Transition Patterns of Multimodality in Suspended Sediment Size Distribution During Flocculation Process and Equilibrium PSD Modes

The transport and fate of cohesive sediments in estuarine and coastal waters, including minerals, nutrients, and contaminants, are significantly influenced by flocculation processes involving particle aggregation and breakage. These dynamic flocculation processes lead to frequent temporal variations in the sizes of suspended flocs, resulting in a particle size distribution (PSD) that can span several orders of magnitude. In estuarine systems, transitions between different PSD patterns are commonly observed, yet the mechanisms driving these transitions remain inadequately understood, contributing to great challenges in predicting cohesive sediment dynamics and thus material transport. This is partly because of the challenges in simulating the temporal evolution of PSD involving these transitions. To tackle this problem, we propose an improved sediment flocculation model by integrating the population balance equation (PBE), fixed pivot algorithm, power-law fractal theory, and typical theory of aggregation or breakage. The proposed model is capable of capturing these transitions. Our numerical results reveal that transition patterns and equilibrium PSD modes are highly sensitive to the shear rate. Specifically, multimodal PSDs (or any non-unimodal form) are generally unstable and tend to transfer towards a unimodal distribution under conditions of higher turbulent shear G (e.g., G = 8, 10, 20, 35 s−1) for the range of parameters investigated in this study. Additionally, we find that an initial unimodal PSD can transfer to a multimodal PSD under lower shear conditions (e.g., G = 2 s−1), suggesting that multimodal equilibrium PSDs can exist even in the absence of organic matter for the range of parameters investigated in this study (this is a model-based prediction requiring further validation). Finally, evaluation of the sedimentation effect based on modified Stokes equations suggests that these cross-mode transitions may contribute to significant variation in settling flux.