Permeability of collapsed cakes formed by deposition of fractal aggregates upon membrane filtration

We have investigated, theoretically, the physical properties of cake layers formed from aggregates to obtain a better understanding of membrane systems used in conjunction with coagulation/flocculation pretreatment. We developed a model based on fractal theory and incorporated a cake collapse effect to predict the porosity and permeability of the cake layers. The floc size, fractal dimension, and transmembrane pressure were main parameters that we used in these model calculations. We performed experiments using a batch cell device and a confocal laser-scanning microscope to verify the predicted specific cake resistances and porosities under various conditions. Based on the results of the model, the reduction in inter-aggregate porosity is more important than that in intra-aggregate porosity during the cake collapsing process. The specific cake resistance decreases upon increasing the aggregate size and decreasing the fractal dimensions. The modeled porosities and specific cake resistances of the collapsed cake layer agreed reasonably well with those obtained experimentally.