Mathematical modelling of glob-driven tear film breakup

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.

Dynamics of Fluorescent Imaging for Rapid Tear Thinning

“…Their data appears to show that level of repeatability in some cases. However, our data shows that dark spots were observed at different positions in the fluorescence images after each blink (Zhong et al, 2018); this implies that Marangoni-driven tangential flow may provide an explanation for many TBU events with rapid thinning. We suspect that both types of TBU may occur.…”

“…In this work, we focus on the effect of Marangoni-driven tangential flow on FL imaging for TBU. To simulate a strong tangential flow, we adapted our previous model (Zhong et al, 2018) which captured the rapid thinning caused by a thicker lipid in the lipid layer. With appropriate glob size, the tangential flow generated in our model can thin the aqueous layer to TBU in well under a second, as seen in vivo .…”

“…Zhong et al (2018) developed a Marangoni-driven model for rapid TBU that was able to explain a significant part of our experimental observations. In the terminology of Bitton and Lovasik (1998), they used both axisymmetric spot models and linear streak models to test the hypothesis that globs can cause a strong tangential flow which subsequently drives TBU near the glob.…”

“…In this article, we use mathematical models for spots and streaks to study rapid TBU near a glob when using fluorescence imaging. Like Zhong et al (2018), we choose appropriate length and time scales in order to derive nonlinear partial differential equations (PDEs) using lubrication theory (Oron et al, 1997; Craster and Matar, 2009). Both models are solved in the local region for the tear film thickness ( h ); the pressure ( p ) and solute concentrations for osmolarity ( c ) and fluorescein ( f ) inside the tear film; and the insoluble surfactant concentration ( Γ ) on the tear/air interface.…”

A model of tear-film breakup with continuous mucin concentration and viscosity profiles – CORRIGENDUM

“…The new H value is thinner than the experimentally reported tear-film thickness by a factor of 7-10. This is based on recent findings that the tear film undergoes a rapid initial thinning owing to factors such as evaporation (Braun et al 2018), lipid clustering on the interface (Zhong et al 2019) and lid-associated thinning, including drainage (King-Smith, Begley & Braun 2018). Thus, within several seconds, the tear film thins from a thickness of about 3.5 µm to 0.5 µm (Braun et al 2018).…”