Breakup of droplets in branching micro-channels

The segmented flow of droplets and bubbles in channels of micrometer size occurs in numerous (bio) chemistry applications and an important question is whether (and how) a droplet (or bubble) entering a branching micro-channel breaks. In this work, we address this question using the T-junction as a paradigm. We performed experiments at low capillary numbers, with droplets of different sizes entering a T-junction. Our experiments show (i) the existence of stable non-breaking droplets (trapped inside the T-junction) at sufficiently low speeds, and (ii) that the critical speed at which the droplets break differs considerably from the scaling rules proposed in the literature. We developed a semi-empirical model that takes into account the 3D nature of the problem (with the flow around the droplet, through the gutters), which is not done in the scaling models proposed in the literature. Our model agrees well with the experimentally observed scaling and explains the change of scaling at low capillary numbers.