Effect of electrostatic repulsive force on the permeate flux and flux modeling in the microfiltration of negatively charged microspheres

A study on the permeate flux was performed in a stirred cell filled with monodispersed carboxylated microspheres (polystyrene/polymethacrylic acid, PS/PMAA), to investigate the effects of surface charge (the number density of surface carboxyl group, N_c; 0.45, 5.94, 9.14, and 10.25 nm^-2) and the stirrer speed (300, 400, and 600 rpm) under constant transmembrane pressure. The permeate flux was found to be dependent on the surface charge, the ionic strength, and the stirrer speed. The permeate flux was proportional to the surface charge of microspheres and inversely proportional to the ionic strength because of electrostatic repulsive interaction and steric hindrance. The cake porosity was estimated by Kozeny-Carman equation from the steady-state permeate flux data. Experimental data elucidated that the cake porosity was extended from 0.211 to 3.04 upon the introduction of carboxyl group on the microsphere surface, leading to the high permeate flux. Consequently, resistance-in-series model was employed for the modeling of the permeate flux and showed a good agreement with the experimental results.