Interdisciplinary Center for Advanced Materials Simulation (ICAMS), Ruhr University Bochum, Bochum, Germany.
J Phys Condens Matter. 2011 May 11;23(18):184112. doi: 10.1088/0953-8984/23/18/184112. Epub 2011 Apr 20.
The stability and dynamics of droplets on solid substrates are studied both theoretically and via experiments. Focusing on our recent achievements within the DFG-priority program 1164 (Nano- and Microfluidics), we first consider the case of (large) droplets on the so-called gradient substrates. Here the term gradient refers to both a change of wettability (chemical gradient) or topography (roughness gradient). While the motion of a droplet on a perfectly flat substrate upon the action of a chemical gradient appears to be a natural consequence of the considered situation, we show that the behavior of a droplet on a gradient of topography is less obvious. Nevertheless, if care is taken in the choice of the topographic patterns (in order to reduce hysteresis effects), a motion may be observed. Interestingly, in this case, simple scaling arguments adequately account for the dependence of the droplet velocity on the roughness gradient (Moradi et al 2010 Europhys. Lett. 89 26006). Another issue addressed in this paper is the behavior of droplets on hydrophobic substrates with a periodic arrangement of square shaped pillars. Here, it is possible to propose an analytically solvable model for the case where the droplet size becomes comparable to the roughness scale (Gross et al 2009 Europhys. Lett. 88 26002). Two important predictions of the model are highlighted here. (i) There exists a state with a finite penetration depth, distinct from the full wetting (Wenzel) and suspended (Cassie-Baxter, CB) states. (ii) Upon quasi-static evaporation, a droplet initially on the top of the pillars (CB state) undergoes a transition to this new state with a finite penetration depth but then (upon further evaporation) climbs up the pillars and goes back to the CB state again. These predictions are confirmed via independent numerical simulations. Moreover, we also address the fundamental issue of the internal droplet dynamics and the terminal center of mass velocity on a flat substrate.
我们首先关注梯度基底上（大）液滴的情况。这里的“梯度”一词指的是润湿性（化学梯度）或形貌（粗糙度梯度）的变化。虽然在化学梯度作用下，完美平坦基底上液滴的运动似乎是考虑情况下的自然结果，但我们表明，在形貌梯度上液滴的行为不那么明显。然而，如果在选择形貌图案时小心谨慎（为了减少滞后效应），则可能观察到运动。有趣的是，在这种情况下，简单的缩放论点充分解释了液滴速度对粗糙度梯度的依赖关系（Moradi 等人，2010 年，《欧洲物理快报》89,26006）。本文还讨论了疏水基底上周期性排列的方形支柱上液滴的行为。在这里，可以为液滴尺寸变得与粗糙度尺度相当的情况提出一个可解析求解的模型（Gross 等人，2009 年，《欧洲物理快报》88,26002）。模型的两个重要预测在这里被强调。（i）存在一个具有有限穿透深度的状态，与完全润湿（Wenzel）和悬停（Cassie-Baxter，CB）状态不同。（ii）在准静态蒸发过程中，最初位于支柱顶部的液滴（CB 状态）经历从有限穿透深度到新状态的转变，但随后（在进一步蒸发时）爬上支柱并再次回到 CB 状态。这些预测通过独立的数值模拟得到证实。此外，我们还解决了在平坦基底上的内部液滴动力学和末端质心速度的基本问题。
