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Fully three-dimensional, time-dependent, direct simulations of the non-idealNavier-Stokes equations for a two-component fluid, shed light into themechanism which inhibits droplet breakup in step emulsifiers below a criticalthreshold 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 topologicaltransition of the fluid from the confined rectangular channel geometry to anisotropic (spherical) expansion of the fluid downstream the nozzle step. Abovesuch threshold, the transition from the inner to the outer space involves aseries of dynamical rearrangements which keep the free surface in mechanicalbalance. Such rearrangements also induce a backflow of the ambient fluid which,in turn, leads to jet pinching and ultimately to its rupture, namely dropletformation. The simulations show remarkable agreement with the experimentalvalue of the threshold, which is found around $w/h \sim 2.56$.

Jetting to dripping transition: critical aspect ratio in step emulsifiers