Recently, the functionality of under oil open microfluidics was expanded from droplet-based operations to include lateral flow in under oil aqueous channels. However, the resolution of the under oil fluidic channels reported so far is still far from comparable with that of closed-channel microfluidics (millimeters versus micrometers). Here, enabled by exclusive liquid repellency and an under oil sweep technique, open microchannels can now be prepared under oil (rather than in air), which shrinks the channel dimensions up to three orders of magnitude compared to previously reported techniques. Spatial trapping of different cellular samples and advanced control of mass transport (i.e., enhanced upper limit of flow rate, steady flow with passive pumping, and reversible fluidic valves) were achieved with open-channel designs. We apply these functional advances to enable dynamic measurements of dispersion from a pathogenic fungal biofilm. The ensemble of added capabilities reshapes the potential application space for open microfluidics.