Skip to main content Accessibility help
×
Home
Hostname: page-component-78bd46657c-gwmzn Total loading time: 0.341 Render date: 2021-05-05T21:22:57.918Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

A model of tear-film breakup with continuous mucin concentration and viscosity profiles – CORRIGENDUM

Published online by Cambridge University Press:  28 February 2020

Rights & Permissions[Opens in a new window]

Abstract

Type
Corrigendum
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Two errors were made in evaluating the dimensional parameters of table 1 and in converting them to the dimensionless parameters in Dey et al. (Reference Dey, Vivek, Dixit, Richhariya and Feng2019). 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 $6\unicode[STIX]{x03C0}$ in the Hamaker constant omitted by mistake; the correct value is ${\mathcal{A}}=6\unicode[STIX]{x03C0}\times 3.5\times 10^{-19}~\text{J}~\text{m}$ (Braun et al. Reference Braun, Driscoll, Begley, King-Smith and Siddique2018). Besides, we revise the tear-film thickness to $H=0.5~\unicode[STIX]{x03BC}\text{m}$. 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. Reference Braun, Driscoll, Begley, King-Smith and Siddique2018), lipid clustering on the interface (Zhong et al. Reference Zhong, Ketelaar, Braun, Begley and King-Smith2019) and lid-associated thinning, including drainage (King-Smith, Begley & Braun Reference King-Smith, Begley and Braun2018). Thus, within several seconds, the tear film thins from a thickness of about $3.5~\unicode[STIX]{x03BC}\text{m}$ to $0.5~\unicode[STIX]{x03BC}\text{m}$ (Braun et al. Reference Braun, Driscoll, Begley, King-Smith and Siddique2018). 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 ${\mathcal{A}}$ and $H$ lead to new values for four dimensionless parameters: ${\mathcal{C}}=0.03$, $Pe_{s}=0.02$, $\unicode[STIX]{x1D6E5}_{b}=10^{-4}$ and ${\mathcal{M}}=0.05$. With the corrected parameters and time scale, figure 1 plots the dimensional rupture time $t_{rup}$ as a function of ${\mathcal{C}}$. This replaces the original figure 12.

Figure 1. Dimensional rupture time $t_{rup}$ as a function of the dimensionless surface tension ${\mathcal{C}}$. The dotted lines are predictions of the two-layer model (TLM) with and without slip on the substrate. This replaces the original figure 12 in Dey et al. (Reference Dey, Vivek, Dixit, Richhariya and Feng2019).

The new $t_{rup}$ turns out to be quite close to that reported in the original figure 12. For a reasonable range of the interfacial tension, ${\mathcal{C}}$ now lies in the range of $10^{-3}$–0.1, over which $t_{rup}$ varies from 2.4 to 135 s. For the baseline value ${\mathcal{C}}=0.03$, the rupture time is $t_{rup}=44.4~\text{s}$. 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.

Acknowledgement

The correction of the errors was largely done by A. Choudhury of the Indian Institute of Technology – Hyderabad during a research visit at the University of British Columbia, Vancouver.

Declaration of interests

The authors report no conflict of interest.

References

Braun, R. J., Driscoll, T. A., Begley, C. G., King-Smith, P. E. & Siddique, J. I. 2018 On tear film breakup (TBU): dynamics and imaging. Math. Med. Biol. 35, 145180.CrossRefGoogle Scholar
Dey, M., Vivek, A. S., Dixit, H. N., Richhariya, A. & Feng, J. J. 2019 A model of tear-film breakup with continuous mucin concentration and viscosity profiles. J. Fluid Mech. 858, 352376.CrossRefGoogle Scholar
King-Smith, P. E., Begley, C. G. & Braun, R. J. 2018 Mechanisms, imaging and structure of tear film breakup. Ocul. Surf. 16, 430.CrossRefGoogle ScholarPubMed
Zhong, L., Ketelaar, C. F., Braun, R. J., Begley, C. G. & King-Smith, P. E. 2019 Mathematical modelling of glob-driven tear film breakup. Math. Med. Biol. 36, 5591.CrossRefGoogle ScholarPubMed
You have Access

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

A model of tear-film breakup with continuous mucin concentration and viscosity profiles – CORRIGENDUM
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

A model of tear-film breakup with continuous mucin concentration and viscosity profiles – CORRIGENDUM
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

A model of tear-film breakup with continuous mucin concentration and viscosity profiles – CORRIGENDUM
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *