粗糙表面上的接触角滞后现象第II部分：微尺度界面动力学中的能量耗散
Contact Angle Hysteresis on Rough Surfaces Part II: Energy Dissipation via Microscale Interface Dynamics
摘要：
表面的润湿行为是非常重要的各种应用，如超疏水表面，提高石油采收率，金属矿石开采和防冰表面等粗糙的表面，这是规则，而不是例外，设计纹理表面的润湿性能，以适应这些应用程序通常涉及生物模仿或试错。现有的润湿理论，如众所周知的Wenzel（1936）和Cassie & Baxter（1944）模型，不能预测润湿状态，重要的是，仅给出单个平衡角，而不是实际观察到的稳定的接触角（滞后）范围。在本文中，我们使用粗糙度尺度的机械能平衡（在第一部分中导出）结合基于开源软件（Surface Evolver（Brakke 1992））的微尺度界面动力学模拟来计算化学均匀粗糙表面上的界面运动过程中的能量耗散。该耗散用于仅根据表面粗糙度形貌和平衡接触角的知识来预测接触角滞后（CAH）。我们模拟的界面动力学与圆边正方形柱的周期性阵列装饰的表面，并表明，能量耗散的变化近似为$ϕlnϕ$与面积分数（$ϕ$），并成为零为$ϕ \to 0$。我们的方法预测的CAH与Forsberg等人的实验结果吻合良好。（2010），特别是在低面积分数。我们还计算CAH的接口移动在45 $°$的表面周期性的方向，表明实验测量括号0 $°$和45 $°$前进方向的结果。
英文摘要：
The wetting behaviour of surfaces is important for various applications like super-hydrophobic surfaces, enhanced oil recovery, mining of metal ores and anti-icing surfaces etc. For rough surfaces, which are the rule rather than the exception, designing textured surfaces that have wetting properties tailored to suit these applications generally involves either bio-mimicry or trial and error. Existing wetting theories such as the well-known Wenzel (1936) and Cassie & Baxter (1944) models do not predict wetting regimes and importantly, only give a single equilibrium angle rather than a range of stable contact angles (hysteresis) as observed in reality. In this paper, we use a roughness-scale mechanical energy balance (derived in part I) combined with simulations of micro-scale interface dynamics based on open-source software (Surface Evolver (Brakke 1992)) to calculate the energy dissipation during the motion of an interface over a chemically homogeneous rough surface. This dissipation is used to predict contact angle hysteresis (CAH) from knowledge of just the surface roughness topography and equilibrium contact angle. We simulate interface dynamics over a surface decorated with a periodic array of round-edge square pillars and show that the energy dissipated varies approximately as $ϕlnϕ$ with the area fraction ($ϕ$), and becomes zero as $ϕ \to 0$. The CAH predicted by our method is in good agreement with the experimental results of Forsberg et al. (2010), especially at low area fractions. We also compute CAH for an interface moving at 45$°$ to the surface periodicity direction, showing that the experimental measurements are bracketed by the 0$°$ and 45$°$ advance direction results.
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