Moving contact line of a volatile fluid

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.

Kinetic effects regularize the mass-flux singularity at the contact line of a thin evaporating drop

We consider the transport of vapour caused by the evaporation of a thin, axisymmetric, partially wetting drop into an inert gas. We take kinetic effects into account through a linear constitutive law that states that the mass flux through the drop surface is proportional to the difference between the vapour concentration in equilibrium and that at the interface. Provided that the vapour concentration is finite, our model leads to a finite mass flux in contrast to the contact-line singularity in the mass flux that is observed in more standard models that neglect kinetic effects. We perform a local analysis near the contact line to investigate the way in which kinetic effects regularize the mass-flux singularity at the contact line. An explicit expression is derived for the mass flux through the free surface of the drop. A matched-asymptotic analysis is used to further investigate the regularization of the mass-flux singularity in the physically relevant regime in which the kinetic timescale is much smaller than the diffusive one. We find that the effect of kinetics is limited to an inner region near the contact line, in which kinetic effects enter at leading order and regularize the mass-flux singularity. The inner problem is solved explicitly using the Wiener-Hopf method and a uniformly valid composite expansion is derived for the mass flux in this asymptotic limit.

Thermal singularity and contact line motion in pool boiling: Effects of substrate wettability

The dynamic van der Waals theory [Phys. Rev. E 75, 036304 (2007)] is employed to model the growth of a single vapor bubble in a superheated liquid on a flat homogeneous substrate. The bubble spreading dynamics in the pool boiling regime has been numerically investigated for one-component van der Waals fluids close to the critical point, with a focus on the effect of the substrate wettability on bubble growth and contact line motion. The substrate wettability is found to control the apparent contact angle and the rate of bubble growth (the rate of total evaporation), through which the contact line speed is determined. An approximate expression is derived for the contact line speed, showing good agreement with the simulation results. This demonstrates that the contact line speed is primarily governed by (1) the circular shape of interface (for slow bubble growth), (2) the constant apparent contact angle, and (3) the constant bubble growth rate. It follows that the contact line speed has a sensitive dependence on the substrate wettability via the apparent contact angle which also determines the bubble growth rate. Compared to hydrophilic surfaces, hydrophobic surfaces give rise to a thinner shape of bubble and a higher rate of total evaporation, which combine to result in a much faster contact line speed. This can be linked to the earlier formation of a vapor film and hence the onset of boiling crisis.

Rapid capillary filling via ion-water interactions over the nanoscale

Giant frictional resistances are grand challenges against the rapid filling of nanoscale capillaries, as encountered in a wide variety of applications ranging from nature to energy. It is commonly believed that partially wettable charged nanocapillaries fill up considerably slower, compared to completely wettable ones, under the influence of a complex interplay between interfacial tension and electrical interactions. In sharp contrast to this common belief, here we discover a new non-intuitive regime of rapid filling of charged capillaries over the nanometer scale, by virtue of which a partially wettable capillary may fill up comparatively faster than a completely wettable one. We attribute the fundamental origin of this remarkable behavior to ion-water interactions over interfacial scales. The underlying novel electro-hydrodynamic mechanism, as unveiled here, may provide deeper insights into the physico-chemical interactions leading to augmentations in the rates of nanocapillary filling over hydrophobic regimes, bearing far-reaching implications in the transport of biological fluids, enhanced oil recovery, and miniaturized energy harvesting applications.

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.