According to one source Print heads and droplet sizes, a picolitre is the standard size of an inkdrop, with 15 billion drops in a tablespoon. These drops are obviously far too small to see without optical aid. If it wasn't engineering, I would extend your post to 3 D printers, but I do believe this aspect is not a directly physics related question.
Bonus (related) question: Could you create an "ink"jet printer that deposited individual molecules by vibrating the liquid at a swifter rate?
Taking a high end printer as an example, the patterns it can "jet" are resolved into 5 micron pixels. 1 micron is about equivalent to 10,000 carbon atoms. On a biological scale, this is the smallest "length" brain neuron. Whether individual molecules can be placed at specific spots on a surface would seem to depend on the size of the molecules, but the integrated chip industry may act as a guide as to how someday we may be able to duplicate their results and improve upon them.
so, from a physics standpoint, how does the print head overcome the surface tension of the ink in order to make such extremely small droplets? – David White
Surfactants are added to the ink, to provide the correct balance between too high a surface tension, which causes uneven dispersion and longer drying times, whereas too low a surface tension may cause flooding /excess ink at the holes of of the print head ,and also cause a lack of precision in forming characters on the page.
As I suppose we both have guessed, this specific formulation of printer fluids may form part of the reason that printer ink is so high in price, with the manufacturers insistence, by means of chipping the cartridge, that you use their refills. From my own experience, in the past, you could substitute generic refills, but no longer.
If surfactants play such an important role in determining surface tension, this will play a part in the range of materials that can be extruded from an ink jet based nozzle design. The nozzle design of 3D printers is probably nothing as precise as firing ink jet drops that are invisible to the naked eye.