Three-Dimensional Trajectory Analysis of Particle Deposition in Constricted Tubes

A 3-D trajectory analysis of particle deposition in unit cells of the constricted-tube type is developed. Creeping newtonian How of the suspension through the unit cells is assumed, and the flow field in each unit cell is computed using the collocation solution provided by Tilton and Payatakes (1984). Particle trajectory equations are developed for the three-dimensional case, taking into account the hydrodynamic forces and torques, gravity, the London-van der Waals force, and the double ionic layer force. The one-step trajectory approach is used to predict the rate and pattern of deposition in a unit cell of arbitrary orientation. Numerical results agree with the experimental observation that deposition in oblique flow channels contributes substantially to the overall rate of deposition. Particle size and pore geometry effects on the rate of deposition are thoroughly studied and shown to be important for various cell orientations. This method can be used in a 3-D network analysis to estimate the overall filter coefficient and the pattern of deposition in deep bed filtration.