Settling Velocity Analysis of Natural Suspended Particles Using Fractal Approach

Abstract

An automated nonintrusive image analysis method is used to measure the settling velocity of particles and characterize their geometric properties using a fractal approach. A range of suspension characteristics is represented by particles collected from four field sites and one laboratory sample of a montmorillonite clay suspension. The field sites are Lake Ontario, Lake Erie, Lake LaSalle (a small lake in Buffalo, New York), and the Buffalo River (also in Buffalo, New York). In fractal descriptions of aggregates, particle areas do not scale with diameter squared, and settling rates vary with size, shape, and porosity. Measured settling rates are found to be less than values estimated by Stokes’ law, which is consistent with other studies of natural floc settling and indicates the flocs are not solid and spherical, as assumed for that law. They also are less than settling predicted with relationships developed for spheres at higher Reynolds number than the range associated with Stokes’ law. A dimensional analysis is performed to determine the relationship of settling rate with size, which is also correlated with other geometric and physical quantities that can be described using fractal geometry. The relationship determined using this approach provides a very good description of the observed settling rates for each of the five samples, and suggests settling velocity varies with particle size, expressed as area equivalent diameter raised to a power of approximately 1.4. Furthermore, a 2- to 7-fold overestimation of the settling velocity of larger aggregates can occur when Stokes’ law is applied. These results are useful for better prediction of particle fate and particle-bound contaminant transport, particularly in estimating contaminant residence time, fate, and overall surface water quality.