Introduction. McDonald and Brubaker(1) observed that after instillation of fluorescein, dark lines appear near the upper and lower lid margins of the human eye immediately following a blink. Methods. This paper numerically models the dynamic black-line formation under the lubrication approximation at low Reynolds number, including gravity and surface tension forces. Results. The hydrodynamic model predicts that menisci at the lid margins draw liquid from the tear film, resulting in local thinning close to the lids (i.e., black lines) due to capillary suction. Once the film thins locally, resistance to further thinning increases. No vertical gravity-induced drainage occurs between blinks, and the tear film is trapped in its initially deposited state or "perched" between the two black lines. Conclusions. We demonstrate quantitatively that due to rapid formation of black lines, the tear film is trapped for extended periods. Lid action is therefore required to disturb the perched tear film.