Béatrice Guerrier

Stick−Slip Patterning at Low Capillary Numbers for an Evaporating Colloidal Suspension

Pattern formation from a silica colloidal suspension that is evaporating has been studied when a movement is imposed to the contact line. This article focuses on the stick-slip regime observed for very low contact line velocities. A capillary rise experiment has been specially designed for the observation and allows us to measure the pinning force that increases during the pinning of the contact line on the growing deposit. We report systematic measurements of this pinning force and derive scaling laws when the velocity of the contact line, the colloid concentration, and the evaporation rate are varied. Our analysis supports the idea that the pinning of the contact line results from a competition between the geometry of the growing deposit and the force due to gravity.

Self-patterning induced by a solutal Marangoni effect in a receding drying meniscus

This paper examines through numerical simulations the impact of a solutal Marangoni effect on the deposit obtained from a polymer solution. A hydrodynamical model with lubrication approximation is used to describe the liquid phase in a dip-coating–like configuration. The studied case considers evaporation in stagnant air (diffusion-limited evaporation), which results in a coupling between the liquid and gas phases. Viscosity, surface tension, and saturated vapor pressure depend on the solute concentration. In the evaporative regime, when the surface tension increases with the polymer concentration, the Marangoni effect induces a periodic regime. This results in a self-organized periodic patterning of the dried film in certain control parameter ranges. A morphological phase diagram as well as meniscus and dry-deposit shapes are provided as a function of the substrate velocity and bulk solute concentration.

Transient Rayleigh-Bénard-Marangoni solutal convection

Solutal driven flow is studied for a binary solution submitted to solvent evaporation at the upper free surface. Evaporation induces an increase in the solute concentration close to the free surface and solutal gradients may induce a convective flow driven by buoyancy and/or surface tension. This problem is studied numerically, using several assumptions deduced from previous experiments on polymer solutions. The stability of the system is investigated as a function of the solutal Rayleigh and Marangoni numbers, the evaporative flux and the Schmidt number. The sensitivity of the thresholds to initial perturbations is analyzed. The effect of viscosity variation during drying is also investigated. At last numerical simulations are presented to study the competition between buoyancy and Marangoni effects in the nonlinear regime.

Drying of Glassy Polymer Varnishes: a Quartz Resonator Study

We report on desorption measurements on polymeric thin films coated onto quartz crystal resonators. Due to the high sensitivity of quartz crystal microbalances, the experiments can be performed on very thin films, which have small diffusion time constants even in the glassy state. When drying is performed slowly enough, diffusion equilibrium can be maintained through the whole process of desorption, including the glassy domain. From these quasi-stationary pressure ramps, we derived the solvent chemical potential as a function of polymer volume fraction μ(o). The results fit well to a model recently proposed by Leibler and Sekimoto. 1 In addition, we have derived the mutual diffusion coefficient D(o) from pressure step experiments. We observe a strong decrease of D(o) for high polymer concentrations typical of hypodiffusive systems like polymers. We investigated the drying of an industrial varnish that is a blend of 2 copolymers as well as the drying of its components separately. Both the solvent chemical potential μ(o) and the mutual diffusion coefficient D(o) of the blend interpolate between the respective quantities of the components.

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.

Numerical simulation of dip-coating in the evaporative regime

Abstract.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.Graphical abstract

Modeling flow coating of colloidal dispersions in the evaporative regime: prediction of deposit thickness

We investigate flow coating processes, i.e., the formation of dry coatings starting from dilute complex fluids confined between a static blade and a moving substrate. In particular, we focus on the evaporative regime encountered at low substrate velocity, at which the coating flow is driven mainly by solvent evaporation in the liquid meniscus. In this regime, general arguments based on mass conservation show that the thickness of the dry film decreases as the substrate velocity increases, unlike the behavior in the well-known Landau-Levich regime. This work focuses on colloidal dispersions, which deserve special attention. Indeed, flow coating is expected to draw first a solvent-saturated film of densely packed colloids, which further dries fully when air invades the pores of the solid film. We first develop a model based on the transport equations for binary mixtures, which can describe this phenomenon continuously, using appropriate boundary conditions and a criterion to take into account pore-emptying in the colloidal film. Extensive numerical simulations of the model then demonstrate two regimes for the deposit thickness as a function of the process parameters (substrate velocity, evaporation rate, bulk concentration, and particle size). We finally derive an analytical model based on simplified transport equations that can reproduce the output of our numerical simulations very well. This model can predict analytically the two observed asymptotic regimes and therefore unifies the models recently reported in the literature.

Humidity-insensitive water evaporation from molecular complex fluids

We investigated theoretically water evaporation from concentrated supramolecular mixtures, such as solutions of polymers or amphiphilic molecules, using numerical resolutions of a one-dimensional model based on mass transport equations. Solvent evaporation leads to the formation of a concentrated solute layer at the drying interface, which slows down evaporation in a long-time-scale regime. In this regime, often referred to as the falling rate period, evaporation is dominated by diffusive mass transport within the solution, as already known. However, we demonstrate that, in this regime, the rate of evaporation does not also depend on the ambient humidity for many molecular complex fluids. Using analytical solutions in some limiting cases, we first demonstrate that a sharp decrease of the water chemical activity at high solute concentration leads to evaporation rates which depend weakly on the humidity, as the solute concentration at the drying interface slightly depends on the humidity. However, we also show that a strong decrease of the mutual diffusion coefficient of the solution enhances considerably this effect, leading to nearly independent evaporation rates over a wide range of humidity. The decrease of the mutual diffusion coefficient indeed induces strong concentration gradients at the drying interface, which shield the concentration profiles from humidity variations, except in a very thin region close to the drying interface.