Power-Law Transition of Drop-impact Crater Collapse

The collapse of immiscible drop-impact craters is studied with two simultaneous ultra-high-speed video cameras. Similar to previous same-liquid impacts$^{\mathrm{1}}$, fastest jets emerge from a dimple at the bottom of the crater which contracts without bubble pinch-off. Different from the capillary-inertial collapse of a drop, where the neck radius scales as $R$\textasciitilde $t^{\mathrm{2/3}}$, the pure inertial collapse follows a power law of $R$\textasciitilde $t^{\mathrm{1/2}}$, where we find an exponent \textasciitilde 0.55 which is explained by a slow logarithmic approach$^{\mathrm{2}}$. For the pinch-off case, we discover a power-law transition from capillary-inertial to inertial when approaching the singularity for both immiscible and miscible liquid impacts, with a cross-over time \textasciitilde 100 $\mu $s before the pinch-off. The capillary-inertial part has a prefactor $C=R$/($\sigma t^{\mathrm{2}}$/$\rho )^{\mathrm{1/3}}=$1.75$\pm $0.2 based on pool properties, while the prefactor for inertial collapse, $C_{\mathrm{inertia}}=R$/(\textit{DUt})$^{\mathrm{0.5}}=$0.30$\pm $0.04, is found. Capillary waves are found to mold the air-dimple into different collapse shapes, such as bamboo and telescopic forms. The finest jets are only 12 $\mu $m in diameter and the normalized jetting speeds are up to one order of magnitude larger than for jets from bursting bubbles. The singular jets show the earliest cross-over into the inertial regime. The fastest jets can pinch off a toroidal micro-bubble from the cusp at the jet base. 1. Thoroddsen \textit{et al}., \textit{J. Fluid Mech.}, \textbf{848}$, $R3 (2018). 2. Eggers \textit{et al}., \textit{Phys. Rev. Lett.}, \textbf{98}, 094502 (2007). 3. Yang \textit{et al.}, Submitted to \textit{J. Fluid Mech.} (2020).