Gunjan Madhu Ranjan, Kumar Alok, Raj Rishi
Thermal and Fluid Transport Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Patna, Patna, Bihar 801103, India.
Langmuir. 2020 Mar 24;36(11):2974-2983. doi: 10.1021/acs.langmuir.9b03927. Epub 2020 Mar 11.
Superior mobility of droplets on lubricant-infused surfaces (LIS) has recently attracted significant attention for designing liquid-repellent surfaces. Unlike sessile droplets on flat surfaces wherein the contact line is easily visible in experiments, the contact line on LIS is masked by the lubricant meniscus, and special imaging techniques are required to visualize the hidden droplet-lubricant interface. Moreover, the overall shape deviates significantly from the spherical cap geometry even at very low droplet volumes. These difficulties necessitate the need to model interfaces in order to assess the effect of surface and fluid properties on LIS. In this work, we first numerically simulate the droplet shapes to show that at very small volumes, droplet-air and droplet-lubricant interfaces are constant mean curvature (CMC) interfaces. Moreover, we elucidate that these mean curvatures are related by the ratio of interfacial tensions of the droplet-air and the droplet-lubricant interfaces. These insights reduce the modeling of LIS interfacial profiles to a simplified geometric problem, which is solved using the parametric equations of CMC surfaces along with the angles of the Neumann triangle as the boundary conditions. Predicted profiles of the droplet-air interface as a spherical cap, the droplet-lubricant interface as a nodoid, and the lubricant-air interface as a catenoid/nodoid show good agreement with experimental results in the literature. Importantly, we for the first time provide a framework, which accurately predicts the true contact angle at the hidden solid contact line by just using the information of the top spherical cap portion visible in experiments.
液滴在注入润滑剂表面（LIS）上的卓越流动性最近在设计拒液表面方面引起了极大关注。与平面上的静态液滴不同，在平面上实验中接触线很容易看到，而LIS上的接触线被润滑剂弯月面掩盖，需要特殊的成像技术来可视化隐藏的液滴 - 润滑剂界面。此外，即使在液滴体积非常小的情况下，其整体形状也与球冠几何形状有很大偏差。这些困难使得有必要对界面进行建模，以评估表面和流体特性对LIS的影响。在这项工作中，我们首先通过数值模拟液滴形状，以表明在非常小的体积下，液滴 - 空气和液滴 - 润滑剂界面是常平均曲率（CMC）界面。此外，我们阐明这些平均曲率通过液滴 - 空气和液滴 - 润滑剂界面的界面张力之比相关。这些见解将LIS界面轮廓的建模简化为一个简化的几何问题，该问题使用CMC表面的参数方程以及诺伊曼三角形的角度作为边界条件来求解。预测的液滴 - 空气界面为球冠、液滴 - 润滑剂界面为卵形线、润滑剂 - 空气界面为悬链面/卵形线的轮廓与文献中的实验结果显示出良好的一致性。重要的是，我们首次提供了一个框架，该框架仅通过使用实验中可见的顶部球冠部分的信息就能准确预测隐藏的固体接触线处的真实接触角。
