期刊
BULLETIN OF MATHEMATICAL BIOLOGY
卷 73, 期 6, 页码 1171-1201出版社
SPRINGER
DOI: 10.1007/s11538-010-9555-y
关键词
Tear films; Lipids; Blinking; Fluid mechanics; Lubrication theory
资金
- EPSRC
- King Abdullah University of Science and Technology [KUK-C1-013-04]
- NSF DMS [0239125]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0239125] Funding Source: National Science Foundation
In this paper, we present a mathematical model describing the effect of polar lipids, excreted by glands in the eyelid and present on the surface of the tear film, on the evolution of a pre-corneal tear film. We aim to explain the interesting experimentally observed phenomenon that the tear film continues to move upward even after the upper eyelid has become stationary. The polar lipid is an insoluble surface species that locally alters the surface tension of the tear film. In the lubrication limit, the model reduces to two coupled non-linear partial differential equations for the film thickness and the concentration of lipid. We solve the system numerically and observe that increasing the concentration of the lipid increases the flow of liquid up the eye. We further exploit the size of the parameters in the problem to explain the initial evolution of the system.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据