Air sheet contraction

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 . In a similar way as for liquid films, three contraction regimes can be identified based on the : vortex shedding, smooth contraction and viscous regime. For , 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 before decreasing due to the drag of the external fluid on the moving rim. This follows a capillary-inertial scaling at low and continuously shifts to a capillary-viscous scaling with increasing . We demonstrate that the decreasing contraction velocity scales as , which is faster than the scaling 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 based on the thickness of the rim. The oscillations of the rim appear at a critical local Weber number . 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.