Ultrafast Inertial-Capillary Self-Healing and Dynamic Rupture of Liquid Membranes

Liquid membranes ("e.g., soap films") can self-heal after ballistic impact by sealing the impact cavity before the film thins to rupture, yet the key parameters and thresholds governing whether a film self-heals or ruptures have not been established to date. Here, we establish scaling relationships for the self-healing (closure) time and the critical impact speed based on nearly 1000 impact tests using spheres of varying size, speed, and wettability. We show that healing proceeds via cavity formation followed by pinch-off; successful sealing requires that surface-tension-driven closure outpaces impact-induced thinning. Closure occurs on sub-millisecond to millisecond time scales─much faster than diffusion-based self-healing in solids─highlighting liquid membranes as an ultrafast self-healing material class. The upper limit for self-healing is captured by a critical Weber number (We_critical ≈ 13,052), beyond which healing is unlikely. These findings define the operational self-healing regime for liquid membranes and establish the practical limits for employing liquid membranes in systems where self-healing is essential to maintain functionality.