Christiaan Ketelaar

Evaporation, viscous flow, and electrostatic interaction of charged interfaces in the apparent contact line region

We consider evaporation of an aqueous solution near an apparent contact line separating a macroscopically dry area of a heated solid substrate and a constant-curvature meniscus far away from the substrate. Viscous flow, described by a lubrication-type model, is coupled to the interaction of electrical double layers formed near the solid-liquid and liquid-vapor interfaces. The electrostatic interaction is described using the nonlinear Poisson-Boltzmann equation and is shown to affect both normal and shear stress balances at the deformable interface. For steady configurations, we find that the apparent contact line region becomes wider and the total evaporation rate there increases as the substrate potential is increased. Motion of the apparent contact line in response to changes in the substrate temperature is also investigated. The contact line speed is found to increase when the electrostatic effects are incorporated into the model.

Mathematical modelling of glob-driven tear film breakup

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.