An energy-based equilibrium contact angle boundary condition on jagged surfaces for phase-field methods
An energy-based equilibrium contact angle boundary condition on jagged surfaces for phase-field methods
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DOI：
10.1016/j.jcis.2018.02.075
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发表时间：
2018-08-01
影响因子：
9.9
通讯作者：
Riviere, Beatrice
中科院分区：
文献类型：
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作者：
Frank, Florian;Liu, Chen;Riviere, Beatrice
我们考虑了一个基于能量的边界条件施加平衡润湿角的Cahn-Hilliard-Navier-Stokes相场模型体素集型计算域。这些域通常源于多孔岩石的μ CT（微计算机断层扫描）成像，并且近似具有一定分辨率的（μ m尺度）光滑域。垂直于主轴的平面表面自然地近似由体素层近似。然而，在任何其他方向上的平面表面和弯曲表面产生由体素近似的锯齿状/拓扑粗糙表面。对于标准Cahn-Hilliard公式，其中扩散界面和域边界（流体-固体界面/壁）之间的接触角为90度，锯齿状表面对接触角没有影响。然而，在锯齿状体素表面上小于或大于90度的规定接触角被放大。作为一种补救措施，我们建议引入表面能量校正因子，用于平衡体素集表面积与底层平滑表面面积的差异。模型方程的离散化与间断Galerkin方法进行然而，所提出的半解析方法校正表面能同样适用于其他直接数值方法，如有限元，有限体积，或有限差分，因为校正因子出现在强制定的模型。(C)2018爱思唯尔公司All rights reserved.
We consider an energy-based boundary condition to impose an equilibrium wetting angle for the Cahn-Hilliard-Navier-Stokes phase-field model on voxel-set-type computational domains. These domains typically stem from mu CT (micro computed tomography) imaging of porous rock and approximate a (on mu m scale) smooth domain with a certain resolution Planar surfaces that are perpendicular to the main axes are naturally approximated by a layer of voxels However, planar surfaces in any other directions and curved surfaces yield a jagged/topologically rough surface approximation by voxels. For the standard Cahn-Hilliard formulation, where the contact angle between the diffuse interface and the domain boundary (fluid-solid interface/wall) is 90 degrees, jagged surfaces have no impact on the contact angle. However, a prescribed contact angle smaller or larger than 90 degrees on jagged voxel surfaces is amplified. As a remedy, we propose the introduction of surface energy correction factors for each fluid-solid voxel face that counterbalance the difference of the voxel-set surface area with the underlying smooth one. The discretization of the model equations is performed with the discontinuous Galerkin method However, the presented semi-analytical approach of correcting the surface energy is equally applicable to other direct numerical methods such as finite elements, finite volumes, or finite differences, since the correction factors appear in the strong formulation of the model. (C) 2018 Elsevier Inc. All rights reserved.