arXiv 2104.003502021-04physics.flu-dyn

复杂几何接触线动力学的完全欧拉混合浸没边界相场模型

A fully Eulerian hybrid Immersed Boundary-Phase Field Model for contact line dynamics on complex geometries

Armin Shahmardi, Marco Edoardo Rosti, Outi Tammisola, Luca Brandt

备注：: 52 pages, 19 figures, Submitted to Journal of Computational Physics
DOI：: 10.1016/j.jcp.2021.110468

摘要：

我们提出了一个完全欧拉混合浸没边界/相场模型来模拟润湿和接触线运动在任何任意的几何形状。固体壁面采用体积penalisation鬼胞浸没边界，而两种流体之间的界面采用扩散界面法。通过动量方程中的滑移速度和Cahn-Hilliard模型中的序参量的静/动态接触角条件来描述复杂壁面上的接触线运动。这种组合需要精确计算标量序参量的法向和切向梯度以及速度分量。然而，本算法需要计算平均权重和其他几何变量作为预处理步骤。几个验证测试报告的手稿，连同2D模拟的液滴传播的正弦曲线的墙壁上具有不同的接触角和滑移长度和球形液滴传播的球体，表明所提出的算法是能够处理的三相接触线运动在任何复杂的墙壁。该算法的欧拉特征便于实现，并提供了一个直接的和潜在的高度可扩展的并行化。所采用的并行化的基础Navier-Stokes求解器可以有效地用于多相部分。这里提出的程序可以直接用于施加任何类型的边界条件（诺依曼，狄利克雷和混合）的任何场变量在一个复杂的几何形状演变，与浸入边界的方法建模（例如，建模可变形的生物膜，红细胞，凝固，蒸发和沸腾，仅举几例）

英文摘要：

We present a fully Eulerian hybrid immersed-boundary/phase-field model to simulate wetting and contact line motion over any arbitrary geometry. The solid wall is described with a volume-penalisation ghost-cell immersed boundary whereas the interface between the two fluids by a diffuse-interface method. The contact line motion on the complex wall is prescribed via slip velocity in the momentum equation and static/dynamic contact angle condition for the order parameter of the Cahn-Hilliard model. This combination requires accurate computations of the normal and tangential gradients of the scalar order parameter and of the components of the velocity. However, the present algorithm requires the computation of averaging weights and other geometrical variables as a preprocessing step. Several validation tests are reported in the manuscript, together with 2D simulations of a droplet spreading over a sinusoidal wall with different contact angles and slip length and a spherical droplet spreading over a sphere, showing that the proposed algorithm is capable to deal with the three-phase contact line motion over any complex wall. The Eulerian feature of the algorithm facilitates the implementation and provides a straight-forward and potentially highly scalable parallelisation. The employed parallelisation of the underlying Navier-Stokes solver can be efficiently used for the multiphase part as well. The procedure proposed here can be directly employed to impose any types of boundary conditions (Neumann, Dirichlet and mixed) for any field variable evolving over a complex geometry, modelled with an immersed-boundary approach (for instance, modelling deformable biological membranes, red blood cells, solidification, evaporation and boiling, to name a few)

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