Using Shannon entropy to model turbulence-induced flocculation of cohesive sediment in water

Turbulence-induced flocculation of cohesive fine-grained sediment plays an important role in the transport characteristics of pollutants and nutrients absorbed on the surface of sediment in estuarine and coastal waters via the complex processes of sediment transport, deposition, resuspension and consolidation. In this study, the concept of Shannon entropy based on probability is applied to modelling turbulence-induced flocculation of cohesive sediment in water. Using the hypothesis regarding the cumulative distribution function, the function of floc size with flocculation time is derived by assuming a characteristic floc size as a random variable and maximizing the Shannon entropy, subject to certain constraints. The Shannon entropy-based model is capable of modelling the variation in floc size as the flocculation time progresses from zero to infinity. The model is tested against some existing experimental data from the literature and against a few deterministic mathematical models. The model yields good agreement with the observed data and yields better prediction accuracy than the other models. The parameter that has been incorporated into the model exhibits an empirical power-law relationship with the flow shear rate. An empirical model formulation is proposed, and it exhibits high prediction accuracy when applied to existing experimental data.