Effects of Cake Collapse Caused by Deposition of Fractal Aggregates on Pressure Drop during Ceramic Filtration

A cake collapse model was developed by taking the combined effects of fractal dimension, relaxation ratio, coordination number, and aggregate diameter into consideration. The cake porosity including intraaggregate and inter-aggregate porosities was modeled successively by three typical coordination numbers (n = 6, 8, and 12). Accordingly, an inversion method made it possible to deduce the coordination number using the measured cake porosities, and the reverse-calculated value with minimum error and the corresponding relaxation ratios were applied as the parameters for the model. As a result, the profiles of intraaggregate and interaggregate porosities and cake porosity were respectively predicted in contrast to the integrated variation of the relaxation ratio and the fractal dimension. Furthermore, a comparison between the model predictions of the cake pressure drop gradients with and without aggregate compression was conducted to validate the presence of cake collapse. The results show that the predictions based on the proposed collapse model are in agreement with the experiments, and the coordination number is one of the key factors that must be incorporated into the cake collapse models.