Application of fractal concepts for analysis and modeling of particle aggregation.

摘要

The effect of particle structure on coagulation-flocculation process kinetics was investigated through the application of fractal geometry, which considers size, shape and distribution of primary particles in the aggregate structure in the analysis. The fractal dimension was determined from aggregation experiments using suspensions of polystyrene latex particles, clay suspensions, and natural lake and river water. The basic motivation for this research was to (1) develop and test a non-intrusive image-based analysis system, (2) evaluate the use of fractal geometry as a means of quantifying aggregate shape and other properties, and (3) develop relationships between shape and size, ambient mixing conditions and aggregation process rates. The experiments were conducted in a two-liter mixing jar apparatus, and images of particles were obtained using a CCD camera. Coagulant was added in most tests to facilitate aggregation, and dose, mixing rate, and particle concentration were varied to produce a range of floc characteristics. Aggregate size was found to be controlled by mixing speed (velocity gradient) and was inversely correlated with porosity, fractal dimension and primary particle number concentration. A fractal-based aggregate model (a modification of Smoluchowski's equation) was developed and tested using measured data.; A major goal of this study was to explore potential advantages of using fractal dimension to describe the effect of aggregate structure for calculating collision frequency functions (β), relative to conventional approaches that assume the particles are spherical (Euclidean model). It was found that for larger aggregates, calculations for β based on fractal dimension yielded values that were more than 20 times the values calculated from the Euclidean model. It was found that the fractal model provides an improved method (also better represents reality) for time-dependent estimates of β, which in turn allows better estimates for collision efficiency (α), which was found to be lower than in traditional approaches (since β is larger). The fractal dimension was found to be a significant parameter for estimating α and β. One of the significant contributions of this study is the identification of α as a time-varying parameter during aggregation, rather than a constant as is usually assumed in conventional modeling approaches.