Escape from pinch-off during contraction of low-viscosity liquid sheets

In spraying and polymer processing, fluid is ejected from a nozzle or a die as a liquid sheet. The cross-sections of sheets are rectangular in shape but with rounded ends which contract towards each other due to surface tension forces. If sufficiently thin, sheets can rupture due to van der Waals forces. However, it has been shown by Burton and Taborek (PoF, 2007) that a contracting inviscid liquid sheet or a 2D drop can break up even in the absence of vdW forces. Here, we demonstrate that in the presence of small yet finite viscosity, contracting liquid sheets escape from pinch-off when vdW forces are absent. We investigate the problem using 2D free-surface flow simulations and the 1D slender-sheet equations, both of which show an escape from pinch-off. However, the physics underlying escape differs in 1D and 2D: in the former it is due to viscous resistance, but in the latter its cause can be attributed to vorticity generated by the free surface. The latter mechanism can only be observed in 2D simulations as the 1D model is vorticity-free at leading-order. Moreover, these two distinct mechanisms also give rise to different scaling laws relating the minimum sheet thickness when escape occurs to the Ohnseorge number (the ratio viscous stress to inertial and capillary stresses).