A drop-on-demand ink jet printing method and apparatus in which the print head has an ink cavity which is filled with ink, and which has a nozzle designed so that ink does not flow out under static conditions. An electromechanical transducer is selectively energized in response to print data signals so that, when energized by an electrical signal, the transducer produces a pressure wave in the ink cavity sufficient to eject one ink drop from the nozzle for each signal above a threshold value. The nozzle is a strongly convergent nozzle and the ink has a viscosity up to 100 centipoise. In the preferred embodiment, the nozzle is formed by anisotropic etching in a silicon substrate. An array of print heads produces a line of high-resolution printing as the print head array is moved across a print medium.