Competition between Local Collisions and Collective Hydrodynamic Feedback Controls Traffic Flows in Microfluidic Networks M. Belloul, 1 W. Engl, 2 A. Colin, 2 P. Panizza, 1, * and A. Ajdari 3 1 IPR, UMR CNRS 6251, Campus Beaulieu, Universite ´ Rennes 1, 35042 Rennes, France 2 LOF, CNRS-Rodia 5258, Universite ´ Bordeaux 1, 33608 Pessac, France 3 Physico-Chimie The ´orique, UMR CNRS Gulliver 7083, 10 rue Vauquelin, 75231 Paris, France (Received 11 December 2008; published 13 May 2009) By studying the repartition of monodisperse droplets at a simple T junction, we show that the traffic of discrete fluid systems in microfluidic networks results from two competing mechanisms, whose signifi- cance is driven by confinement. Traffic is dominated by collisions occurring at the junction for small droplets and by collective hydrodynamic feedback for large ones. For each mechanism, we present simple models in terms of the pertinent dimensionless parameters of the problem. DOI: 10.1103/PhysRevLett.102.194502 PACS numbers: 47.61.k, 47.55.D When studying flows of dispersions in microfluidic net- works, a central goal is to understand the mechanisms that govern flow partitioning at the nodes. Known as ‘‘plasma skimming’’ in blood microcirculation, this issue is funda- mental for well functioning cardiovascular systems [1], whereas in digital microfluidic devices it is essential for the traffic flow control of droplets [2]. This problem is also challenging in the field of nonlinear physics. For instance, consider the simplest situation where a droplet train reaches a T intersection and ask how the droplets divide between the two outlets. When a droplet arrives at the junction, it flows into the arm having the lowest hydro- dynamic resistance. Since the presence of droplets in mi- crochannels increases the resistance to flow, there is a nonlinear collective feedback between successive droplets’ trajectories [3,4]. The outcome turns out to be a complex nonlinear dynamical system, now drawing much interest as it lays the foundations of promising applications for the design of logical microfluidic devices [5–7]. In this Letter, we demonstrate the crucial role played by confinement and dilution on the traffic of discrete fluid elements in microfluidic networks. To address this issue, we study the repartition of trains of monodisperse droplets at a T junction. By systematically varying the asymmetry of the junction, the dilution, and the confinement of the droplets, we show that droplet traffic results from the competition of two distinct physical mechanisms, gov- erned by the confinement. Traffic is dominated by local collisions, occurring at the junction for small droplets, whereas it results from collective hydrodynamic feedback (CHF) for large ones. For each regime, simple models, yielding universal behaviors in terms of the relevant di- mensionless numbers of the problem, are proposed and tested in experiments. These models capture the main features of the problem and provide a general picture of traffic flows in microfluidic networks. Experiments.—In our experiments (inset, Fig. 1), a pe- riodic train of water-oil monodisperse droplets is produced using a double cylindrical capillary module, consisting of a calibrated syringe needle (diameter 510 m or 230 m) centered in a tube (radius r c ¼ 750 m). Using two sy- ringe pumps (Harvard PHD 2000), millipore water (vis- cosity  w ¼ 1 mPa s) and sunflower oil (from Maurel Inc., France, viscosity  o ¼ 50 mPa s) are, respectively, in- fused through and around the central needle, so that drop- lets form at the tip of the needle with a constant rate of production, f. By fine-tuning both Q w and Q f o , the respec- tive flow rates of water and oil, we control , the droplet volume. An additional infusion of oil performed down- stream, at constant flow rate Q d o , increases , the distance between two successive droplets while keeping their size unchanged. The behavior of this train at a bifurcation is studied by directing it towards a simple asymmetric T junction whose outlets have different lengths, L 2 >L 1 , but the same cross sections and whose two extremities are connected to the same air pressure P o . Images of the 0.5 1 1.5 2 0 1 2 3 0 0.2 0.4 0.6 0.8 1 ↔ FIG. 1.  () and L d (d), versus . The dashed line corre- sponds to the asymptotic model of [9]:  ¼ 2  4 3þ2  2 where  ¼  o  w . Inset: Schematic of the setup. PRL 102, 194502 (2009) PHYSICAL REVIEW LETTERS week ending 15 MAY 2009 0031-9007= 09=102(19)=194502(4) 194502-1 Ó 2009 The American Physical Society