Retention dynamics for small particles on cylindrical fibers

by Dyer, David A.

The mechanisms controlling the retention of small particles within a fibrous porous medium are of basic importance to many processes within the paper industry. Therefore, a better understanding of the retention process could prove to be of economic and environmental value. This thesis was proposed to clarify some questions related to the process of particle collection. The objective of the thesis was an investigation into the relative importance of hydrodynamic and colloidal forces thought to exist within a retention system. Such forces were assumed to affect the transport mechanisms of inertial impaction, flow-line interception, and diffusion. In addition, the effects of molecular attractive forces and double-layer interaction were studied. Each was evaluated by investigating which type of interaction produced the greatest change in retention. In this way relevant data could be obtained concerning how particulate matter is removed from a flow stream by a fiber assemblage. The objective has been accomplished through the construction of a mathematical model, developed to predict retention occurring in a simplified flow system. The model is based on the equivalent unit cell approach and a set of particle motion equations, which describe a particle's trajectory through this cell. The unit cell is composed of two concentric cylinders, the inner one represents the fiber, while the outer one is called the fluid envelope, with a radius dependent on system porosity. Creeping motion equations are the basis for a description of flow through the cell. Two equations were derived which describe the particle's trajectory; these equations can be modified to investigate, separately, each of the forces mentioned above. Determination of trajectories in this manner permitted the calculation of a collection efficiency representing the amount of particulate matter retained by a single fiber. -2- An experimental program was performed to provide data for a comparison with model predictions. A simplified permeation procedure was followed in which titanium dioxide particles were retained in a pad of synthetic fibers. By adjusting system variables of the experiment to conform to those utilized in the model, an adequate comparison between theory and experiment was realized. Calculations indicate that the inclusion of molecular attractive forces in the model is necessary for any appreciable retention. Double-layer repulsion was also found important, but it could be controlled by modifying the ionic suspension conditions. Inertial impaction was found negligible and diffusion only slightly affected overall retention. From both the model and experiment, it was shown that retention decreases with increasing porosity and with increasing bulk velocity. The model has also predicted that retention will decrease as particle size decreases. -3-