Revisiting flocculation process of cohesive sediments with variable yield strength

Accurate prediction of floc strength is essential for understanding aggregation–breakup dynamics in cohesive suspensions and for reliable integration into sediment transport models. Earlier formulations linked yield strength to interparticle bonding and floc geometry, but they had key shortcomings. These included unphysical negative interparticle distances, equilibrium size relations that required iterative solvers, and unrealistic behavior regarding fractal dimension. In this study, we present a revised framework that introduces a compact empirical expression for the interparticle distance, eliminating non-physical values and removing the structural singularity in the yield strength equation. The reformulation yields an explicit closed-form solution for equilibrium floc size, substantially simplifying calibration and interpretation. In addition, the coupled treatment of size and strength provides direct evaluation of characteristic buildup and breakup time scales, enabling dynamic responses to vary consistently with evolving floc strength and microstructure. Heat-map analyses across shear rate and solid volume fraction reveal bounded, physically consistent trends: compact aggregates strengthen with growth, whereas tenuous flocs attain maximum strength at intermediate sizes, challenging the classical assumption that larger flocs are always stronger. The new formulation ensures smooth, stable predictions across parameter space and improves agreement with experimental observations, providing a transparent, singularity-free basis for process-based modeling of cohesive sediments in environmental and engineering applications.