Thermodynamically consistent phase-field modelling of contact angle hysteresis
Thermodynamically consistent phase-field modelling of contact angle hysteresis
复制标题
DOI：
10.1017/jfm.2020.465
复制
发表时间：
2020-09-25
影响因子：
3.7
通讯作者：
Yue, Pengtao
中科院分区：
文献类型：
--
作者：
Yue, Pengtao
在动接触线问题的相场描述中，可以用自由能来描述两相系统，并基于能量耗散的假设推导出本构关系。在这项工作中，我们通过探索壁能量弛豫提出了一种新颖的接触角滞后边界条件，这使得系统在接触线处处于非平衡状态。我们的方法自动捕获钉扎、前进和后退，而无需明确了解接触线速度和接触角。微观动态接触角作为解决方案的一部分进行计算，而不是强加。此外，该公式满足耗散能量定律，其中耗散项都有其物理起源。基于能量定律，我们开发了一种时间二阶隐式有限元方法。该数值方案被证明对于匹配密度和零接触角滞后是无条件能量稳定的，并且通过数值验证对于更广泛的参数范围是能量耗散的。我们通过计算平面泊肃叶流中的固定液滴和移动界面来对我们的方法进行基准测试。当接触线移动时，其动力学符合考克斯理论。在振荡跌落的测试案例中，接触线在钉扎、前进和后退之间平滑过渡。我们的方法可以直接应用于三维问题，如倾斜墙上滑动水滴的测试案例所证明的那样。
In the phase-field description of moving contact line problems, the two-phase system can be described by free energies, and the constitutive relations can be derived based on the assumption of energy dissipation. In this work we propose a novel boundary condition for contact angle hysteresis by exploring wall energy relaxation, which allows the system to be in non-equilibrium at the contact line. Our method captures pinning, advancing and receding automatically without the explicit knowledge of contact line velocity and contact angle. The microscopic dynamic contact angle is computed as part of the solution instead of being imposed. Furthermore, the formulation satisfies a dissipative energy law, where the dissipation terms all have their physical origin. Based on the energy law, we develop an implicit finite element method that is second order in time. The numerical scheme is proven to be unconditionally energy stable for matched density and zero contact angle hysteresis, and is numerically verified to be energy dissipative for a broader range of parameters. We benchmark our method by computing pinned drops and moving interfaces in the plane Poiseuille flow. When the contact line moves, its dynamics agrees with the Cox theory. In the test case of oscillating drops, the contact line transitions smoothly between pinning, advancing and receding. Our method can be directly applied to three-dimensional problems as demonstrated by the test case of sliding drops on an inclined wall.