zlacker

The container has to have holes through which to squirt the ink onto the page, and when ink is dispensed it is replaced in the container with air.

>>stonog+(OP)
You could make one that doesn't have an air hole. Put a membrane between the air and the ink. Consider a standard reverse osmosis water tank--inside there's basically a big bag, pressurized air on the outside, water on the inside. The outside should stay dry, the inside shouldn't contact the air.

You still have the problem at the print head, though.