I'm picturing something like a shower head, too, but with a few enhancements.
1. Lots of holes. Okay, this is obvious.
2. The upstream side of each hole is countersunk a little, about the volume of a drop, maybe a little more.
3. Instead of a mixer, the supply vat has a pump that maintains a flow across the upstream side of the shower head, through a wide, shallow channel.
4. Upstream of the shallow channel is a flexible diaphragm.
5. Upstream of the diaphragm is a chamber that is alternately pressurized and vented, so the diaphragm moves 'forward' in the direction of discharge periodically.
6. As the diaphragm contacts the back surface of the showerhead, it makes intimate contact with the periphery of each countersunk hole.
7. As the diaphragm is further pressurized, it displaces the goo from each counterbore, individually, dispensing a drop per hole.
As for producing, say 10,000 precisely countersunk holes, I'll have to think about that for a while.
Mike Halloran
Pembroke Pines, FL, USA