I've worked on small scale systems where vessels were kept pressurized (~0.5 barg) with air to move and dispense salt water without pumps.
Disadvantage; the gas goes into solution in the liquid, so when the liquid's pressure is reduced, you get gas bubbles. To minimize that, you might vent the vessel when you are not pumping. Costs a valve, releases some vapor.
Disadvantage; the flow rate changes as the liquid level goes down. It can be offset by introducing the gas near the bottom of the vessel, but then you can't use a self- relieving air regulator, and the gassing gets worse.
Disadvantage; you have to vent the vessel to replenish the liquid. If you don't put a manual vent valve in the cap, the cap and pickup tube will get launched by the stored air pressure, and customers will complain about the liquid being splashed on their neckties.
Disadvantage; the particular system was a medical instrument, and had no other need for an air compressor. Small air compressors are not remarkably reliable, and small quiet ones, e.g. for office use, are expensive.
Disadvantage; when you cycle the pressure to minimize gassing, you will eventually fatigue a polypropylene bottle and crack it, so you need a catch basin.
Aside from that ... well, it was better than peristaltic pumps for our purposes, but it did provide some interesting problems.
Mike Halloran
Pembroke Pines, FL, USA