Modeling coagulation kinetics incorporating fractal theories: A fractal rectilinear approach

Conventional coagulation kinetic models are usually based on Smoluchowski's work, which employs the coalesced sphere assumption. Much evidence, howeve r, has recently been provided that particle aggregates from natural waters and engineered systems have fractal structures. Consequently, the tradition al models should be modified to include the fractal nature of aggregates. T his paper describes a modeling approach that simulates changes in particle size distribution (PSD) due to coagulation by incorporating recently propos ed fractal mathematics and introducing a new conceptual framework called th e coalesced fractal sphere (CFS) assumption. The developed modeling method, which includes the traditional Euclidean case as a subset, was applied to a 2-m settling column system with estuarine sediment particles, and a one-d imensional numerical model was developed. Model simulations were conducted varying the fractal dimension (D-F) and the collision efficiency factor (al pha). For the conventional Euclidean case, the model indicated that coagula tion played an important role in the vertical transport of the estuarine se diment particles. The simulations with the fractal cases indicated that bot h D-F and alpha significantly affected the evolution of PSD, and that with lower values of D-F and alpha the model predicted a trend of PSD similar to that of the Euclidean case. This finding may be interpreted as dependence of alpha on the assumed collision models (or D-F), that seems to leave a ne w challenge to our understanding of alpha. The developed model may be used in various particle aggregation systems. (C) 2000 Elsevier Science Ltd. All rights reserved.