Influence of curvature on tear film dynamics

This paper generalizes the model of Aydemir et al. (2010) by approximating the cornea surface as spherical rather than flat. The model, which consists of a pair of coupled nonlinear partial differential equations for the thickness of the aqueous layer and the concentration of the lipid, is solved in the domain squeezed between a moving upper lid and fixed lower lid. Away the upper lid the curvature has a weak influence on the film thickness; this confirms the conclusion of Braun et al. (2012). However, the curvature influences the thinning rate of the tear film near the upper eyelid.