Nonlinear phenomena in two-phase flows in microfluidic systems

Experiments with drops produced in soft (PDMS) microfluidic systems show interesting behavior that underline the importance of nonlinear phenomena, which may be understood using dynamical systems theory and be exploited for practical purposes. First, water droplets are driven in oil along a main channel, across which a fraction of the flow is sucked off. Droplet sizes and velocites are measured by tracking interface velocities using PIV. In these experiments, there are two regimes: when the derivated flow-rate is small, the continuous phase can be sucked off without breaking up the droplets. When more flow is sucked off, the droplets break up to generate two droplets, one flowing in the main channel, the other in the derivation. Our theoretical explanation for the break-up condition fits remarkably well with hundreds of different experimental conditions. Second, we placed actuators close to a T junction where water droplets are produced in an oil stream. When the coupling between the flow and the actuation is large, the actuation accurately imposes the droplet sizes and emission frequency. More complex behaviour occurs when the coupling is weaker: frequency locking states and quasiperiodic regimes, organized into Arnold tongues and devil staircases. This behavior is captured by the circle map, a standard model for nonlinear coupling between an external forcing (the actuator) and an oscillating process (drop formation).