The Rough Tear

The tear film is a thin fluid layer coating the cornea, and its rupture — dry spots appearing between blinks — drives most dry eye disease. Models have treated the cornea as smooth: a flat substrate beneath a draining film. The instability comes from van der Waals forces, evaporation, lipid-layer thinning. The surface itself was inert geometry.

Kumar and Pushpavanam (arXiv:2603.18491) add corneal topography — the actual roughness of the surface — and find it dominates. Periodic surface undulations accelerate tear film breakup, and critically, the location of rupture depends on the texture. The thin film doesn’t just drain faster on a rough surface; it breaks at positions dictated by the surface geometry. The roughness doesn’t add noise to an existing instability. It determines where the instability nucleates.

The analysis uses Floquet theory, treating surface undulations as periodic perturbations and solving for the modified stability spectrum. The nonlinear corrections to the baseline film profile shift both the critical thickness and the rupture timescale. Slip conditions at the corneal surface interact with roughness to produce effects neither would create alone: slip on a smooth surface changes drainage rate; roughness on a no-slip surface changes rupture location; together, they produce qualitatively different breakup patterns.

This matters for contact lenses. A contact lens replaces the corneal surface with an artificial one. If rupture location is set by surface texture, then the lens surface finish — not just its curvature or wettability — determines where dry spots form. The design parameter isn’t the bulk geometry but the microstructure.

The structural point: in thin-film instabilities, the substrate isn’t passive. The surface the film sits on participates in selecting which instability mode wins. The roughness isn’t a perturbation to the dynamics. It’s a boundary condition that reshapes the dynamics entirely.

Kumar and Pushpavanam, “The Effect of Corneal Topography and Mucins on Tear Film Rupture,” arXiv:2603.18491 (2026).