Effect of ambient air temperature on tear film dynamics

Motivated by the understanding of fluid mechanics behind dry eye syndrome during the winter season, we perform the linear and nonlinear stability analysis of the tear film. To reflect the biological structure of the tear film, we model it as a viscoelastic film on a substrate with an insoluble surfactant at the air–film interface, destabilisation by van der Waals forces, variation of viscosity and elasticity along the film height, and impose a substrate-normal temperature gradient. The air–film interface tension is assumed to decrease linearly with temperature and surfactant concentration. To conduct general linear stability analysis (GLSA), we employ the pseudo-spectral method. The GLSA predicts the existence of a longwave thermocapillary-induced instability, which overcomes the stabilisation by the solutocapillary effect due to the surfactant. The elasticity of the film, van der Waals forces and slip at the film–substrate interface contribute to further destabilisation, while a decrease in viscosity along the film height stabilises the film. The longwave instability is the dominant mode of instability. Thus, we derive longwave evolution equations whose linear stability analysis confirms the predictions of GLSA. The nonlinear analysis of the derived evolution equations, carried out using COMSOL 6.2, demonstrates tear-film rupture due to pure thermocapillary instability for sufficiently high thermal Marangoni numbers. In contrast, diseased eyes suffering from lipid layer dysfunction can undergo tear-film rupture at a much lower temperature difference between the ambient air and the cornea. Consideration of a viscosity decrease with increasing film height delays tear film rupture, while van der Waals forces decrease tear film rupture time. The rupture time range predicted by our model is in good agreement with clinical observations, thereby confirming the impact of the winter season on tear film dynamics.