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, however, has recently been provided that particle aggregates from natural waters and engineered systems have fractal structures. Consequently, the traditional models should be modified to include the fractal nature of aggregates. This paper describes a modeling approach that simulates changes in particle size distribution (PSD) due to coagulation by incorporating recently proposed fractal mathematics and introducing a new conceptual framework called the 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-dimensional numerical model was developed. Model simulations were conducted varying the fractal dimension (DF) and the collision efficiency factor (α). For the conventional Euclidean case, the model indicated that coagulation played an important role in the vertical transport of the estuarine sediment particles. The simulations with the fractal cases indicated that both DF and α significantly affected the evolution of PSD, and that with lower values of DF and α, the model predicted a trend of PSD similar to that of the Euclidean case. This finding may be interpreted as dependence of α on the assumed collision models (or DF), that seems to leave a new challenge to our understanding of α. The developed model may be used in various particle aggregation systems.