Theoretical framework for modeling flocculation in cohesive sediments with variable yield strength

While several models have been developed to describe the temporal evolution of flocs, many assume constant yield strength, which limits their applicability under different flow and sediment conditions. This study aims to improve existing flocculation models by introducing a more accurate parameterization of the floc yield strength, a critical factor in the breakup process. Building on previous work on variable yield strength, a new theoretical formulation for the yield strength of cohesive sediments is derived based on inter-particle bonding within a floc and under more realistic physical assumptions. The proposed model challenges the earlier conceptions, which suggested a direct correlation between floc size and yield strength. This formulation is integrated into a flocculation model based on a constant fractal dimension and validated with experimental data on the temporal evolution of floc size. The study also derives equations for equilibrium floc size and yield strength and demonstrates accurate predictive capabilities. Comparisons with the previous model of Son and Hsu (2009) show significant improvements in capturing the dynamic behavior of floc growth, especially during the transient phase. The results indicate that the proposed model is more consistent with measured floc sizes in several case studies and suggest that the proposed model provides a more robust understanding of floc formation processes.