发表机构
University of Utah（犹他大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对双周期粗糙表面润湿，提出两尺度交替区域分解方法计算方向性接触角滞后区间，揭示强各向异性并约束宏观润湿区域。
AI 中文摘要
我们研究三维空间中双周期粗糙表面上的润湿现象。尽管液-气界面在局部满足杨氏角与固体接触，但微观粗糙度可能导致宏观表观角与该值显著不同。我们根据与钉扎微观构型相关的表观角来表述方向性接触角滞后（CAH）区间。为了逼近其后退端点和前进端点，我们将毛细管平均曲率流（CMCF）演化至极值稳态。计算这些状态是困难的，因为产生滞后的钉扎发生在粗糙度尺度上，而表观角仅在宏观尺度上才有意义，因此单一均匀网格必须同时分辨这两个尺度。因此，我们引入一种基于Schwarz分解的两尺度交替（TSA）方法：一种Merriman-Bence-Osher（MBO）扩散生成方案用于分辨接触线附近区域，而一个线性化的极小曲面问题用于更新远场区域。对于理想化的参考迭代，我们证明了近似界面能量的衰减。在代表性双周期表面上的数值实验显示，强各向异性的CAH区间，其宽度随接触线方向变化超过三倍，并在对角线方向附近急剧变化。由于静止液滴必须以该区间内的表观角与固体接触，计算出的各向异性约束了表面能够支撑的宏观润湿区域；这与方形静止液滴的边沿对角线方向排列一致。
英文摘要
We study wetting on a doubly periodic rough surface in three dimensions. Although the liquid-vapor interface meets the solid at the local Young's angle, microscale roughness can cause the macroscopic apparent angle to differ substantially from this value. We formulate the directional contact angle hysteresis (CAH) interval in terms of apparent angles associated with pinned microscopic configurations. To approximate its receding and advancing endpoints, we evolve capillary mean curvature flow (CMCF) toward extremal stationary states. Computing these states is difficult because the pinning that produces hysteresis is generated at the scale of the roughness, whereas the apparent angle is only meaningful at the macroscopic scale, so a single uniform grid must resolve both. We therefore introduce a two-scale alternating (TSA) method based on a Schwarz decomposition: a Merriman-Bence-Osher (MBO) diffusion-generated scheme resolves the contact-line near region, while a linearized minimal-surface problem updates the far region. For an idealized reference iteration, we prove decay of an approximate interfacial energy. Numerical experiments on a representative doubly periodic surface show a strongly anisotropic CAH interval whose width varies by more than a factor of three with contact-line orientation and changes sharply near the diagonal directions. Because a stationary droplet must meet the solid at an apparent angle inside this interval, the computed anisotropy constrains which macroscopic wetted regions the surface can support; it is consistent with a square-like stationary droplet whose sides align with the diagonal directions.
Comments33 pages, 15 figures
