Theory meets experiment in the blink of an eye

Theory meets experiment in the blink of an eye. A healthy human eye has a thin, moist tear film that protects it, removes waste, and provides a smooth optical surface. The film—containing layers of lipids, water, and mucin—evaporates as the eye stays open and is replenished with a blink. Mathematical models typically show that the film warms between blinks. But precise noncontact laboratory measurements show that it actually cools by a degree or two Celsius as the film evaporates, especially in the thinnest region near the center of the cornea. Mathematicians Richard Braun and Longfei Li at the University of Delaware have now resolved the discrepancy. Along with the usual physical parameters of the problem—surface tension, viscosity, lipid concentration gradients, corneal wettability, and so on—they included heat diffusion in both the tear film and the eye beneath it. Allowing for heat transport in a realistically thick substrate that includes the cornea proved to be crucial. In addition to simulating the observed cooling, the new model also reproduces the experimental thinning rate of the film, a rate that is higher for people with so-called dry eye. In the next stage, to better capture blinking dynamics, Braun and coworkers are letting one boundary of their model eye move. (L. Li, R. J. Braun, Phys. Fluids, in press.)