A review article on tear films in the Annual Review of Fluid Mechanics will appear in print in January 2012. "Dynamics of the Tear Film" is currently available online in volume 44 of the journal.
Tear film dynamics in 2D
Kara has also developed 2D models of the post-blink tear film using the Overture framework; Bill Henshaw (LLNL) is helping considerably with this effort. In the first case, we used lubrication equations for the tear film and the boundary conditions that specify the film thickness and the pressure at the boundary. This work is has appeared elctronically in Mathematical Medicine and Biology (doi:10.1093/imammb/dqp023).
The image at right is the thickness distribution at time 10 when gravity is included in the simulation. Maroon indicates greater than or equal to 3 microns; the dark blue is the minimum thickness. The drooping area of maroon indicates a bulge in the meniscus outward from the lid margin. For the flux boundary conditions we used, the fluid in the upper meniscus can break through the black line if enough time is allowed between blinks. This work with flux BCs specified is accepted for publication in Journal of Fluid Mechanics and will be out in March 2010.
Dan Anderson and Kat Winter (then a CSUMS undergrad at George Mason) worked with Dr Braun on a model of the tear film that has a wetting cornea and evaporation from the tear film. The model was compared with some in vivo observations from King-Smith at Ohio State, and choosing two parameters to fit the "dry" film thickness and the opening speed of the thin region seemed to give reasonable agreement between this most basic theory and the experiment. This work has appeared electronically in Mathematical Medicine and Biology (doi:10.1093/imammb/dqp019). A talk including some of these results is given in the next section. The talk also includes some extensions from Pete Ucciferro, an REU student in Summer 09 and an independent study student in Fall 09; the work was done as part of a GEMS team that included graduate studente Jiahua Tang, Pam, Chris Raymond and me.
Ms. Xiaolin Yang, an MS student in the Department of Computer and Information Sciences, who worked with Dr Braun on capturing the lid motion during a blink automatically from high speed digital movies of blinks. The movies were made in the MEC Lab in the UD Department of Mathematical Sciences with the help of Dr. John Pelesko. She developed a code that could extract least squares polynomial fits from the blink movies using Sobel edge detection with some pre- and post-processing. That mathematical approximation that she generated of a blink has already been incorporated into our efforts to compute the tear film evolution in two dimensions. She worked with Braun in summer 2006 and January 2007. The code was developed in Matlab, and the code with some results will appear on this website in the near future.
Mr. Peter Ucciferro (a Quantitative Biology major) and Mr. Paul Parsons (a Physics major) were supported by an REU supplement for this NSF grant for the summer of 2007. They worked on evaluating and extending Xiaolin's algorithms for capturing and mathematically representing eyelid motion during a blink. Ucciferro and Parsons recorded some observations of blinks and extended the software for this aspect of the project. One aspect of their work was to use roifill to blur regions around the eye so that more blink movies could be used. They presented their results in an excellent joint presentation during the Departmental symposium on summer undergraduate research in August 2007.
Last modified 02/25/11 by RJ Braun