Mathematical modelling of glob-driven tear film breakup.

IF 0.8 4区 数学 Q4 BIOLOGY
L Zhong, C F Ketelaar, R J Braun, C G Begley, P E King-Smith
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引用次数: 0

Abstract

Evaporation is a recognized contributor to tear film thinning and tear breakup (TBU). Recently, a different type of TBU is observed, where TBU happens under or around a thick area of lipid within a second after a blink. The thick lipid corresponds to a glob. Evaporation alone is too slow to offer a complete explanation of this breakup. It has been argued that the major reason of this rapid tear film thinning is divergent flow driven by a lower surface tension of the glob (via the Marangoni effect). We examine the glob-driven TBU hypothesis in a 1D streak model and axisymmetric spot model. In the model, the streak or spot glob has a localized high surfactant concentration, which is assumed to lower the tear/air surface tension and also to have a fixed size. Both streak and spot models show that the Marangoni effect can lead to strong tangential flow away from the glob and may cause TBU. The models predict that smaller globs or thinner films will decrease TBU time (TBUT). TBU is located underneath small globs, but may occur outside larger globs. In addition to tangential flow, evaporation can also contribute to TBU. This study provides insights about mechanism of rapid thinning and TBU which occurs very rapidly after a blink and how the properties of the globs affect the TBUT.

Abstract Image

Abstract Image

球体驱动的泪膜破裂的数学模型。
蒸发是公认的泪膜变薄和撕裂(TBU)的原因。最近,观察到了一种不同类型的TBU,在眨眼后的一秒钟内,TBU发生在厚厚的脂质区域下方或周围。厚厚的脂质相当于一个球体。蒸发本身太慢了,无法完全解释这种破裂。有人认为,这种快速泪膜变薄的主要原因是由较低的球体表面张力驱动的发散流(通过Marangoni效应)。我们在一维条纹模型和轴对称斑点模型中检验了球驱动的TBU假说。在该模型中,条纹或斑点球具有局部的高表面活性剂浓度,这被认为降低了撕裂/空气表面张力,并且也具有固定的尺寸。条纹和斑点模型都表明,Marangoni效应会导致强烈的切向流离开球体,并可能导致TBU。模型预测,较小的球或较薄的薄膜将减少TBU时间(TBUT)。TBU位于小球体下方,但可能发生在较大球体外部。除了切向流动外,蒸发也有助于TBU。这项研究提供了关于快速变薄和眨眼后迅速发生的TBU的机制,以及球体的性质如何影响TBUT的见解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
15
审稿时长
>12 weeks
期刊介绍: Formerly the IMA Journal of Mathematics Applied in Medicine and Biology. Mathematical Medicine and Biology publishes original articles with a significant mathematical content addressing topics in medicine and biology. Papers exploiting modern developments in applied mathematics are particularly welcome. The biomedical relevance of mathematical models should be demonstrated clearly and validation by comparison against experiment is strongly encouraged. The journal welcomes contributions relevant to any area of the life sciences including: -biomechanics- biophysics- cell biology- developmental biology- ecology and the environment- epidemiology- immunology- infectious diseases- neuroscience- pharmacology- physiology- population biology
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