Models for the Dynamics of the Human Tear Film

Every time one blinks, a tear film is left on the front of the eye to protect the cornea and to help provide a smooth optical surface, as well as other functions. We adopt the accepted view that the tear film layer contains a primarily aqueous layer, and we develop models for the formation and evolution of the aqueous layer over one or more blink cycles using lubrication theory. The models incorporate surface tension, viscosity, surfactant transport, Marangoni effects and slip on the cornea. A comparison with in vivo interferometry is made for a half blink and it is favorable. In two models and one set of conditions, the amount of lid closure required for the tear film to be completely restarted is found to be about 7/8 from considerations due solely to fluid dynamics; that is, if the eyelids close to about 1/8 of the fully open width, that is enough to fully refresh the tear film.