This disclosure provides for devices, methods, and systems for generating a plurality of droplets within a collecting container at an extremely high rate (e.g., of at least 1 million droplets per minute, etc.), each of the plurality of droplets comprising an aqueous mixture for a digital analysis, wherein upon generation, the plurality of droplets is stabilized in position within a region of the collecting container. The inventions enable partitioning of samples for digital analyses at unprecedented rates, where readout of signals from targets within such partitions can still be achieved in accordance with various assays.