A model for cross-flow ultrafiltration of dairy whey based on the rheology of the compressible cake

In the dairy industry, whey protein is concentrated by means of cross-flow ultrafiltration (UF). In cross-flow UF, it is considered that the surface part of the fouling layer can be removed by the effect of the shear stress exerted by the feed flow. As a result, the flux decline is suppressed and a steady state flux eventuates. However, the means to express the relationship between the feed flow and the permeate process has not been come to definite conclusion. In this study, the compressive yield stress model for the permeation through a fouling layer on a membrane in dead-end UF was applied to cross-flow UF considering the removal rate of the fouling layer. The time course of permeate flux estimated based on the model. In the estimation, the concentration at the top of the fouling layer must be specified and the concentration distribution in the layer should be calculated. The rheology of a whey protein concentrate (WPC) suspension, which is used as a model fluid, was investigated. The concentration at the top of the fouling layer was determined based on the relation between the shear stress exerted by the feed flow and the rheology investigated. The validity of the model was discussed by comparing the results of estimation by the model and experiments.