Collision efficiencies of diffusing spherical particles: hydrodynamic, van der Waals and electrostatic forces

A practical limitation of the application of Smoluchowski's classical estimate for the collisions probability of two diffusing spherical particles in Brownian motion is the non-consideration of interparticle forcves. For suspended particles in water such forces can arise from the disturbance the particle causes in the fluid (hydrodynamic forces), from the cloud of ions which surround an electrically charged particle (double layer forces) or they can be of molecular origin (van der Waals forces). In this paper corrections to Smoluckhowski's collision probability are computed when such forces operate Scoluchowski's collision probability are computed when such forces operate between two approaching particles of various sizes. Results for several values of the van der Waals energy of attraction and the ionic strength of the electrolyte are presented in a way convenient for particle collision modeling

Numerical Simulation of a Sedimentation Basin. 1. Model Development

A method for the numerical simulation of a rectangular sedimentation basin operating under steady or unsteady conditions is described. The computer model follows the spatial and temporal development of the influent particle size distribution toward the outlet of the tank. It is based on the fundamental mechanisms which govern particle motion and growth. The model accounts for the variability of the flow field and the particle size distribution in the tank and, from the local development of the particle size spectrum, predicts the overall performance of the settling basin

Numerical simulation of a sedimentation basin. 2. Design application

A numerical model of a rectangular settling tank is used to study the importance of selective variables on the settling process while demonstrating the capabilities of the computer simulation. The computer model follows the spatial and temporal development of the influent particle size distribution toward the outlet of the tank based on the fundamental mechanisms which govern particle motion and growth. It is shown that both the removal efficiency of a flocculating suspension and the effluent particle size distribution are influenced strongly by the mass concentration in the inflow, the influent particle size distribution, the floc size-density relationship, and the collision efficiencies of the particles. It is suggested that future experimental work should focus on obtaining information on the size-density relationship, the reentrainment of the deposits, and the collision efficiencies of floes