title: Passive droplet trafficking at microfluidic junctions under geometric and flow asymmetries.
abstract: When droplets enter a junction they sort to the channel with the highest flow rate at that instant. Transport is regulated by a discrete time-delayed feedback that results in a highly periodic behavior where specific patterns can continue to cycle indefinitely. Between these highly ordered regimes are chaotic structures where no pattern is evident. Here we develop a model that describes droplet sorting under various asymmetries: branch geometry (length, cross-section), droplet resistance and pressures. First, a model is developed based on the continuum assumption and then, with the assistance of numerical simulations, a discrete model is derived to predict the length and composition of the sorting pattern. Furthermore we derive all unique sequences that are possible for a given distribution and develop a preliminary estimation of why chaotic regimes form. The model is validated by comparing it to numerical simulations and results from microfluidic experiments in PDMS chips with good agreement.
authors.affiliation: Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, Canada.
authors.forename: Tomasz
authors.initials: T
authors.lastname: Glawdel
authors.forename: Caglar
authors.initials: C
authors.lastname: Elbuken
authors.forename: Carolyn
authors.initials: C
authors.lastname: Ren