Droplet microfluidic networks as hybrid dynamical systems: Inlet spacing optimization for sorting of drops

The ability to manipulate drops is essential for integrating multiple processes in droplet microfluidics-based lab-on-a-chip devices. Examples of such droplet manipulation operations include sorting, sequencing, synchronization, and so forth. Microfluidic networks are promising platforms for performing these functionalities. This work explores the design of entry times of drops, a set of operating parameters, in a microfluidic network to achieve a desired functionality. Here, we specifically focus on sorting of drops at the exit of the network. For the first time, droplet microfluidic networks are perceived as hybrid dynamical systems. This viewpoint allows us to develop a methodology for designing the entry times of drops in microfluidic networks to achieve desired functionalities through the notion of constraint satisfaction. The solution to this constraint satisfaction problem provides entry times that result in the desired functionality. The proposed method allows one to establish the existence/nonexistence of entry time solutions for a desired functionality.