Path selection rules for droplet trains in single-lane microfluidic networks

摘要

We investigate the transport of periodic trains of droplets through microfluidic networks having one inlet, onenoutlet, and nodes consisting of T junctions. Variations of the dilution of the trains, i.e., the distance between drops,nreveal the existence of various hydrodynamic regimes characterized by the number of preferential paths taken bynthe drops. As the dilution increases, this number continuously decreases until only one path remains explored.nBuilding on a continuous approach used to treat droplet traffic through a single asymmetric loop, we determinenselection rules for the paths taken by the drops and we predict the variations of the fraction of droplets takingnthese paths with the parameters at play including the dilution. Our results show that as dilution decreases, thenpaths are selected according to the ascending order of their hydrodynamic resistance in the absence of droplets.nThe dynamics of these systems controlled by time-delayed feedback is complex: We observe a succession ofnperiodic regimes separated by a wealth of bifurcations as the dilution is varied. In contrast to droplet traffic innsingle asymmetric loops, the dynamical behavior in networks of loops is sensitive to initial conditions becausenof extra degrees of freedom.