Predicting the flocculation kinetics of fine particles in a turbulent flow using a Budyko-type model

Through an analogy with the Budyko curves in catchment hydrology science, this study defines the supply and demand limits for the flocculation system of cohesive particles (the supply limit can be represented by the potential floc size growth, whereas the demand limit can be represented by the steady-state floc size) and attempts to adopt Budyko-type models to estimate the temporal evolution of floc size during flocculation. Seventeen experimental datasets are collected to test the accuracy of the Budyko model with an average high correlation coefficient of 0.9784 and average low relative error and root mean squared error values of 0.1304 and 0.0605, respectively. Either the potential floc size growth or the steady-state floc size is a monotonic function of the flow shear rate, and a simple empiric power law function can be used to describe them. Other Budyko-type models are also found to show good prediction accuracies against the experimental datasets. This study indicates that Budyko-type models have potential as a good addition to existing flocculation models for predicting the temporal variation in the size population of flocs in a turbulent flow, provided that some coefficients have been calibrated by limited data points prior.