Thin wedge evaporation/condensation controlled by the vapor dynamics in the atmosphere.

Evaporation or condensation in the vicinity of the immobile (pinned) contact line in an atmosphere of some inert (noncondensable) gas is considered here in a partial wetting configuration. Such a problem is relevant to many situations, in particular to a drop or a liquid film drying in open air. The thermal effects are not important and the mass exchange rate is controlled by the vapor dynamics in the gas. By following previous works, we account for the weak coupling between the diffusion in the gas and flow in the liquid through the Kelvin effect. Such a problem is nonlocal because of the diffusion in the gas. For generality, we consider a geometry of a liquid wedge posed on a flat and homogeneous substrate surrounded by a gas phase with a diffusion boundary layer of uniform thickness [Formula: see text]. Similarly to the moving contact line problem, the phase change leads to the hydrodynamic contact line singularity. The asymptotic analysis of this problem is carried out for the liquid wedge of the length [Formula: see text]. Three asymptotic regions are identified: the microscopic one (in which the singularity is relaxed, in the present case with the Kelvin effect) and two intermediate regions. The Kelvin effect alone turns to be sufficient to relax the singularity. The scaling laws for the interface slope and mass evaporation/condensation flux in each region are discussed. It is found that the difference of the apparent contact angle (i.e., interface slope in the second intermediate region) and the equilibrium contact angle is inversely proportional to the square root of [Formula: see text] and square root of the microscopic length, whatever is the singularity relaxation mechanism.

Drying of a solution in a meniscus: a model coupling the liquid and the gas phases.

A model simulating the drying of a solution in a meniscus in contact with a moving substrate is developed. It takes into account the hydrodynamics in the solution in the framework of the lubrication approximation, the vapor diffusion in the gas phase, and the variation of physical properties during drying. The free surface profile and spatial evaporation flux are not imposed a priori but result from the simulation of the mass transfer in the liquid/gas system (1.5-sided model). Several regimes are observed depending on the substrate velocity. For a large substrate velocity, the classical Landau-Levich regime is obtained. For smaller velocities, a drying front appears that is characterized by a strong concentration gradient and a peak in the evaporation flux. The coupling between the evaporation flux and the meniscus shape in this regime is analyzed. Another regime appears at a very low substrate velocity and seems to be driven by a competition between advection and diffusion. This macroscopic model simulates recent experimental results, namely, the dependence of the deposit thickness on the substrate velocity, which scales as 1/V in the regime dominated by evaporation.

Drying of colloidal suspensions and polymer solutions near the contact line: deposit thickness at low capillary number.

Drying experiments with a receding contact line have been performed with silica colloidal suspensions and polyacrylamide (PAAm) polymer solutions. The experimental setup allows to control the receding movement of the contact line and the evaporation flux separately. Deposit thickness as a function of these two control parameters has been investigated. The different systems exhibit a similar behavior: in the regime of very low capillary numbers the deposit thickness scaled by the solute volume concentration and the evaporation rate is proportional to the inverse of the contact line velocity. Both the scaling exponent and the constant (which has the dimension of a length) do not depend on the system under study. The observation of this evaporative regime confirms some recent results obtained by Le Berre et al. on a very different system (phospholipidic molecules) and fully supports their interpretation. Following their approach, a simple model based on mass balance accounts for these results. This implies that this regime is dominated by the evaporation and that the deformation of the meniscus induced by viscous forces does not play any significant role. When increasing the velocity, another regime is observed where the thickness does not depend significantly on the velocity.

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.

Physical aging of glassy PMMA/toluene films: influence of drying/swelling history.

Gravimetry experiments in a well-controlled environment have been performed to investigate aging for a glassy PMMA/toluene film. The temperature is constant and the control parameter is the solvent vapor pressure above the film (i.e. the activity). Several experimental protocols have been used, starting from a high activity where the film is swollen and rubbery and then aging the film at different activities below the glass transition. Desorption and resorption curves have been compared for the different protocols, in particular in terms of the softening time, i.e. the time needed by the sample to recover an equilibrium state at high activity. Non-trivial behaviors have been observed, especially at small activities (deep quench). A model is proposed, extending the Leibler-Sekimoto approach to take into account the structural relaxation in the glassy state, using the Tool formalism. This model well captures some of the observed phenomena, but fails in describing the specific kinetics observed when aging is followed by a short but deep quench.