Department of Mechanical and Aerospace Engineering, Indian Institute of Technology Hyderabad, Telangana 502285, India and Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada.
Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada.
Phys Rev E. 2021 Jan;103(1-1):013108. doi: 10.1103/PhysRevE.103.013108.
Mucin polymers in the tear film protect the corneal surface from pathogens and modulate the tear-film flow characteristics. Recent studies have suggested a relationship between the loss of membrane-associated mucins and premature rupture of the tear film in various eye diseases. This work aims to elucidate the hydrodynamic mechanisms by which loss of membrane-associated mucins causes premature tear-film rupture. We model the bulk of the tear film as a Newtonian fluid in a two-dimensional periodic domain, and the lipid layer at the air-tear interface as insoluble surfactants. Gradual loss of membrane-associated mucins produces growing areas of exposed cornea in direct contact with the tear fluid. We represent the hydrodynamic consequences of this morphological change through two mechanisms: an increased van der Waals attraction due to loss of wettability on the exposed area, and a change of boundary condition from an effective negative slip on the mucin-covered areas to the no-slip condition on exposed cornea. Finite-element computations, with an arbitrary Lagrangian-Eulerian scheme to handle the moving interface, demonstrate a strong effect of the elevated van der Waals attraction on precipitating tear-film breakup. The change in boundary condition on the cornea has a relatively minor role. Using realistic parameters, our heterogeneous mucin model is able to predict quantitatively the shortening of tear-film breakup time observed in diseased eyes.
泪膜中的粘蛋白聚合物可保护角膜表面免受病原体侵害，并调节泪膜流动特性。最近的研究表明，在各种眼部疾病中，膜相关粘蛋白的丧失与泪膜的过早破裂之间存在关联。本工作旨在阐明膜相关粘蛋白丧失导致泪膜过早破裂的流体动力学机制。我们将泪膜的大部分建模为二维周期域中的牛顿流体，将空气-泪液界面处的脂质层建模为不可溶的表面活性剂。膜相关粘蛋白的逐渐丧失会导致暴露的角膜区域直接与泪液接触，从而产生不断扩大的区域。我们通过两种机制来表示这种形态变化的流体动力学后果：暴露区域润湿性丧失导致范德华吸引力增加，以及覆盖粘蛋白区域的有效负滑移边界条件变为暴露角膜的无滑移条件。使用任意拉格朗日-欧拉方法来处理移动界面的有限元计算，证明了升高的范德华吸引力对诱发泪膜破裂有很强的影响。角膜边界条件的变化作用相对较小。使用现实参数，我们的非均匀粘蛋白模型能够定量预测疾病眼中观察到的泪膜破裂时间缩短。
