Two decades of research on droplet formation in microchannels have led to the widely accepted view that droplets form through the squeezing mechanism when interfacial forces dominate over viscous forces. The initially surprising finding that the volume of the droplets is insensitive to the relative importance of these two forces is nowadays well understood from the constrained deformation of the droplet interface during formation. In this work, we show a lower limit of the squeezing mechanism for droplets produced in microfluidic cross-junctions. Below this limit, in the leaking regime, which was recently discovered for droplets produced in T-junctions, the volume of the produced droplets strongly depends on the relative importance of interfacial and viscous forces, as captured by the capillary number. We reveal a fundamental difference in the mechanisms at play in the leaking regime between T- and cross-junctions. In cross-junctions, the droplet neck elongates substantially, and unlike the case of the T-junction, the magnitude of this elongation depends strongly on the value of the capillary number. This elongation significantly affects the final droplet volume in a low capillary number regime. Generalizing the classical squeezing law by lifting the original assumptions and incorporating both identified mechanisms of leaking through gutters and neck elongation, we derive a model for droplet formation and show that it agrees with our experiments.

While shear emulsification is a well understood industrial process, geometrical confinement in microfluidic systems introduces fascinating complexity, so far prohibiting complete understanding of droplet formation. The size of confined droplets is controlled by the ratio between shear and capillary forces when both are of the same order, in a regime known as jetting, while being surprisingly insensitive to this ratio when shear is orders of magnitude smaller than capillary forces, in a regime known as squeezing. Here, we reveal that further reduction of—already negligibly small—shear unexpectedly re-introduces the dependence of droplet size on shear/capillary-force ratio. For the first time we formally account for the flow around forming droplets, to predict and discover experimentally an additional regime—leaking. Our model predicts droplet size and characterizes the transitions from leaking into squeezing and from squeezing into jetting, unifying the description for confined droplet generation, and offering a practical guide for applications.