Comparison between two analytical models to study the flocculation of mineral clay by polyelectrolytes

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In the present article two flocculation models, given in Chassagne (2021) (LG model) and Winterwerp (1998) (S model) are compared. Both models give the time evolution dL/dt where L is the size of a particle undergoing flocculation, and t is the time. The LG model is based on logistic growth theory, whereas the S model is based on the theory originally derived by Smoluchowski. Both models have the advantage of easy implementation in, for instance, large-scale sediment transport numerical models. However, it is found that they do not obey the same kinetics. A series of laboratory experiments is presented where the flocculation of a mineral clay by polyelectrolyte is studied as a function of clay concentration and shear rate. From modelling these experiments, it is found that the LG model reproduces the time dependence of the floc sizes found experimentally, whereas the S model does not. It is shown that the LG model can be used to model the data over the whole range of clay concentration and shear investigated. Based on the study presented in this article, it was found that the average floc growth in time for the clay type and conditions applied in the experiments could be modelled by: dL/dt=40×10−4G0.75×[exp(−2×10−4G0.75t)]/[1+20exp(−2×10−4G0.75t)]L.