Pertubations on a liquid curtain near break-up: Wakes and free edges

Abstract

We report experiments on liquid curtains falling between two vertical wires. The flow is mainly driven by gravity, so that the Weber number (We) (ratio of momentum flux to twice the surface tension) is close to zero at the top of the curtain and increases downstream, with the possible existence of a location where We equals 1 (which turns out to be a singular point in the sheet, in terms of waves propagation). In the present paper, we focus on the curtain response to localized perturbations, i.e., formation of either surface waves or free edges behind a thin needle touching the curtain, with a special emphasis to what happens near the break-up limit. We extract and compare the shapes of two kind of “wakes” left behind the obstacle: classical triangular wake of standing sinuous waves and stationary hole involving two free edges pinned on the needle. It is found that these two wakes are very similar for high enough We, but behave very differently when We reaches 1 from above; the sinuous wake disappears, while the “hole wake” still exists, and its shape becomes rounded. Below We=1, the hole can either stay stable, oscillate or expand and break the curtain. We provide exact analytical expressions for stationary free-edges that compare very well with experiments.