Abstract
A two-dimensional air sheet in a surrounding liquid contracts under surface tension. We investigate numerically and analytically this contraction dynamics for a range of Ohnesorge numbers $Oh$. In a similar way as for liquid films, three contraction regimes can be identified based on the $Oh$: vortex shedding, smooth contraction and viscous regime. For $Oh\leqslant 0.02$, the rim can even pinch-off due to the rim deformations caused by the vortex shedding. In contrast with a liquid film that continuously accelerates towards the Taylor–Culick velocity when the surrounding fluid can be neglected, the air film contraction velocity first rises to a maximum value $U_{max}$ before decreasing due to the drag of the external fluid on the moving rim. This $U_{max}$ follows a capillary-inertial scaling at low $Oh$ and continuously shifts to a capillary-viscous scaling with increasing $Oh$. We demonstrate that the decreasing contraction velocity scales as $t^{-0.15}$, which is faster than the scaling $t^{-0.2}$ derived under the assumption of a constant drag coefficient. The transition between the capillary-inertial and capillary-viscous regimes can be characterised by the local time evolving Ohnesorge number $Oh_{\unicode[STIX]{x1D6FF}}$ based on the thickness of the rim. The oscillations of the rim appear at a critical local Weber number $We_{\unicode[STIX]{x1D6FF}}$. Then they follow a well-defined oscillation frequency with a characteristic Strouhal number. Beyond a local Reynolds number larger than 200, the oscillations become more irregular with more complex vortex sheddings, eventually leading to the pinch-off of the rim.