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A multifunctional microfluidic platform combining on-demand aqueous-phase droplet generation, multi-droplet storage, and controlled merging of droplets selected from a storage library in a single integrated microfluidic device is described. A unique aspect of the technology is a microfluidic trap design comprising a droplet trap chamber and lateral bypass channels integrated with a microvalve that supports the capture and merger of multiple droplets over a wide range of individual droplet sizes. A storage unit comprising an array of microfluidic traps operates in a first-in first-out manner, allowing droplets stored within the library to be analyzed before sequentially delivering selected droplets to a downstream merging zone, while shunting other droplets to waste. Performance of the microfluidic trap is investigated for variations in bypass/chamber hydrodynamic resistance ratio, micro-chamber geometry, trapped droplet volume, and overall flow rate. The integrated microfluidic platform is then utilized to demonstrate the operational steps necessary for cell-based assays requiring the isolation of defined cell populations with single cell resolution, including encapsulation of individual cells within an aqueous-phase droplet carrier, screening or incubation of the immobilized cell-encapsulated droplets, and generation of controlled combinations of individual cells through the sequential droplet merging process. Beyond its utility for cell analysis, the presented platform represents a versatile approach to robust droplet generation, storage, and merging for use in a wide range of droplet-based microfluidics applications.