  Step-emulsification is a microfluidic technique for droplet generation which
relies on the abrupt decrease of confinement of a liquid filament surrounded by
a continuous phase. A striking feature of this geometry is the transition
between two distinct droplet breakup regimes, the "step-regime" and
"jet-regime", at a critical capillary number. In the step-regime, small and
monodisperse droplets break off from the filament directly at a topographic
step, while in the jet-regime a jet protrudes into the larger channel region
and large plug-like droplets are produced. We characterize the breakup behavior
as a function of the filament geometry and the capillary number and present
experimental results on the shape and evolution of the filament for a wide
range of capillary numbers in the jet-regime. We compare the experimental
results with numerical simulations. Assumptions based on the smallness of the
depth of the microfluidic channel allow to reduce the governing equations to
the Hele-Shaw problem with surface tension. The full nonlinear equations are
then solved numerically using a volume-of-fluid based algorithm. The
computational framework also captures the transition between both regimes,
offering a deeper understanding of the underlying breakup mechanism.
