Mathematical Models for Evaporation of Thin Films
Date
2013-05
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Publisher
University of Delaware
Abstract
Evaporation is a major cause of thinning of tear film which can eventually cause damage to ocular surface. The aim of the presented research was to analyze some of the many facets of evaporation of the aqueous layer of the tear film through development of mathematical models. In chapter 2, using the assumption of negligible film thickness, no fluid motion and a flat air/film interface, the diffusion equation for the water vapor concentration was solved numerically on a fixed domain and solutions were analyzed. Theoretical steady state predictions were also matched with solution profiles obtained from numerical simulation. Later, in chapter 3, film thickness was not overlooked and decrease in film thickness due to evaporation changed the domain for the vapor diffusion with time. The partial differential equations describing the diffusion of water vapors were then solved numerically on this moving domain by introducing a new independent variable which mapped the moving domain into fixed domain. Comparison between solution for the fixed boundary and moving boundary problems revealed that the use negligible thickness assumption did not represent the behavior of the system as accurately as expected. Lastly, in chapter 4, a lubrication model was derived using a thin film approximation which related film thickness, evaporation rate and fluid motion. Further, expression for evaporation rate was developed for the deformed thin film where vapor diffusion outside the film limited the evaporation of liquid molecules. We hope to adapt this model of thin film dynamics to more complex tear film models in future research.
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Keywords
chemical engineering, thin films, mathematical models