Doumenc F, Janeček V, Nikolayev V S
Laboratoire FAST, Univ. Paris-Sud, CNRS, Université Paris-Saclay, F-91405, Orsay, France.
Sorbonne Université, UFR 919, 4 place Jussieu, F-75252, Paris Cedex 05, France.
Eur Phys J E Soft Matter. 2018 Dec 19;41(12):147. doi: 10.1140/epje/i2018-11758-8.
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.
本文考虑了在部分润湿构型下，在某种惰性（不可冷凝）气体氛围中，固定（钉扎）接触线附近的蒸发或冷凝现象。这类问题与许多情况相关，特别是与露天环境中液滴或液膜的干燥过程有关。热效应并不重要，质量交换速率由气体中的蒸汽动力学控制。沿用先前的研究成果，我们考虑了气体扩散与液体流动之间通过开尔文效应产生的弱耦合。由于气体中的扩散，这类问题是非局部的。为了具有普遍性，我们考虑了置于平坦均匀基底上的液体楔形体的几何形状，其周围为气相，气相中有厚度均匀的扩散边界层[公式：见原文]。与移动接触线问题类似，相变导致了流体动力学接触线奇点。针对长度为[公式：见原文]的液体楔形体对该问题进行了渐近分析。确定了三个渐近区域：微观区域（在该区域奇点得到缓和，在当前情况下是通过开尔文效应）以及两个中间区域。仅开尔文效应就足以缓和奇点。讨论了每个区域中界面斜率和质量蒸发/冷凝通量的标度律。结果发现，无论奇点缓和机制如何，表观接触角（即第二中间区域中的界面斜率）与平衡接触角之差与[公式：见原文]的平方根以及微观长度的平方根成反比。
