Slip-mediated dewetting of polymer microdroplets.

Classical hydrodynamic models predict that infinite work is required to move a three-phase contact line, defined here as the line where a liquid/vapor interface intersects a solid surface. Assuming a slip boundary condition, in which the liquid slides against the solid, such an unphysical prediction is avoided. In this article, we present the results of experiments in which a contact line moves and where slip is a dominating and controllable factor. Spherical cap-shaped polystyrene microdroplets, with nonequilibrium contact angle, are placed on solid self-assembled monolayer coatings from which they dewet. The relaxation is monitored using in situ atomic force microscopy. We find that slip has a strong influence on the droplet evolutions, both on the transient nonspherical shapes and contact line dynamics. The observations are in agreement with scaling analysis and boundary element numerical integration of the governing Stokes equations, including a Navier slip boundary condition.

A mathematical model and mesh-free numerical method for contact-line motion in lubrication theory.

Abstract: We introduce a mathematical model with a mesh-free numerical method to describe contact-line motion in lubrication theory. We show how the model resolves the singularity at the contact line, and generates smooth profiles for an evolving, spreading droplet. The model describes well the physics of droplet spreading-including Tanner's Law for the evolution of the contact line. The model can be configured to describe complete wetting or partial wetting, and we explore both cases numerically. In the case of partial wetting, the model also admits analytical solutions for the droplet profile, which we present here. Article highlights: We formulate a mathematical model to regularize the contact-line singularity for droplet spreading.The model can be solved using a fast, accurate mesh-free numerical method.Numerical simulations confirm that the model describes the quantitative aspects of droplet spreading well.

From coffee stains to uniform deposits: Significance of the contact-line mobility.

HYPOTHESIS: Contact-line motion upon drying of a sessile droplet strongly affects the solute transport and solvent evaporation profile. Hence, it should have a strong impact on the deposit formation and might be responsible for volcano-like, dome-like and flat deposit morphologies. EXPERIMENTS: A method based on a thin-film interference was used to track the drop height profile and contact line motion during the drying. A diverse set of drying scenarios was obtained by using inks with different solvent compositions and by adjusting the substrate wetting properties. The experimental data was compared to the predictions of a phenomenological model. FINDINGS: We highlight the essential role of contact-line mobility on the deposit morphology of solution-based inks. A pinned contact line produces exclusively ring-like deposits under normal conditions. On the contrary, drops with a mobile contact line can produce ring-, flat- or dome-like morphology. The developed phenomenological model shows that the deposit morphology depends on solvent evaporation profile, evolution of the drop radius relative to its contact angle, and the ratio between initial and maximal (gelling) solute concentration. These parameters can be adjusted by the ink solvent composition and substrate wetting behaviour, which provides a way for deposition of uniform and flat deposits via inkjet printing.

Contact line stick-slip motion and meniscus evolution on micrometer-size wavy fibres.

HYPOTHESIS: The architecture of complex-shaped fibres affects the motion of the contact line and the evolution of its associated menisci when a fibre is immersed into a liquid. Understanding and predicting the motion of the contact line is critical in the design of complex-shaped fibres for many engineering applications as well as for surface science. While wetting on classic circular cylinders has been well studied, singularities during the wetting process of complex-shaped fibres are not yet well understood. EXPERIMENTS: The dynamic wetting behaviour of axisymmetric sinus-shaped fibres immersed vertically in a liquid volume was investigated. Fibres were 3D-printed down to micrometre dimensions, and the Wilhelmy method was used in parallel with meniscus shape analysis. Moreover, a quasi-static theoretical model predicting the contact line movement and free energy of the system evolution on these fibres is also proposed. FINDINGS: The observation of liquid advancing and receding fronts highlighted a stick-slip motion of the meniscus depending on both the fibre surface curvature and its intrinsic wettability. The model predicts that the behaviour of the seemingly pinned and then jumping contact line, with associated changes in apparent contact angles, can be explained by the interplay between a constant local contact angle and the movement of the bulk liquid, leading to the storage of energy which is suddenly released when the contact line passes a given point of fibre curvature. Besides, acceleration/deceleration events that take place before and after the jumps are experimentally observed in good agreement with the model.

Can hydrodynamic contact line paradox be solved by evaporation-condensation?

We investigate a possibility to regularize the hydrodynamic contact line singularity in the configuration of partial wetting (liquid wedge on a solid substrate) via evaporation-condensation, when an inert gas is present in the atmosphere above the liquid. The no-slip condition is imposed at the solid-liquid interface and the system is assumed to be isothermal. The mass exchange dynamics is controlled by vapor diffusion in the inert gas and interfacial kinetic resistance. The coupling between the liquid meniscus curvature and mass exchange is provided by the Kelvin effect. The atmosphere is saturated and the substrate moves at a steady velocity with respect to the liquid wedge. A multi-scale analysis is performed. The liquid dynamics description in the phase-change-controlled microregion and visco-capillary intermediate region is based on the lubrication equations. The vapor diffusion is considered in the gas phase. It is shown that from the mathematical point of view, the phase exchange relieves the contact line singularity. The liquid mass is conserved: evaporation existing on a part of the meniscus and condensation occurring over another part compensate exactly each other. However, numerical estimations carried out for three common fluids (ethanol, water and glycerol) at the ambient conditions show that the characteristic length scales are tiny.