Commensurability-driven structural defects in double emulsions produced with two-step microfluidic techniques

The combination of two drop makers such as flow focusing geometries or ┬ junctions is commonly used in microfluidics to fabricate monodisperse double emulsions and novel fluid-based materials. Here we investigate the physics of the encapsulation of small droplets inside large drops that is at the core of such processes. The number of droplets per drop studied over time for large sequences of consecutive drops reveals that the dynamics of these systems are complex: we find a succession of well-defined elementary patterns and defects. We present a simple model based on a discrete approach that predicts the nature of these patterns and their non-trivial scheme of arrangement in a sequence as a function of the ratio of the two timescales of the problem, the production times of droplets and drops. Experiments validate our model as they concur very well with predictions.