Models for Tear Film Dynamics

Rich Braun
University of Delaware

Experimental in vivo results will be sampled, and the basics of visualization with fluorescein will be explained. The flow over a two dimensional eye-shaped domain with time dependent boundary conditions will the be discussed. The flow is described by lubrication theory, which is a limiting case of the Navier-Stokes equations in a thin geometry.
The resulting PDEs for the fluid thickness are nonlinear, fourth order in space and first order in time. Additional PDEs are added for additional effects, and typically those are only second order in space. The resulting nonlinear PDE systems are solved numerically in several ways.
Physiologically, the fresh tear fluid supplied to the eye is typically unable to flow into the middle area of the exposed ocular surface without blinking, particularly with evaporation. The deformation of the meniscus in vivo and from the model closely resemble each other.

Then, local dynamics for the tear film emphasizing the role
of the lipid layer and osmolarity (saltiness) will be presented. A
mechanism for tear
film breakup (film rupture) involving evaporation and excess polar lipid (insoluble
surfactant) gives a prediction for the increased osmolarity in the breakup regions; no experimental results are available that measure this quantity though it is thought to be critical to the development of symptoms in dry eye.

Back to Mathematical Challenges in Ophthalmology