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Global existence of solutions to a tear film model with locally elevated evaporation rates

Publication ,  Journal Article
Gao, Y; Ji, H; Liu, JG; Witelski, TP
Published in: Physica D: Nonlinear Phenomena
July 1, 2017

Motivated by a model proposed by Peng et al. (2014) for break-up of tear films on human eyes, we study the dynamics of a generalized thin film model. The governing equations form a fourth-order coupled system of nonlinear parabolic PDEs for the film thickness and salt concentration subject to non-conservative effects representing evaporation. We analytically prove the global existence of solutions to this model with mobility exponents in several different ranges and present numerical simulations that are in agreement with the analytic results. We also numerically capture other interesting dynamics of the model, including finite-time rupture–shock phenomenon due to the instabilities caused by locally elevated evaporation rates, convergence to equilibrium and infinite-time thinning.

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Published In

Physica D: Nonlinear Phenomena

DOI

ISSN

0167-2789

Publication Date

July 1, 2017

Volume

350

Start / End Page

13 / 25

Related Subject Headings

  • Fluids & Plasmas
  • 4903 Numerical and computational mathematics
  • 4902 Mathematical physics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
 

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Gao, Y., Ji, H., Liu, J. G., & Witelski, T. P. (2017). Global existence of solutions to a tear film model with locally elevated evaporation rates. Physica D: Nonlinear Phenomena, 350, 13–25. https://doi.org/10.1016/j.physd.2017.03.005
Gao, Y., H. Ji, J. G. Liu, and T. P. Witelski. “Global existence of solutions to a tear film model with locally elevated evaporation rates.” Physica D: Nonlinear Phenomena 350 (July 1, 2017): 13–25. https://doi.org/10.1016/j.physd.2017.03.005.
Gao Y, Ji H, Liu JG, Witelski TP. Global existence of solutions to a tear film model with locally elevated evaporation rates. Physica D: Nonlinear Phenomena. 2017 Jul 1;350:13–25.
Gao, Y., et al. “Global existence of solutions to a tear film model with locally elevated evaporation rates.” Physica D: Nonlinear Phenomena, vol. 350, July 2017, pp. 13–25. Scopus, doi:10.1016/j.physd.2017.03.005.
Gao Y, Ji H, Liu JG, Witelski TP. Global existence of solutions to a tear film model with locally elevated evaporation rates. Physica D: Nonlinear Phenomena. 2017 Jul 1;350:13–25.
Journal cover image

Published In

Physica D: Nonlinear Phenomena

DOI

ISSN

0167-2789

Publication Date

July 1, 2017

Volume

350

Start / End Page

13 / 25

Related Subject Headings

  • Fluids & Plasmas
  • 4903 Numerical and computational mathematics
  • 4902 Mathematical physics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics