Synchronization of interacting waves in microfluidic oil-water interfaces*

Two oscillating fluid-fluid interfaces can interact hydrodynamically and serve as a model system to study synchronization behavior in fluids. Previously we have discovered the simultaneous breakup of droplets (in-phase synchronization) from two interacting oil-water interfaces in a microfluidics double T-junction, which transits from the alternating breakup mode (anti-phase synchronization) depending on the relative distance between the droplet protrusions. In this work, we investigate the intermediate regime between droplet generation and continuous jetting. In this regime, the oscillating interfaces of wavy shapes also exhibit hydrodynamic interaction depending on the distance between the interfaces. When the interfaces are close, we observe an anti-phase synchronization of the waves similar to G. I. Taylor's synchronous infinite sheets. However, when the distance between the interfacial waves increases, the state of in-phase synchronization can be stable, reminiscing biflagellate cells' motion. We study the relations of hydrodynamic synchronization modes of interfaces to parameters such as the flow rates, viscosity of fluids, and channel dimensions, as well as the shapes of the waves.