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Peter Ewen King-Smith, Rayanne A Luke, Carolyn G Begley, Richard J Braun; Evaporation through small “holes” in the lipid layer. Invest. Ophthalmol. Vis. Sci. 2020;61(7):130.
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Analysis of evaporation from the tear film is difficult because it depends on the unknown pattern of air flow over the tear film. However, Hisatake et al. (1995, J Appl Phys 77, 6664) has shown that a minimum value of evaporation rate, independent of air flow, may be calculated for small water surfaces. Here we apply his formula to calculate expected thinning rates of the tear film over small circular holes in the lipid layer, assuming that the holes correspond to bare surface with no evaporation barrier. These results can be compared with observed thinning rates of the tear film of up to about 20 μm/min (Nichols et al., 2005, IOVS 46, 2353).
We used a mathematical model of tear film thinning and breakup which assumed an initial tear thickness of 3.5 μm, and included the effects of pressure-gradient flow into the hole region, osmotic flow of water out of the cornea into the hyperosmotic tears in the hole region, and diffusion and flow of solutes in the tear film (Braun et al., 2018, Math Med Biol 35, 145). The hole was considered to be a bare aqueous surface with no evaporation barrier, whose evaporation rate is given in the Appendix to Hisatake et al.’s paper. Tear film temperature used was 35C, with an air temperature of 20C and 30% relative humidity.
Fig. 1 gives plots of central tear thickness as a function of time for holes of radius 25, 100 and 500 μm. By Hisatake et al.’s equation, thinning rate in μm/min is inversely proportional to radius, so thinning for 100 μm radius is faster than for 500 μm. However, thinning for 25 μm radius is slowed by increased pressure-gradient inward flow. For a 100 μm hole, the tear film would thin from 3.5 to 0.175 μm in about 0.4 s, implying a thinning rate of about 500 μm/min. Fig. 2 shows how breakup time would vary as a function of hole radius.
Tear film thinning and breakup can been related to either evaporation through thin lipid or to divergent flow of tears under thick lipid. Our results confirm that evaporation through lipid holes could be fast enough to explain their associated thinning rate and breakup time. However the calculated thinning rates are greater than that observed for lipid “holes”, implying that there is still some barrier to evaporation in the holes. More rapid breakup can occur for divergent flow of tears under thick, expanding “globs” of lipid (King-Smith et al., 2018, Ocul Surf 16, 4).
This is a 2020 ARVO Annual Meeting abstract.
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