Microstructure of moving and/or evaporating contact lines

The accurate modeling of processes involving moving contact lines, such sessile droplet evapo- ration, nucleate boiling or imbibition in capillary structures, still faces considerable difficulties nowadays. This stems not only from the well-known viscous singularity induced by contact line motion, but also from other singularities associated with evaporation or condensation processes. Direct numerical simulation at a macroscopic scale generally fails in the vicinity of contact lines, where the rates of viscous dissipation and of heat/mass transfer can become extremely high. It is therefore necessary to build analytical (or semi-analytical) models describing the so-called microstructure of the contact line, i.e. the detailed shape of the liquid/vapor interface in the direct vicinity of the rigid wall. These microstructure models have to incorporate the rele- vant microscale effects, which hopefully enables regularization of the contact line singularities, thereby yielding a finite force exerted on the substrate, as well as a finite rate of phase change.In this presentation, we highlight recent progresses in this direction, focusing on the role of disjoining (Derjaguin) pressure, as well as on the Kelvin effect (dependence of saturation con- ditions on the curvature of the liquid/vapor interface). No other small-scale regularization mechanism (such as slip, diffuse interfaces, ) is considered. Consideration is limited to pure apolar liquids in contact with their pure vapor, on a flat homogeneous substrate.Within the lubrication approximation (small slope of the liquid/vapor interface relative to the substrate), it is first shown that a Cox-Voinov solution is generally valid at scales intermediate between the macroscopic (outer) and the microscopic (inner) scales, provided the rate of phase change decreases sufficiently fast with film thickness (which is generally the case). This well- known relationship expresses the apparent slope of the liquid/vapor interface as a function of the contact line velocity, and can therefore be used as an effective boundary condition in macroscopic codes. Yet, this law contains two parameters that first need to be calculated by proper asymptotic matching with the inner scale region: the apparent contact angle of the motionless microstructure, and a microlength entering the logarithmic (motion-induced) term. This matching is here accomplished in quite a variety of situations [1]: complete or partial wetting, non-volatile or volatile case, with or without kinetic effects, Importantly, depending on the disjoining pressure isotherm characterizing the considered fluid/solid pair, some microstructures are found to be associated with an extended microfilm covering the substrate ahead of the contact line (sometimes called precursor or adsorbed film), while some other kinds of microstructures are truncated, i.e. there is a point beyond which the surface may be considered as bare [2]. In particular, a minimalist model based on the Kelvin effect alone (without disjoining pressure) [3] is also described, and is shown to admit solutions with truncated microfilms while fully escaping both viscous and phase change singularities. This stems from a generic mechanism where the curvature of the liquid/vapor interface in the inner region self-adjusts to contact line motion in such a way that the liquid always has vanish- ing velocity at contact with the substrate (while the interface moves by Kelvin-effect-induced evaporation or condensation).Another important feature emphasized in the present talk is the occurrence of finite evaporation-induced contact angles, even for completely wetting situations and negligible con- tact line velocity. Such non-vanishing angles are due to intense microflows and corresponding stresses induced in the microregion, and are parametrically calculated as a function of the gov- erning dimensionless parameters of the problem (see also the recent book chapter [4]). Finally, some interferometric measurements of the apparent contact angles of sessile droplets of various HFEs evaporating into ambient air are presented, and shown to compare satisfactorily with a disjoining-pressure-based model appropriately modified to account for evaporation into an inert gas such as air.This work has been realized in collaboration with Dr Alexey Rednikov, Dr Sam Dehaeck and Dr Yannis Tsoumpas. The author gratefully acknowledges financial support of ESA and BELSPO (Prodex - Evaporation and Prodex - Heat Transfer contracts), of ULB and of the Fonds de la Recherche Scientifique – FNRS.References[1] P. Colinet and A. Rednikov, On integrable singularities and apparent contact angles within a classical paradigm. Partial and complete wetting regimes with or without phase change, Eur. Phys. J. – Special Topics, 197, 89-113 (2011).[2] A. Rednikov and P. Colinet, Truncated versus extended microfilms at a vapor-liquid con- tact line on a heated substrate, Langmuir, 27, 1758-1769 (2011).[3] A. Rednikov and P. Colinet, Singularity-free description of moving contact lines for volatile liquids, Phys. Rev. E, 87, 010401(R) (2013).[4] P. Colinet and A. Rednikov, Precursor films and contact line microstructures, in Droplet Wetting and Evaporation, Ed. D. Brutin, Elsevier (2015).