Mechanistic Flocculation Model Incorporating the Fractal Properties of Settling Particles

A mechanistic isopercentile flocculent sedimentation model was derived from basic fractal behavior of colloidal particles in turbid water. The model showed the fractal nature of growing particles, which was in opposition to the most commonly used semiempirical models that assume growth of particles as compact spheres. The model development was based on particle size distribution (PSD) analysis results from settling batch column experiments. The experimental batches were conducted at initial concentrations ranging from 150 to $350\mathrm{mg}/\mathrm{L}$ and coagulant doses in the range of 10–$70\mathrm{mg}/\mathrm{L}$. From the collected PSD data, a fractal dimension $D$ ($L$), fractal settling velocity $a_v$ ($L{T}^{-1}$), and model-fit parameters affecting the shape of isopercentile removal trajectories were obtained. The resulting calibrated model performed better than previously proposed semiempirical models. Lower degrees of fitting error, represented by sum of squares error (SSE) = 0.44–0.90, were achieved using the new model, which was much lower than the SSE range of 3.10–9.44 from previous models fitted to the same data set. The improved fitness of the new model was attributed to its ability to capture the fractal growth property of settling particles, which resulted in incipient buoyancy and settling deceleration of the formed flocs–properties that were not represented in previous models.