Droplet traffic in microfluidic networks: a simple model for understanding and designing.

We propose a simple model to analyze the traffic of droplets in microfluidic "dual networks." Such functional networks which consist of two types of channels, namely, those accessible or forbidden to droplets, often display a complex behavior characteristic of dynamical systems. By focusing on three recently proposed configurations, we offer an explanation for their remarkable behavior. Additionally, the model allows us to predict the behavior in different parameter regimes. A verification will clarify fundamental issues, such as the network symmetry, the role of the driving conditions, and of the occurrence of reversible behavior. The model lends itself to a fast numerical implementation, thus can help designing devices, identifying parameter windows where the behavior is sufficiently robust for a device to be practically useful, and exploring new functionalities.