## Bubble formation in a planar coflow configuration

We are also working on a different system to generate bubbles, a co-flow configuration to reduce the bubble size, but with an innovative geometry. It consists on a planar nozzle where an air film is confined by two parallel liquid streams. Figure 1. (a) Sketch of the side view of the experimental set-up indicating the main geometrical characteristics. The spanwise length of the air-water nozzle is 41.75 mm. (b) Detail of the air and water sheets at the exit of the nozzle showing the parameters of the physical problem.

We have found two different flow regimes, a bubbling and a jetting regime, and the jetting to bubbling transition has been characterized by means of experiments, theory and numerical simulations. The experimental measurements were carried out by recording high-speed movies in the spanwise view. Figure 2. (a)-(d) Sequence of experimental images corresponding to $We = rho_w,u_{w,0}^{*2},h_{a,0}^*/sigma=26.68$ at different water-to-air velocity ratios $Lambda$: (a) $Lambda = 0.167$, (b) $Lambda = 0.151$, (c) $Lambda= 0.134$ and (d) $Lambda = 0.110$. (e)-(h) Sequence of images obtained from the numerical simulations corresponding to $We = 24.9$ to different water-to-air velocity ratios: (e) $Lambda = 0.169$, (f) $Lambda =0.145$, (g) $Lambda = 0.127$ and (h) $Lambda = 0.112$.

This is a high-speed movie recorded at 10 000 fps showing the bubbling regime:

The numerical simulations were performed with the open source Computational Fluid Dynamics software OpenFOAM. The next movie shows the transition from jetting to bubbling calculated numerically. Notice that a long wavelenght pertutbation destabilizes, which is the varicose mode of instability, as observed in the experiments.

Our experiments have allowed us to obtain transition curves for the jetting to the bubbling regimes and for the bubbling to the jetting regimes in a wide region of the $We-Lambda$ parameter plane, which exhibit a hysteretic behavior. Motivated by the fact that the downstream variation of the flow field is slow in the jetting regime, we perform a linear spatiotemporal stability study under the assumption of quasi-parallel flow, with the aim at explaining if the transition from the jetting to bubbling regime is related to a convective/absolute instability transition, as it was obtained in the homologous cylindrical configuration. Nevertheless, it is shown that the transition is not directly related to a convective/absolute unstable flow, but a region of absolute instability of the order of the absolute wavelength at the nozzle exit, is necessary to observe the transition. Additionally, we propose a simple model that incorporates the downstream evolution of the sheets using boundary layer theory, showing an excellent agreement with the experiments. Figure 1.Comparison of the transition curve predicted by our full and simplified theoretical model (solid line and crosses respectively) with the experimental results and the numerical simulations

Carlos Martínez Bazán

Alejandro Sevilla Santiago

Javier Ruiz Rus

Enrique Sanmiguel Rojas

Cándido Gutiérrez Montes 