Self-similar breakup of a liquid ligament with a solid particle

The breakup of thinning (stretching) liquid ligaments is strongly influenced by localized perturbations arising from impurities or suspended particles. Using numerical simulations and analytical modelling, we investigate the role of a solid particle on the breakup dynamics of a stretching liquid ligament. We show that particle-induced perturbations trigger a universal pinch-off dynamics in the viscous regime. Once the ligament surface approaches the particle, the subsequent breakup becomes self-similar and independent of the particle size. We derive an analytical expression for the pinch-off time based on the interplay between ligament stretching and Rayleigh-Plateau instability, which agrees quantitatively with simulations. Our results reveal a universal mechanism by which localized perturbations control the breakup of ligaments containing solid particles.