Breakup and coalescence of particle aggregates at the interface of turbulent liquids

The breakup and coalescence of particle aggregates confined at the interface of turbulent liquid layers are investigated experimentally and theoretically. In particular, we consider conductive fluid layers driven by Lorentz forces and laden with millimetre-scale floating particles. These form aggregates held together by capillary attraction and disrupted by the turbulent motion. The process is fully characterised by imaging at high spatio-temporal resolution. The breakup frequency $\varOmega$ is proportional to the mean strain rate and follows a power-law scaling $\varOmega \sim D^{3\text{/}2}$ , where $D$ is the size of the aggregate, attributed to the juxtaposition of particle-scale strain cells. The daughter aggregate size distribution exhibits a robust U-shape, which implies erosion of small fragments as opposed to even splitting. The coalescence kernel $\varGamma$ between pairs of aggregates of size $D_{1}$ and $D_{2}$ scales as $\varGamma \sim ( D_{1} + D_{2} )^{2}$ , which is consistent with gas-kinetic dynamics. These relations, which apply to regimes dominated both by capillary-driven aggregation and by drag-driven breakup, are implemented into the population balance equation for the evolution of the aggregate number density. Comparison with the experiments shows that the framework captures the observed distribution for aggregates smaller than the forcing length scale.