Breakup of thin liquid sheets through hole–hole and hole–rim merging

The dynamics of the merging of two distinct holes (hole–hole) and a single hole with a straight rim (hole–rim) are investigated using three-dimensional numerical simulations. Thin liquid sheets with thicknesses ranging from $25$ to 150\ μ m are considered using air/water conditions. Preliminary simulations of a single hole expansion and the retraction of a bounded liquid sheet edge have shown good agreements with the well-known Taylor–Culick end rim regime. For the hole–hole and the hole–rim cases, our computations reveal that the liquid bridge, formed after the merging, is subjected to three different motions: the extension of the bridge, the mid-plane contraction and vertical/horizontal oscillations of its diameter, with an exponentially decaying amplitude. The mid-plane diameter of the liquid bridge is shown to decrease linearly with time for the hole–rim case while a faster quadratic decrease is observed for the hole–hole case. The small ratio of the extension rate to the capillary contraction rate indicates a slow extension limit of the bridge. However, the liquid bridge does not contract and pinch off on a single point, as predicted in the literature, and its central part forms a cylindrical ligament. Thus, this cylindrical part pinches off at its ends and forms a receding ligament with bulbous ends which can either detach by the end-pinching mechanism or remain attached, recoil and merge into a single large drop. The size of the formed drop, in the case where the ligament does not break, is later expressed as a power-law function of the initial liquid sheet thickness.