Investigation of the Sheltering Effects on the Mobilization of Microplastics in Open-Channel Flow

Microplastics (MPs) can be sheltered by bed grains, resulting in a higher threshold of mobilization compared with those moving on a smooth bed. Only one formula considering the sheltering effects has been proposed for the critical shear stress (<i>τ</i>_<i>c</i>) of MP mobilization by including the densities and sizes of MPs and bed grains, but it is inaccurate for MPs of certain materials such as PS and shows limitations in understanding the sheltering effects. Additionally, no method exists for the critical depth-averaged velocity (<i>U</i>_<i>c</i>). In this study, experiments were conducted measuring both <i>τ</i>_<i>c</i> and <i>U</i>_<i>c</i> of MPs (made of PA, PVC, and PET) deposited on rough beds of different roughnesses, with a focus on the sheltering effects. A power law relationship between <i>τ</i>_<i>c</i> and the density and size of MPs was found, and a new formula for estimating <i>τ</i>_<i>c</i> was proposed for MPs, which reduced the errors by approximately 40% compared with that of the previous formula (27.8%). To explicitly quantify the sheltering effects in MP mobilizations, hiddenness (<i>ΔZ</i>), exposure (<i>ΔH</i>), and longitudinal exposure (<i>ΔX</i>) were introduced, all of which were observed to follow a normal distribution. A semiempirical method for <i>U</i>_<i>c</i> was then proposed incorporating the new measures, which reduced the errors by around 70% compared to the methods developed for estimating the <i>U</i>_<i>c</i> values of sediments.