Modeling of the initial deposition of individual particles during the cross-flow membrane filtration

This study is devoted to the modeling of the deposition of individual particles onto a clean membrane surface in cross-flow filtration systems. Comprehensive force analysis approach is applied, which accounts for the random Brownian force and the polar component of the particle–membrane interactive forces. The inclusion of the polar interactive force is important in that when a hydrophilic membrane is involved, it can easily predominate over the rest of lateral forces in the near-field. The repulsive polar particle–membrane interaction can greatly decrease the stability of the particle on the membrane surface. In the far-field that is about 0.1 μm or farther away from the membrane, the particle transport is primarily dictated by the hydrodynamic lift and drag forces and the Brownian force. In sharp contrast to semi- or non-Brownian particles, the transport trajectory of Brownian particle is hardly definitive. The filtration flux and the cross-flow velocity can influence the particle transport trajectory of all sizes. Nevertheless, the existence of critical flux or critical cross-flow velocity is more evident for non-Brownian particles. Above the critical cross-flow rate or below the critical flux, particle deposition is minimized. Under appropriate operational conditions, a force-balanced level exists in the viscous sub-layer for a particular particle size, which is independent of the initial position of the particle. The model can be expanded further for more complicated water filtration conditions.