A Simple Explicit Expression for the Flocculation Dynamics Modeling of Cohesive Sediment Based on Entropy Considerations

The flocculation of cohesive sediment plays an important role in affecting morphological changes to coastal areas, to dredging operations in navigational canals, to sediment siltation in reservoirs and lakes, and to the variation of water quality in estuarine waters. Many studies have been conducted recently to formulate a turbulence-induced flocculation model (described by a characteristic floc size with respect to flocculation time) of cohesive sediment by virtue of theoretical analysis, numerical modeling, and/or experimental observation. However, a probability study to formulate the flocculation model is still lacking in the literature. The present study, therefore, aims to derive an explicit expression for the flocculation of cohesive sediment in a turbulent fluid environment based on two common entropy theories: Shannon entropy and Tsallis entropy. This study derives an explicit expression for the characteristic floc size, assumed to be a random variable, as a function of flocculation time by maximizing the entropy function subject to the constraint equation using a hypothesis regarding the cumulative distribution function of floc size. It was found that both the Shannon entropy and the Tsallis entropy theories lead to the same expression. Furthermore, the derived expression was tested with experimental data from the literature and the results were compared with those of existing deterministic models, showing that it has good agreement with the experimental data and that it has a better prediction accuracy for the logarithmic growth pattern of data in comparison to the other models, whereas, for the sigmoid growth pattern of experimental data, the model of Keyvani and Strom or Son and Hsu model could be the better choice for floc size prediction. Finally, the maximum capacity of floc size growth, a key parameter incorporated into this expression, was found to exhibit an empirical power relationship with the flow shear rate.