Predictive model for the size of bubbles and droplets created in microfluidic T-junctions.

We present a closed-form expression that allows the reader to predict the size of bubbles and droplets created in T-junctions without fitting. Despite the wide use of microfluidic devices to create bubbles and droplets, a physically sound expression for the size of bubbles and droplets, key in many applications, did not yet exist. The theoretical foundation of our expression comprises three main ingredients: continuity, geometrics and recently gained understanding of the mechanism which leads to pinch-off. Our simple theoretical model explains why the size of bubbles and droplets strongly depends on the shape of a T-junction, and teaches how the shape can be tuned to obtain the desired size. We successfully validated our model experimentally by analyzing the formation of gas bubbles, as well as liquid droplets, in T-junctions with a wide variety of shapes under conditions typical to multiphase microfluidics.