Jetting-to-bubbling transition in planar coflowing air-water sheets*

We study the transition between the two regimes experimentally observed when a plane air sheet surrounded by a coflowing water sheet discharges into stagnant air: a bubbling regime, which leads to the periodic break-up of the air sheet, and a jetting regime, where both sheets evolve slowly downstream without breaking. A jetting-to-bubbling transition curve has been experimentally obtained for a fixed liquid-to-gas thickness ratio, $h = h_{w,0}^*/h_{a,0}^*\simeq 5.27$, as a function on the values of two control parameters, namely, the Weber number, $We=\rho_w\,u_{w,0}^{*2}\,h_{a,0}^*/\sigma$, and the velocity ratio, $\Lambda=u_{w,0}^*/\bar u_{a,0}^*$, where $u_{w,0}^*$ and $\bar u_{a,0}^*$ are the water velocity and the mean air velocity at the exit slit, respectively, and $h_{a,0}^*$ and $h_{w,0}^*$ are the half-thicknesses of the air and water sheets at the exit. A linear spatiotemporal stability analysis, contemplating the downstream evolution of the sheets, shows good agreement with the experiments if a sufficiently long region of absolute instability is postulated.