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Lan Zhong, Christiaan F. Ketelaar, Richard J. Braun, Tobin A. Driscoll, Peter Ewen King-Smith, Carolyn G Begley; Mathematical Modeling of Glob-Driven Tear Film Breakup. Invest. Ophthalmol. Vis. Sci. 2016;57(12):6171.
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© ARVO (1962-2015); The Authors (2016-present)
Tear film thinning and breakup are often correlated with thin lipid due to higher evaporation rates in such areas. However, tear film break-up (TBU) has also been observed in the corresponding thicker lipid area that causes significant tangential flow and thinning. For the purposes of brevity, we call these thick lipid regions globs. This study used a mathematical model to test the hypothesis that lipid globs with different composition can cause tangential flow, which subsequently drives TBU near the glob.
We developed a mathematical model to simulate the glob’s different composition by assuming that the glob has a higher surfactant (polar lipid) concentration. Increased surfactant concentration was assumed to lower the tear film surface tension according to a linear equation of state; this is how the model incorporates the “Marangoni effect.” The corresponding math models were solved in the local region for the tear film thickness (h), the pressure inside the film and insoluble surfactant concentration (Γ) using a custom MATLAB program.
When the glob has an elevated surfactant concentration, the surface tension is lower at the glob compared to the surrounding fluid; this leads to strong tangential flow away from the glob and may cause TBU. The figures show that TBU can be observed in about a second (0.63s). Flow away from the glob extracts fluid from under the glob. The model predicts that smaller globs (down to 45µm radius) or thinner tear films will decrease TBU time (TBUT). For spots smaller than 45 µm in a 3.5 µm tear film, TBUT increases; where the increase begins depends on the tear film parameters. The model predicts increasing evaporation rate and stronger Marangoni effect decreases TBUT.
This model predicts that excess polar lipid can lead to TBU in appropriate time and length scales. The model predicts that TBUT decreases with decreasing glob size (up to a point) and tear film thickness, as well as increasing evaporation rate and surface tension difference (Marangoni effect).
This is an abstract that was submitted for the 2016 ARVO Annual Meeting, held in Seattle, Wash., May 1-5, 2016.
Tear film thickness, initially 3.5 µm, with blob size = 0.0594mm and no evaporation.
Surfactant distribution for same conditions as Figure 1.
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