl and H ₂ O. Maxwell-Stefan Equations expressed as function of the components' volume fractions were used for an easier consideration of the non-idealities of the system. These non-idealities (hydration, adsorption, electrical interactions and volume exclusion) were critical in the local fluxes calculation, for which an increase in the thickness of the boundary layer along the filtration channel was considered. The developed model proved to be suitable for the estimation of fluxes lower than the limiting flux. Since the non-idealities of the system can be calculated along the concentration polarization layer, no extra information on the protein diffusivity was needed. Additionally, the fact that the model includes all the components from the solution offers the possibility of including the rejection of the accompanying ions in the calculations.