Tear-film breakup: The role of membrane-associated mucin polymers.

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.

Numerical simulation of dip-coating in the evaporative regime.

A hydrodynamic model is used for numerical simulations of a polymer solution in a dip-coating-like experiment. We focus on the regime of small capillary numbers where the liquid flow is driven by evaporation, in contrast to the well-known Landau-Levich regime dominated by viscous forces. Lubrication approximation is used to describe the flow in the liquid phase. Evaporation in stagnant air is considered (diffusion-limited evaporation), which results in a coupling between liquid and gas phases. Self-patterning due to the solutal Marangoni effect is observed for some ranges of the control parameters. We first investigate the effect of evaporation rate on the deposit morphology. Then the role of the spatial variations in the evaporative flux on the wavelength and mean thickness of the dried deposit is ascertained, by comparing the 2D and 1D diffusion models for the gas phase. Finally, for the very low substrate velocities, we discuss the relative importance of diffusive and advective components of the polymer flux, and consequences on the choice of the boundary conditions.

Electric-field-induced interfacial instabilities of a soft elastic membrane confined between viscous layers.

We explore the electric-field-induced interfacial instabilities of a trilayer composed of a thin elastic film confined between two viscous layers. A linear stability analysis (LSA) is performed to uncover the growth rate and length scale of the different unstable modes. Application of a normal external electric field on such a configuration can deform the two coupled elastic-viscous interfaces either by an in-phase bending or an antiphase squeezing mode. The bending mode has a long-wave nature, and is present even at a vanishingly small destabilizing field. In contrast, the squeezing mode has finite wave-number characteristics and originates only beyond a threshold strength of the electric field. This is in contrast to the instabilities of the viscous films with multiple interfaces where both modes are found to possess long-wave characteristics. The elastic film is unstable by bending mode when the stabilizing forces due to the in-plane curvature and the elastic stiffness are strong and the destabilizing electric field is relatively weak. In comparison, as the electric field increases, a subdominant squeezing mode can also appear beyond a threshold destabilizing field. A dominant squeezing mode is observed when the destabilizing field is significantly strong and the elastic films are relatively softer with lower elastic modulus. In the absence of liquid layers, a free elastic film is also found to be unstable by long-wave bending and finite wave-number squeezing modes. The LSA asymptotically recovers the results obtained by the previous formulations where the membrane bending elasticity is approximately incorporated as a correction term in the normal stress boundary condition. Interestingly, the presence of a very weak stabilizing influence due to a smaller interfacial tension at the elastic-viscous interfaces opens up the possibility of fabricating submicron patterns exploiting the instabilities of a trilayer.