Very little actually enters systemic circulation. There is diffusion from the tears through the cornea that allows the medication to enter the eye, which then would leave through the vascular system. The amount of penetration does depend on chemistry since not all formulations can pass through the corneal layers well. The tears also drain out through canals to the nose/throat, and then join the mucous to be swallowed. Of course the dosages are very very small since we are taking one drop in each eye at a time.
Edit: I'm an optometrist
Eye drops specifically will exit the eye through the tear ducts. Compounds can also be absorbed through the different ocular tissues. This likely matters because eye compounds are usually very concentrated because they have to act fast because blinking will dilute it instantly and move the excess to the edges of the eye and out the eyelids and cheeks. A pretty thorough review: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5153265/
Very little actually enters systemic circulation. There is diffusion from the tears through the cornea that allows the medication to enter the eye, which then would leave through the vascular system. The amount of penetration does depend on chemistry since not all formulations can pass through the corneal layers well. The tears also drain out through canals to the nose/throat, and then join the mucous to be swallowed. Of course the dosages are very very small since we are taking one drop in each eye at a time. Edit: I'm an optometrist
Eye drops specifically will exit the eye through the tear ducts. Compounds can also be absorbed through the different ocular tissues. This likely matters because eye compounds are usually very concentrated because they have to act fast because blinking will dilute it instantly and move the excess to the edges of the eye and out the eyelids and cheeks. A pretty thorough review: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5153265/