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Erratum: A model of tear-film breakup with continuous mucin concentration and viscosity profiles (Journal of Fluid Mechanics (2020) 889 (E1) DOI: 10.1017/jfm.2018.776)
M. Dey, A.S. Vivek, , A. Richhariya, J.J. Feng
Published in Cambridge University Press
2020
Volume: 889
   
Abstract
Two errors were made in evaluating the dimensional parameters of table 1 and in converting them to the dimensionless parameters in Dey et al. (2019). This led to an incorrect time scale in computing the dimensional tear-film breakup time in figure 12. All the other results, presented in figures 3 11, are dimensionless and remain correct for the dimensionless parameters employed therein. To rectify the errors, we first reinstate a factor of 6p in the Hamaker constant omitted by mistake; the correct value is AD6p3:510-19 J m (Braun et al. 2018). Besides, we revise the tear-film thickness to H D0:5 mm. The new H value is thinner than the experimentally reported tear-film thickness by a factor of 7 10. This is based on recent findings that the tear film undergoes a rapid initial thinning owing to factors such as evaporation (Braun et al. 2018), lipid clustering on the interface (Zhong et al. 2019) and lid-associated thinning, including drainage (King-Smith, Begley & Braun 2018). Thus, within several seconds, the tear film thins from a thickness of about 3:5 mm to 0:5 mm (Braun et al. 2018). It is only after this initial phase that the van der Waals force becomes the dominant driving force for tear-film rupture. As our continuous viscosity model (CVM) focuses solely on the van der Waals-driven rupture and ignores the initial rapid thinning, we should adopt the H value at the end of the rapid thinning. The changes in A and H lead to new values for four dimensionless parameters: C D 0:03, Pes D 0:02, b D 10-4 and MD 0:05. With the corrected parameters and time scale, figure 1 plots the dimensional rupture time trup as a function of C. This replaces the original figure 12. The new trup turns out to be quite close to that reported in the original figure 12. For a reasonable range of the interfacial tension, C now lies in the range of 10-3 0.1, over which trup varies from 2.4 to 135 s. For the baseline value C D0:03, the rupture time is trup D44:4 s. Hence, the previous conclusion drawn from comparisons with experimental data and two-layer model predictions stands: the CVM is superior in reproducing experimental measurements of healthy-eye tear film breakup time. © The Author(s), 2020. Published by Cambridge University Press.
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JournalData powered by TypesetJournal of Fluid Mechanics
PublisherData powered by TypesetCambridge University Press
ISSN00221120