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Turbulence-informed kinetic theory of inertial-range fibre fragmentation
Summary
Scientists developed a new model to predict how tiny plastic fibers (like those from synthetic clothing) break apart in ocean water due to turbulent currents and waves. The model successfully explains why environmental studies consistently find certain sizes of plastic microfibers in the ocean. This research helps us better understand how plastic pollution spreads in marine environments, which is important since these microfibers can enter the food chain and potentially affect human health.
Slender fibres, including textile-derived microplastics, are abundant in aquatic environments and often extend beyond the Kolmogorov length scale. While breakup at dissipative scales has been characterised by velocity-gradient statistics, no closure existed for inertial-range spans where eddy turnover sets the clock. Here we develop a turbulence-informed kinetic theory of fibre fragmentation bridging turbulence forcing and slender-beam mechanics. First, we derive a load-to-curvature mapping showing that spanwise forcing generates peak bending moments scaling as $\sim U_L L^2$ , with $U_L$ the velocity increment across fibre length $L$ . Second, we construct a breakup hazard $h(L)$ from curvature-threshold exceedances over eddy-time blocks, which identifies a turbulence-defined critical span $\ell _c$ . For $L\gt \ell _c$ , breakup is eddy-time-limited, $h(L)=O(\bar \varepsilon ^{1/3}L^{-2/3})$ with $\bar \varepsilon$ the mean turbulent energy dissipation rate, whereas for $L\lt \ell _c$ , it is a rare-event process with $h(L)\propto L^{5/3+\alpha }$ , $\alpha$ denoting the small correction from intermittency. Embedding this hazard in a self-similar binary kernel yields a closed population-balance equation for the fragment distribution $n(L,t)$ with sources and sinks. The framework produces explicit predictions: intermittency-corrected curvature scalings, critical spans set by material and flow parameters, start-up and halving times linked to surf-zone conditions and scaling profiles in the cascade. The steady-state bulk distribution on the subcritical branch, with vertical removal induced by horizontal convergence, follows $n(L)\propto L^{-8/3-\alpha }\simeq L^{-2.7}$ , in striking agreement with the mean slope $\simeq -2.68$ observed for environmental microfibres in recent surveys. The reported variability of slopes is naturally explained in our framework by the coexistence of supercritical and subcritical branches together with $L$ -dependent removal-driven sinks.
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