[A-CG48] Water and sediment dynamics from land to coastal zones

[ACG48-P03] Theoretical Considerations on Stickiness Estimation from Tank Experiments and Attempts to Incorporate Polydispersity

*Keisuke Nishino^1,2, Yutaka Yoshikawa¹ (1.Kyoto University Graduate School of Science, 2.Central Research Institute of Electric Power Industry)

Keywords:particles, coagulation, polydispersity, stickiness, stirred tank

Coagulation of suspended particles, also known as flocculation or aggregation, is a ubiquitous phenomenon observed in various geophysical contexts, such as cohesive sediment in estuarine zones, phytoplankton in ocean surface, or volcanic ash. To numerically model the coagulation process, the stickiness parameter—also referred to as flocculation efficiency or stability factor depending on the discipline—is critical. The stickiness parameter reflects the particle composition and the forces governing particle interactions. However, such detailed information is not always available, and numerical simulations often assume a constant stickiness parameter, which is estimated through field or tank experiments. Edzwald et al. (1974) proposed a convenient experimental method to estimate the stickiness parameter from stirred tank experiments, and this method has been developed by subsequent studies. This method is based on the Smoluchowski equation and relates the reduction rate of particle number due to coagulation in a closed tank to the stickiness parameter. However, this method assumes a critical condition regarding the particle size distribution (PSD) used in the experiments, therefore we consider the applicability of this method is limited. In this study, we investigated how the PSD shape distorts the estimated stickiness parameter and explored an improved estimation method that incorporates a correction coming from the PSD shapes. As our first result, we analytically showed that the previous method is valid only for mono-dispersed particles. For poly-dispersed particles, the method yields only an apparent stickiness rather than the true stickiness. The correction factor required to convert the apparent stickiness into the true stickiness can be explicitly evaluated based on the moments of radius derived from the PSD shape. Using these theoretical outcomes, we developed a novel estimation method that incorporates the poly-dispersity of the PSD, using simple stirred tank experiments similar to the previous method. We performed tank experiments as equivalent numerical simulations using Lagrangian cloud model (Riechelmann et al., 2012; Nishino and Yoshikawa, 2014). The realistic poly-disperse PSDs of suspended particles were reconstructed from tank experiments performed in previous literatures (Edzwald et al., 1974; Ou et al., 2016). As a result, we showed that the initial correction factor calculated from the initial PSD could not yield the stickiness estimation in high precision: We should consider the time change of the correction factor (i.e., the temporal transformation of the PSD) at the same. Therefore, our method requires additional measurements of the PSD shape (e.g., using LISST) compared to the previous method, but it enables high-precision estimation of the true stickiness (the relative error < 1%) even for realistic poly-disperse PSDs.