(142at) Formation of Droplets in Microfluidic T-Junction At Small Capillary Number

Microfluidic devices can generate monodisperse drops with precise control over their size and contents. The mechanism for drop formation in cross-junctions and T-junctions is well established. A drop grows into the main channel and obstructs the flow of the continuous phase, which then squeezes the interface of the forming drop until it breaks and a drop releases into the main channel. Drops formed by this squeezing mechanism have a volume that linearly scales with the ratio of flow rates, that is, for a fixed value of the capillary number (Ca). However, for non-fixed values of Ca, drop size also depends on the capillary number, because the fraction of the continuous phase flowing around forming drops is Ca-dependent. Current models for drop size prediction either ignore the flow of the continuous phase around forming drops completely or set it to a fixed value independent of the capillary number.

Here, we present a theoretical model that overcomes these limitations by taking into account these flows and their dependence on the capillary number. We found good quantitative agreement between our model and our experiments, which show that the fraction of the continuous phase flowing around forming drops significantly increases for decreasing Ca. To further validate our model, we formed partially-wetting drops, which do not allow the continuous phase to flow around them. As expected, their dynamics can be predicted based on continuity arguments only, in sharp contrast to non-wetting drops.