Modelling drainage of the precorneal tear film after a blink. (English) Zbl 1042.92004

Braun, R. J.; Fitt, A. D.

Math. Med. Biol. 20, No. 1, 1-28 (2003).

Summary: We study the drainage of the precorneal tear film in humans. A fluid dynamic model for the drainage of the aqueous layer is developed that includes the effects of evaporation and gravity. The model may be reduced to a single nonlinear partial differential equation for the thickness of the aqueous layer. The equation is solved numerically and accurate times for film rupture are obtained for physically realistic parameters. The results indicate that although gravity and evaporation are not the most dominant effects in some parts of the film, they can nevertheless materially affect the film drainage process and should therefore be included in models for tear film drainage.

MSC:

92C35	Physiological flow
92C30	Physiology (general)
35Q92	PDEs in connection with biology, chemistry and other natural sciences

Keywords:

precorneal tear film; film drainage; dry eye; lubrication theory