The Effect of Polar Lipids on Tear Film Dynamics
The Effect of Polar Lipids on Tear Film Dynamics
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DOI：
10.1007/s11538-010-9555-y
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发表时间：
2011-06-01
影响因子：
3.5
通讯作者：
Witelski, T. P.
中科院分区：
文献类型：
--
作者：
Aydemir, E.;Breward, C. J. W.;Witelski, T. P.
在这篇文章中，我们提出了一个数学模型，描述了眼睑腺体分泌的、存在于泪膜表面的极性脂对角膜前泪膜演变的影响。我们的目的是解释在实验中观察到的有趣现象，即泪膜在上眼睑静止后仍继续向上移动。极性脂是一种不溶于水的表面物种，可以局部改变泪膜的表面张力。在润滑极限条件下，模型简化为两个关于油膜厚度和脂类浓度的耦合非线性偏微分方程组。我们数值求解了这个系统，观察到增加脂质的浓度会增加液体沿眼睛向上的流量。我们进一步利用问题中参数的大小来解释系统的初始演化。
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.