https://doi.org/10.1140/epje/s10189-026-00574-y
Research - Flowing Matter
Thermal and solutal capillary effects in tear film dynamics
Department of Chemical Engineering, Indian Institute of Technology Jodhpur, 342030, Jodhpur, India
a
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Received:
20
September
2025
Accepted:
2
March
2026
Published online:
17
April
2026
Abstract
An analytical and numerical study is carried out for the stability of a thin tear film considering a single-layered model. The mass, momentum, and energy equations are simplified under the lubrication approximation to obtain nonlinear partial differential spatiotemporal evolution equations for the film height and surfactant concentration. These evolution equations involve various physical mechanisms such as thermo- and solutocapillary stresses, van der Waals forces, surface tension forces, and slip at the corneal surface. Linear stability analysis reveals that solutocapillary stresses enhance the stability of the tear film by driving fluid from thicker to thinner regions. The thermocapillary stresses are found to enhance the instability, where the fluid is driven from a thinner (low surface tension) region to a thicker (high surface tension) region. Convective cooling due to cold wind flow also affects the growth rate of perturbations, with higher convection leading to a higher growth rate. The solutocapillary stresses dominate over the thermocapillary stresses beyond a certain critical value of the solutal Marangoni number. This critical threshold decreases with increasing Péclet number, indicating that the influence of solutocapillary effects becomes more pronounced under stronger advective transport. Numerical computations are carried out and show that the nonlinear stability results are in good agreement with those obtained from linear stability analysis. Furthermore, the computations reveal that the rupture time decreases with increasing thermal Marangoni number and slip coefficient, whereas it increases with the solutal Marangoni number.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
