Modeling coagulation kinetics incorporating fractal theories: comparison with observed data

There are currently four possible approaches in modeling coagulation kinetics: the traditional Euclidean rectilinear; the Euclidean curvilinear; the fractal rectilinear; and the fractal curvilinear. The fractal model includes the Euclidean case as a subset. The primary purpose of this research is to investigate which of the rectilinear models among these best predicts the evolution of experimental observed particle size distribution (PSD). Using a fractal rectilinear model previously developed by the authors, model predictions were compared with a series of observed PSD data obtained from estuarine sediment particles in a 2 m settling column, where the average velocity gradient (G) was 20 or 40 s−1. Nonlinear parameter estimation was performed to estimate two free parameters for the fractal model (the fractal dimension, DF, and the collision efficiency factor, α), and one free parameter (the collision efficiency factor, α) for the Euclidean model. Compared with the observed PSD, the simulation showed that the fractal rectilinear model was best, and that this model fit better for the larger size particles. The estimated DF was between 2.6 and 3.0. The research demonstrated that the αʹs have multiple values for the same observed data, depending on the coagulation model used. This finding is significant because α is currently used as a single value based on the conventional Euclidean rectilinear model.