Global existence of solutions to a tear film model with locally elevated evaporation rates
| Autor: | Jian-Guo Liu, Thomas P. Witelski, Hangjie Ji, Yuan Gao |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Materials science
Evaporation FOS: Physical sciences Statistical and Nonlinear Physics Mathematical Physics (math-ph) Mechanics Condensed Matter Physics 01 natural sciences 010305 fluids & plasmas 010101 applied mathematics Nonlinear system Mathematics - Analysis of PDEs 0103 physical sciences Convergence (routing) FOS: Mathematics Thin-film equation 0101 mathematics Thin film Mathematical Physics Analysis of PDEs (math.AP) |
| Zdroj: | Physica D: Nonlinear Phenomena. 350:13-25 |
| ISSN: | 0167-2789 |
| DOI: | 10.1016/j.physd.2017.03.005 |
| Popis: | Motivated by a model proposed by Peng et al. [Advances in Coll. and Interf. Sci. 206 (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 PDE 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 the results are then validated against PDE simulations. 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. |
| Databáze: | OpenAIRE |
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