Global existence of solutions to a tear film model with locally elevated evaporation rates
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.
Duke Scholars
Altmetric Attention Stats
Dimensions Citation Stats
Published In
DOI
ISSN
Publication Date
Volume
Start / End Page
Related Subject Headings
- Fluids & Plasmas
- 4903 Numerical and computational mathematics
- 4902 Mathematical physics
- 4901 Applied mathematics
- 0102 Applied Mathematics
Citation
Published In
DOI
ISSN
Publication Date
Volume
Start / End Page
Related Subject Headings
- Fluids & Plasmas
- 4903 Numerical and computational mathematics
- 4902 Mathematical physics
- 4901 Applied mathematics
- 0102 Applied Mathematics