Trajectory calculation of particle deposition in deep bed filtration: Part I. Model formulation

The packed bed model developed by Payatakes, Tien, and Turian (1973a, 1973b) is used as a basis for the study of particle deposition in deep bed filtration. The size of the particulate matters present in the suspension is assumed to be sufficiently large for Brownian motion to be negligible, but small enough for straining to be unimportant. The prediction of the rate of particle deposition is based on the one-step trajectory approach. The collector is represented by a unit bed element of the porous media model and the particle trajectory equation is formulated to include the gravitational force, the hydrodynamic force and torque (including the correction for the presence of the unit cell wall), the London force (including the retardation effect, which is shown to be of primary importance under conditions usually met in deep bed filtration systems), and the electrokinetic force. Sample capture trajectories, including the limiting capture trajectories, are given. Based on the limiting trajectories and the assumption of uniform particle distribution at the entrance of each unit cell, the number fractions (of suspended particles) impacted on each unit cell are determined and then used to calculate the fraction impacted on the entire unit collector and also the value of the filter coefficient for a clean bed. It is also shown how the capture trajectory calculation can be used to determine the local rate of deposition along the wall of a given unit cell.