A novel approach to evaluate the permeability of cake layer during cross-flow filtration in the flocculants added membrane bioreactors

► A new model was successfully developed to predict the porosity and permeability of cake layers in flocculants added MBRs. ► The model was based on body-centered cubic packed structure considering cake collapse effect and frictional force balance. ► Important characteristics of flocs and operating parameters of MBRs were considered in the force balance equation. ► Cross-flow velocity had profound and complex effects on membrane fouling. In order to obtain a better understanding of the cake layer formation mechanism in the flocculants added MBRs, a model was developed on the basis of particle packing model considering cake collapse effect and a frictional force balance equation to predict the porosity and permeability of the cake layers. The important characteristic parameters of the flocs (e.g., floc size, fractal dimensions) and operating parameters of MBRs (e.g., transmembrane pressure, cross-flow velocity) are considered in this model. With this new model, the calculated results of porosities and specific cake resistances under different MBR operational conditions agree fairly well with the experimental data.