The physical mechanisms of step emulsification

We revisit the physical balance that takes place when an interface between two immiscible fluids reaches a step change in the height of a microchannel. This situation leads to the production of droplets in a process known as 'step emulsification'. However, the mechanism that is responsible for the drop breakup and that determines its size has not been explained in simple terms. We propose a geometric model for drop breakup based on a quasi-static balance between the curvature of the thread inside the inlet channel and the curvature of the bulb downstream of the step. We find that the confinement limits the lowest values of curvature that can be adopted by the thread. In contrast, the bulb curvature decreases as its size increases, which leads to a critical bulb radius beyond which the two regions cannot be in static equilibrium. This leads to a flow which breaks the bulb into a droplet. The critical bulb radius predicted by the geometric analysis is in good agreement with experimental measurements for different step and inlet channel geometries. The radius of the drop that detaches is therefore bounded from below by this value and increases slowly with the dispersed phase flow rate.