Heat transfer and tear film dynamics over multiple blink cycles

Abstract

We consider model problems for the tear film over multiple blink cycles with heat transfer from the posterior side of the tear film. A nonlinear partial differential equation governs the film thickness on a moving domain in one space dimension and time. One end of the tear film moves in order to mimic blinking in the eye. The film thickness is coupled with the diffusion of heat from the posterior of the film, where the underlying cornea and aqueous humor are modeled as a rectangular domain. The domain of the tear film is located on one edge of the rectangle. The resulting problem is solved using the method of lines with a Chebyshev spectral method in space. Evaporation is included in the model, with end fluxes specified to compensate for the evaporation from the film. The numerical results reveal a similarity to quantitative in vivo observations of the film dynamics and measured ocular surface temperature. Periodicity in the film and temperature dynamics is explored with different flux conditions and end motions, and a transition between periodic and non-periodic solutions is analyzed.