Villanueva Walter, Grönhagen Klara, Amberg Gustav, Agren John
Linné Flow Centre, Department of Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 May;77(5 Pt 2):056313. doi: 10.1103/PhysRevE.77.056313. Epub 2008 May 28.
A multicomponent and multiphase model with fluid motion is developed. The model is used to study reactive wetting in the case where concentration change of the spreading liquid and the substrate occurs. With the introduction of a Gibbs energy functional, the governing equations are derived, consisting of convective concentration and phase-field equations which are coupled to the Navier-Stokes equations with surface tension forces. The solid substrate is modeled hydrodynamically with a very high viscosity. Arbitrary phase diagrams, surface energies, and typical dimensionless numbers are some input parameters into the model. An axisymmetric model with an adaptive finite element method is utilized. Numerical simulations were done revealing two stages in the wetting process. First, the convection-dominated stage where rapid spreading occurs. The dynamics of the wetting is found to match with a known hydrodynamic theory for spreading liquids. Second, the diffusion-dominated stage where we observed depression of the substrate-liquid interface and elevation of the contact line region.
建立了一个包含流体运动的多组分多相模型。该模型用于研究铺展液体和基底浓度发生变化时的反应性润湿。通过引入吉布斯能量泛函，推导了控制方程，包括对流浓度方程和相场方程，它们与带有表面张力的纳维-斯托克斯方程相耦合。固体基底采用高粘度流体动力学模型。任意相图、表面能和典型无量纲数是该模型的一些输入参数。采用了具有自适应有限元方法的轴对称模型。进行了数值模拟，揭示了润湿过程中的两个阶段。第一，对流主导阶段，在此阶段发生快速铺展。发现润湿动力学与已知的铺展液体流体动力学理论相匹配。第二，扩散主导阶段，在此阶段我们观察到基底-液体界面凹陷和接触线区域升高。
