Theory of microfluidic step-emulsification

We present a comprehensive study of the microfluidic step-emulsification process for high-throughput production of monodisperse colloidal droplets. The ``microfluidic step emulsifier'' combines a shallow microchannel operating with two co-flowing immiscible fluids and an abrupt (step-like) opening to a deep and wide reservoir. Based on Hele-Shaw hydrodynamics, we determine the quasi-static shape of the fluid interface prior to transition to oscillatory step-emulsification at low capillary numbers. The transition threshold obtained from scaling arguments yields an excellent agreement with experimental data. A closed-form expression for the size of the droplets generated in the step-emulsification regime and derived using geometric arguments also shows a very good agreement with the experiment.