Most HP and Epson printers are drop on demand printers. They use electrical pulses to fulfill requests for ink. The ink is expelled out of the print head by a bubble which forms as a reaction to being heated. Once the ink is propelled out of the cartridge, the bubble cools, contracts, and forms a vacuum of sorts, which pulls more ink into the nozzle.
HP DeskJets and BubbleJets are popular examples of printers that use this technology.
Epson printers work on the same principal with the exception of a minor twist