Janeček V, Doumenc F, Guerrier B, Nikolayev V S
University Paris-Sud, CNRS, Lab FAST, Bat 502, Campus Universitaire, Orsay 91405, France.
University Paris-Sud, CNRS, Lab FAST, Bat 502, Campus Universitaire, Orsay 91405, France; Sorbonne Universités, UPMC Univ Paris 06, UFR 919, 75005 Paris, France.
J Colloid Interface Sci. 2015 Dec 15;460:329-38. doi: 10.1016/j.jcis.2015.08.062. Epub 2015 Aug 28.
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.
我们研究了在部分润湿（固体基底上的液楔）构型中，通过蒸发 - 冷凝来正则化流体动力学接触线奇异性的可能性，此时液体上方的大气中存在惰性气体。在固 - 液界面施加无滑移条件，并假设系统是等温的。质量交换动力学由惰性气体中的蒸汽扩散和界面动力学阻力控制。液体弯月面曲率与质量交换之间的耦合由开尔文效应提供。大气是饱和的，并且基底相对于液楔以稳定速度移动。进行了多尺度分析。在相变控制的微区域和粘弹性 - 毛细管中间区域的液体动力学描述基于润滑方程。在气相中考虑蒸汽扩散。结果表明，从数学角度来看，相交换缓解了接触线奇异性。液体质量守恒：弯月面一部分上的蒸发和另一部分上的冷凝恰好相互补偿。然而，在环境条件下对三种常见流体（乙醇、水和甘油）进行的数值估计表明，特征长度尺度非常小。
