On the hydrodynamic focusing for producing microemulsions via tip streaming

In this work we study experimentally and numerically the stability of hydrodynamic focusing to produce microemulsions. The jetting regime was produced experimentally for the lowest outer viscosity, while microdripping was obtained for the highest outer viscosity. The liquid ejection for small capillary numbers stabilizes as the distance between the feeding capillary and the focusing orifice decreases. The comparison between confined selective withdrawal and stretched flow focusing for the largest outer viscosity shows that confined selective withdrawal significantly enhances the stability of the microdripping mode, which entails a significant reduction of the minimum value of the droplet diameter. When surfactants are dissolved in the inner liquid at sufficiently large concentrations, we observe a significant decrease in both the minimum flow rate leading to tip streaming and the droplet diameter. The surfactant monolayer stabilizes the meniscus and promotes the transition from microdripping to jetting. The global stability analysis shows that jetting via tip streaming becomes unstable due to the growth of an oscillatory perturbation. The unstable perturbation affects the tapering meniscus for the lowest outer viscosity, which explains why the meniscus oscillates in the experiments. The critical flow rate ratio is accurately predicted by the global stability analysis in most of the experiments with the lowest outer viscosity. For the highest outer viscosity, the global stability analysis correctly predicts the microdripping mode and allows one to calculate the droplet emission frequency in that mode.