(189d) Generation and Geometrical Analysis of Dense Clusters with Variable Fractal Dimension Providing a Basis for the Interpretation of Data from Optical Particle Characterication Techniques
In the solid-liquid separation of colloidal matter, e.g., in the case of waste-water treatment, in the downstreaming of emulsion polymers or wet born nano-particles, usually smaller particles are aggregated to from larger clusters to enhance and facilitate the separation step. By doing so, initially formed open clusters are restructured and reversibly broken and aggregated by the shearing of the fluid to produce dense clusters. A methodology to artificially generate dense clusters with variable fractal dimension is proposed. It is based on the algorithm of Thouy and Jullien , which provides clusters with a fractal dimension up to 2.5, where an additional densification routine was implemented that utilizes voronoi tessellation in order to provide clusters of densest random packing (for the given framework). In this way, cluster populations with fractal dimensions up to the Euclidian limit of 3 can be obtained. Hence, cluster populations with fractal dimensions ranging from 2.2 to 3 were generated and, consequently, analyzed with respect to common geometric measures that are typical for optical particle characterization techniques, such as microscopy, light scattering, and focused beam reflectance. To assure the representativeness of the provided averages sufficiently large cluster populations were analyzed, which was particularly important for the smaller clusters. Relations between fractal dimension, cluster mass, and certain geometric measures are discussed and compared to data available in literature. Special attention is given to the effect of blur that is unavoidable when the objects fine characteristics become comparable with the wave length of the light source used. Such results can serve as a basis for the interpretation of data from optical particle characterization techniques for systems containing aggregated matter.
 R. Thouy, R. Jullien, A Cluster-Cluster Aggregation Model with Tunable Fractal Dimension. Journal of Physics a-Mathematical and General. 1994, 27, 2953-2963.