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.

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.

Apparent-contact-angle model at partial wetting and evaporation: impact of surface forces.

This theoretical and numerical study deals with evaporation of a fluid wedge in contact with its pure vapor. The model describes a regime where the continuous wetting film is absent and the actual line of the triple gas-liquid-solid contact appears. A constant temperature higher than the saturation temperature is imposed at the solid substrate. The fluid flow is solved in the lubrication approximation. The introduction of the surface forces in the case of the partial wetting is discussed. The apparent contact angle (the gas-liquid interface slope far from the contact line) is studied numerically as a function of the substrate superheating, contact line velocity, and parameters related to the solid-fluid interaction (Young and microscopic contact angles, Hamaker constant, etc.). The dependence of the apparent contact angle on the substrate temperature is in agreement with existing approaches. For water, the apparent contact angle may be 20° larger than the Young contact angle for 1 K superheating. The effect of the surface forces on the apparent contact angle is found to be weak.

Moving contact line of a volatile fluid.

Interfacial flows close to a moving contact line are inherently multiscale. The shape of the interface and the flow at meso- and macroscopic scales inherit an apparent interface slope and a regularization length, both named after Voinov, from the microscopic inner region. Here, we solve the inner problem associated with the contact line motion for a volatile fluid at equilibrium with its vapor. The evaporation or condensation flux is then controlled by the dependence of the saturation temperature on interface curvature-the so-called Kelvin effect. We derive the dependencies of the Voinov angle and of the Voinov length as functions of the parameters of the problem. We then identify the conditions under which the Kelvin effect is indeed the mechanism regularizing the contact line motion.

[Characteristics of gene pools of three Pinus pumila (Pall.) Regel populations at the range margins].

Genetic variation of Siberian dwarf pine Pinus pumila (Pall.) Regel was characterized in three marginal populations in southwestern, southern and eastern parts of the natural species range (Transbaikalia, Primorye, Kamchatka) using isozyme analysis. Analysis involving 16 isozyme loci encoding ten enzyme systems was conducted. Our results confirm that P. pumila is among the most polymorphic species in the family Pinus. Three marginal populations exhibited high genetic variation (P95 = 68.8%, Ho = 0.247, He = 0.291). Populations heterogeneity and significantly high level of divergence in coniferous (F(ST) = 0.050, D(N) = 0.044) reflect their genetic originality. In summary, it was shown that the level of genetic variation characteristic for P. pumila in other parts of the not only is reproduced in the populations examined but even is close to maximum there.