Microfluidic system, including methods and apparatus, for processing fluid, such as by droplet generation. In an exemplary method, a sample-containing fluid may be dispensed into a well through a sample port of a channel component. The channel component may include (a) a body having a bottom surface attached to the well, and a top surface with a microchannel formed therein, and (b) an input tube projecting into the well from the bottom surface of the body. The sample-containing fluid when dispensed may contact a bottom end of the input tube and may be retained, with assistance from gravity, out of contact with the microchannel. A pressure differential may be created that drives at least a portion of the sample-containing fluid from the well via the input tube and through the microchannel.