The effects of particle size distribution on the cake properties and the performance of cross-flow microfiltration of dual-sized particles are studied. An equation based on the force analysis at the critical condition of particle deposition is derived to relate the filtration rate and the cake properties. The packing porosities of dual-sized particles under various mixing fractions are predicted theoretically in accordance with two limiting conditions, cavern and displacement effects, and are compared to the simulated results and experimental data. The results show that either the theoretical predictions or simulation results agree with the experimental data except in the region near the lowest packing porosity. There has been an overestimation on cake porosity using simulation method and an overestimation using theoretical prediction about 30% near the lowest packing porosity. The average specific filtration resistance of cake can be estimated accurately by substituting the average particle diameter based on the surface area and the Kozeny constant calculated from the cell model into the Kozeny equation. The increase in the mixing fraction of large particles results in a decrease in specific filtration resistance of cake but in an increase in the cake mass. Therefore, the pseudo-steady filtration rate increases with an increase in the mixing fraction of large particles. Once the values of porosity and specific filtration resistance of cakes formed by mono-sized particles are known, the cake properties and the pseudo-steady filtration rates for various mixing ratios of dual-sized particles can be estimated using the proposed theory. The agreements between the calculated results and the experimental data demonstrate the reliability of the proposed method.
Separation science and technology 37(10), pp.2231-2249