This answer mentions that some astronauts use eye drops to relieve irritation caused by dust and lint in the air. How do they do get the drops in their eyes in microgravity?
When I put drops in my eyes, I look upward, place the bottle above my eye, and let the drop fall into my eye. Obviously, this will not work in microgravity. Do they touch the bottle to their eye? Or squirt out a bubble, and then move their eye into it?
Surface tension!
The short answer is you’re close with your first guess - by squeezing the bottle a drop forms at the tip that is stable due to surface tension, and then steering that drop into an open eye (usually with the help of a partner doing the actual instilling). This means the bottle tip itself never touches the eye if you’re doing it right, which is good as these bottles are reused throughout the mission (though they are crewmember specific, so you’re not using someone else’s eye drops).
Most of the eye drop use is related to SANS (Spaceflight Associated Neuro-ocular Syndrome) imagery or data collection, which occurs periodically during the mission. While we no longer require fundoscopy, pupil dilation aids in image acquisition for other modalities, and anesthetic drops for tonometry are a must.
CSA’s Hadfield posted a good description of how the entire tonometry process works, including drop instillation, here:
Eye medications can also be instilled by soaking the drop into a strip of sterile blotter paper, then touching the paper to the inside of the lower lid.
The volume of a drop is at least 10 times the volume of the tear film, so the majority of a drop is squeezed out onto the cheek with the first blink.
The blotter paper technique also has the advantage of avoiding back-contamination of the dropper bottle, so a single bottle can be used for multiple patients.
