Increases in complexity attainable in molecular self-assembly necessitates both advanced molecular design as well as microenvironmental control. Such control is offered by microfluidics, where precise chemical compositions and gradients can be readily established. A droplet microfluidic platform combining upstream step emulsification with downstream hydrodynamic microtraps has been designed to facilitate molecular self-assembly. The step emulsification rapidly generates uniform droplets which act as reaction chambers. The hydrodynamic microtraps hold droplets against the flow ensuring they are exposed to a continuous supply of fresh fluid for constant reagent extraction and/or delivery. Additionally, the droplet immobilization permits real-time droplet characterization and reaction monitoring. Subsequently, droplets can be released from the traps through flow reversal, allowing post-process characterization. The microfluidic system was demonstrated by the phase separation of lyotropic droplets. Ethanol/water droplets were created in a continuous ambient squalene/monoolein microflow, causing the continuous extraction of ethanol from the droplets and delivery of monoolein from the ambient microflow. Unlike conventional bulk techniques and continuous microfluidics, where finite microchannel lengths necessarily impose limits to the extent to which slow processes can proceed, this approach allows extended duration reactions whilst enabling real time process monitoring.