A new combined cake-complete model with the cake resistance corrected by cake filtration equilibrium coefficient in cross-flow microfiltration

Accurate flux prediction in constant pressure cross-flow microfiltration is of great significance for industrial cleaning process. In this study, a new combined mechanism (cake filtration and complete blocking) model was developed to accurately predict the flux decline in constant pressure cross-flow microfiltration, which based on the Bolton's model with considering both the cake resistance and the available membrane frontal area tending to be a constant after a certain period of filtration by using both cake filtration equilibrium coefficient (K_d) and the steady frontal membrane area (K). The proposed model was validated by different membranes and various feed suspensions for both laminar and turbulent regions. The results showed that the new cake-complete model possessed good prediction accuracy for different membranes (0.1 µm PAN, PVDF and PES membranes) (R² ≥ 0.9603) and different feed suspensions (yeast, kaolin and activated sludge suspensions) (R² ≥ 0.9309). Meanwhile, the prediction accuracy of the proposed model was higher than that of others and the sequence of average adjust R square (R²¯) was: 0.9696 (the proposed model) > 0.8755 (Silva's model) > 0.8193 (Bolton's model) > 0.6141 (cake model). In addition, low Reynolds number, high concentration and big pressure would decrease the available membrane frontal area and increase K_d, which ultimately leaded to more serious membrane fouling.