The oil extractor can remove controlled volumes of oil from an emulsion. To control the amount of oil removed, the outlet pressure of the oil extraction channel is controlled by gravity. Alternatively, for better reproducibility, a syringe pump in the withdrawing mode can be used to extract a controlled flow rate of oil from the extraction channel. For low draw rates, the droplets at the outlet are still unpacked, but for moderate and high draw rates, the droplets pack and order due to their monodispersity. High packing gives rise to plug flow, in which droplets travel through the delay line at equal speed.