  Fully three-dimensional, time-dependent, direct simulations of the non-ideal
Navier-Stokes equations for a two-component fluid, shed light into the
mechanism which inhibits droplet breakup in step emulsifiers below a critical
threshold of the the width-to-height ($w/h$) ratio of the microfluidic nozzle.
Below $w/h \sim 2.6$, the simulations provide evidence of a smooth topological
transition of the fluid from the confined rectangular channel geometry to an
isotropic (spherical) expansion of the fluid downstream the nozzle step. Above
such threshold, the transition from the inner to the outer space involves a
series of dynamical rearrangements which keep the free surface in mechanical
balance. Such rearrangements also induce a backflow of the ambient fluid which,
in turn, leads to jet pinching and ultimately to its rupture, namely droplet
formation. The simulations show remarkable agreement with the experimental
value of the threshold, which is found around $w/h \sim 2.56$.
