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 UL L², with UL 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 c. For L c, breakup is eddy-time-limited, h (L) =O (^1/3L^-2/3) with the mean turbulent energy dissipation rate, whereas for L c, it is a rare-event process with h (L) L^5/3+, 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) L^-8/3- L^-2. 7, in striking agreement with the mean slope -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.
Andrea Mazzino (Fri,) studied this question.