Improving the staircase approximation for wettability implementation of phase-field model: Part 1 - Static contact angle
Improving the staircase approximation for wettability implementation of phase-field model: Part 1 - Static contact angle
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DOI：
10.1016/j.camwa.2021.07.013
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
A. Zarareh;S. Khajepor;Stephen B. Burnside;Baixin Chen
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文献类型：
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作者：
A. Zarareh;S. Khajepor;Stephen B. Burnside;Baixin Chen
本文提出了两种处理复杂边界上流固相互作用的方案，并在格子Boltzmann方法框架下求解。该方案被应用于基于相场的润湿性实现方法的二元和三元流体模拟静态接触角的圆形表面上产生的阶梯近似。对于二元体系，采用表面能和几何润湿条件，而对于三元体系，表面能模型与两个离散方案，导致显式和隐式润湿条件的开发和检查。结果表明，将边界节点上的序参量值近似为相邻流体节点和固体节点之间序参量值的平均值的隐式润湿条件，提高了接触角预测的精度。为了模拟圆形表面上的接触角，并确定纳入润湿条件所需的法向量的方向，计算流固场的梯度。讨论了在给定边界节点法向量方向的情况下，如何利用相邻节点信息的两种方法，即舍入法和插值法。它示出的插值方法的结果表现出良好的协议与分析解决方案，而不是四舍五入的情况下，静态接触角的圆形表面上的二元和三元系统进行测试时。最后，它示出将不同的润湿条件与适当的方式处理法向量，并结合保守的相场模型可以模拟静态接触角在高密度比的二元和三元流体具有良好的精度。
In this study, two schemes to treat fluid-solid interaction on complex boundaries are proposed and solved in the framework of lattice Boltzmann method. The schemes are applied on the phase-field-based wettability implementation methods for binary and ternary fluids to simulate static contact angle on a circular surface generated by the staircase approximation. For the binary system, surface-energy and geometric wetting conditions are adopted, while for the ternary system, surface-energy model with two discretization schemes resulting in explicit and implicit wetting conditions are developed and examined. It is proven that the implicit wetting condition approximating the value of order parameters on the boundary node, as the average of their value between the neighboring fluid node and solid node, enhances the accuracy of predicted contact angles. For modeling of contact angle on the circular surface and identifying the direction of normal vectors required for incorporating wetting condition, the gradient of fluid-solid field is calculated. Two methods namely, round-off and interpolation describing how the information of neighboring nodes given the direction of normal vector on the boundary nodes should be used, are discussed. It is illustrated that results of the interpolation method exhibit a good agreement with the analytical solution as opposed to the round-off when tested in the case of static contact angle on a circular surface for both binary and ternary systems. Finally, it is shown incorporating different wetting conditions with the appropriate way of handling normal vectors and in combination with the conservative phase-field model can model static contact angle at high-density ratios for both binary and ternary fluids with good accuracy.