Kinematic assessment of floc formation using a Monte Carlo model

A simple stochastic model is proposed to simulate floc formation due to simultaneous aggregation and breakage processes. The model is based on the constant-number Monte Carlo method where the number of flocs is kept constant during simulations. To produce equilibrium floc-size distributions, it uses established models of flocculation and new simple formulations of breakage probability and of the probability of producing fragments of a given size from broken flocs. The concept of fractal geometry is used to describe the geometry of flocs. The maximum size of flocs allowed, the median size of component particles, and their density are the main inputs needed to simulate floc formation. Simulated steady-state floc-size distributions were compared with field data observed at different locations, and good agreement was obtained. Dimensional analysis applied to measured and simulated data revealed that floc-size distributions are self-similar and can be described by the same function, regardless of the conditions of their formation.