Dynamics of the Human Tear Film

Summary:

Each time someone blinks, a thin multilayered film of fluid must reestablish itself, within a second or so, on the front of the eye. This thin film is essential for both the health and optical quality of the human eye. An important first step towards effectively managing eye syndromes, like dry eye, is understanding the fluid dynamics of the tear film. Mathematical models for the tear film thickness are derived from the Navier-Stokes equations using lubrication theory. The highly nonlinear governing evolution equations are simulated with overset grid based computational methods in the Overture framework. We have found that the shape of the eye itself helps to steer fluid into the canthi regions.

Publications:

1. Tear film dynamics on an eye-shaped domain II: Flux Boundary Conditions, K. L. Maki, R. J. Braun, P. Ucciferro, W. D. Henshaw, and P. E. King-Smith, Journal of Fluid Mechanics 165 (2010), 1373-1385.


2. Tear film dynamics on an eye-shaped domain I: Pressure Boundary Conditions, K. L. Maki, R. J. Braun, W. D. Henshaw, and P. E. King-Smith, Mathematical Medicine and Biology 27 (2010), 227-254.


3. An overset grid method for the study of reflex tearing, K. L. Maki, R. J. Braun, T. A. Driscoll, and P. E. King-Smith, Mathematical Medicine and Biology 25 (2008), 187-214.

Collaborators:

Tobin Driscoll (University of Delaware)
Peter King-Smith (Ohio State)
Bill Henshaw (Lawrence Livermore National Laboratory)
Richard Braun (University of Delaware)