Tear film dynamics with evaporation, osmolarity and surfactant transport

In this article we develop a model for the evaporation and rupture of the tear film. The tear film is generally considered a multi-layer structure which we simplify to a single layer in our modeling. We examine how well the floating lipid layer can be approximated by a mobile insoluble surfactant monolayer in the context of lubrication theory with film rupture "breakup" in the tear film literature. This model includes the effects of surface tension, insoluble surfactant monolayer transport, solutal Marangoni effects, evaporation, osmolarity transport, osmosis and wettability of corneal surface. Evaporation is hypothesized to be dependent on pressure, temperature and surface concentration at the surface of the film. A focus of this paper is to study the competition between the effect of increasing surfactant concentration to (1) slowing down evaporation and (2) lowering surface tension. The solutal Marangoni effect, for local increases in surfactant concentration, can induce local thinning and this effect always seems to dominate the reduction in thinning rate due to evaporation in our model. It also seems to eliminate any localized area of increased evaporation due to reduced surfactant concentration. Osmolarity in the tear film increases because water lost to the average evaporation rate and to a lesser extent by flow inside the film. The presence of van der Waals conjoining pressure is only significant when osmosis is very small or absent. The model predicts that the Marangoni effect coupled with evaporation can determine the location of first breakup; it also agrees with another model of breakup that predicts elevated osmolarity when breakup occurs.