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Step-emulsification is a microfluidic technique for droplet generation whichrelies on the abrupt decrease of confinement of a liquid filament surrounded bya continuous phase. A striking feature of this geometry is the transitionbetween two distinct droplet breakup regimes, the "step-regime" and"jet-regime", at a critical capillary number. In the step-regime, small andmonodisperse droplets break off from the filament directly at a topographicstep, while in the jet-regime a jet protrudes into the larger channel regionand large plug-like droplets are produced. We characterize the breakup behavioras a function of the filament geometry and the capillary number and presentexperimental results on the shape and evolution of the filament for a widerange of capillary numbers in the jet-regime. We compare the experimentalresults with numerical simulations. Assumptions based on the smallness of thedepth of the microfluidic channel allow to reduce the governing equations tothe Hele-Shaw problem with surface tension. The full nonlinear equations arethen solved numerically using a volume-of-fluid based algorithm. Thecomputational framework also captures the transition between both regimes,offering a deeper understanding of the underlying breakup mechanism.

Capillary focusing close to a topographic step: Shape and instability of confined liquid filaments