A computational study of the role of particle size standard deviation on the collision frequency in differential settling

Abstract

The results of a simple computational model for differential settling are presented illustrating the significant role that particle size distribution plays in collision frequency and sedimentation rate of particles in a quiescent environment. The model tracks a large number of particles (order 105) with log-normally distributed diameters, as they settle at their Stokes settling velocities. Particle collisions are detected and result in larger particles that fall more rapidly. A number of simplifying assumptions are made in the model in order to avoid empirical correlations for phenomena such as collision efficiency and particle shape. These simplifying assumptions were needed to isolate and quantify the role of the particle size distribution. Simulated concentration profiles indicate that, even in the absence of collisions, the standard deviation (σD) of the particle size strongly influences the bulk mass settling rate as, for larger σD, more mass is concentrated in larger, faster falling particles. The collision frequency is also a strong function of σD. For a given mass concentration the collision frequency first increases linearly with increasing σD as greater variation in particle size leads to greater variation in particle velocity, and shorter times for particles to catch each other. For larger σD more mass is concentrated in larger particles, so, for a given mass concentration, there are fewer particles per unit volume, increasing the mean distance between the particles and reducing the collision frequency. The implications of these results for sedimentation measurement using optical attenuation techniques are discussed.