三相接触线垂直于化学条纹衬底的传播模型
Modelling the corrugation of the three-phase contact line perpendicular to a chemically striped substrate
摘要：
我们模拟了一个无限长的液体桥，限制在两个板之间的化学图案的条纹相同的宽度和不同的接触角，其中的三相接触线运行，平均而言，垂直的条纹。这使我们能够研究在没有钉扎的情况下接触线的弯曲。我们发现，如果板之间的间距与表面图案化的长度尺度相比较大，则宏观接触角的余弦对应于条纹的内角的余弦的平均值，如Cassie方程所预测的。然而，如果间距变得与图案的长度尺度相当，则存在到宏观接触角在每个条纹的固有接触角之间变化的状态的急剧交叉，如局部Young方程所预测的。结果得到使用两种数值方法，格子玻尔兹曼（扩散界面方法）和表面进化（尖锐的接口方法），从而给出了一个直接比较两个流行的数值方法来计算液滴形状时，应用到一个非平凡的接触线问题。我们发现，这两种方法得到一致的结果，如果我们考虑到线张力的自由能。在格子玻尔兹曼方法中，线张力来自扩散三相接触线处的离散化效应。
英文摘要：
We model an infinitely long liquid bridge confined between two plates chemically patterned by stripes of same width and different contact angle, where the three-phase contact line runs, on average, perpendicular to the stripes. This allows us to study the corrugation of a contact line in the absence of pinning. We find that, if the spacing between the plates is large compared to the length scale of the surface patterning, the cosine of the macroscopic contact angle corresponds to an average of cosines of the intrinsic angles of the stripes, as predicted by the Cassie equation. If, however, the spacing becomes of order the length scale of the pattern there is a sharp crossover to a regime where the macroscopic contact angle varies between the intrinsic contact angle of each stripe, as predicted by the local Young equation. The results are obtained using two numerical methods, Lattice Boltzmann (a diffuse interface approach) and Surface Evolver (a sharp interface approach), thus giving a direct comparison of two popular numerical approaches to calculating drop shapes when applied to a non-trivial contact line problem. We find that the two methods give consistent results if we take into account a line tension in the free energy. In the lattice Boltzmann approach, the line tension arises from discretisation effects at the diffuse three phase contact line.
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