A rectangular grid formed by liquid filaments on a partially wetting substrate evolves in a series of breakups leading to arrays of drops with different shapes distributed in a rather regular bidimensional pattern. Our study is focused on the configuration produced when two long parallel filaments of silicone oil, which are placed upon a glass substrate previously coated with a fluorinated solution, are crossed perpendicularly by another pair of long parallel filaments. A remarkable feature of this kind of grids is that there are two qualitatively different types of drops. While one set is formed at the crossing points, the rest are consequence of the breakup of shorter filaments formed between the crossings. Here, we analyze the main geometric features of all types of drops, such as shape of the footprint and contact angle distribution along the drop periphery. The formation of a series of short filaments with similar geometric and physical properties allows us to have simultaneously quasi identical experiments to study the subsequent breakups. We develop a simple hydrodynamic model to predict the number of drops that results from a filament of given initial length and width. This model is able to yield the length intervals corresponding to a small number of drops and its predictions are successfully compared with the experimental data as well as with numerical simulations of the full Navier--Stokes equation that provide a detailed time evolution of the dewetting motion of the filament till the breakup into drops. Finally, the prediction for finite filaments is contrasted with the existing theories for infinite ones.

中文翻译：

---

由液体细丝二维网格破裂引起的液滴图案

由液体细丝在部分润湿的基材上形成的矩形网格在一系列破裂中演变，导致具有不同形状的液滴阵列以相当规则的二维图案分布。我们的研究重点是当两条平行的长硅油细丝放置在先前涂有氟化溶液的玻璃基板上时，与另一对平行长细丝垂直交叉时产生的配置。这种网格的一个显着特点是有两种性质不同的液滴。虽然在交叉点形成一组，但其余是交叉点之间形成的较短长丝断裂的结果。在这里，我们分析了所有类型液滴的主要几何特征，例如足迹的形状和沿液滴周边的接触角分布。一系列具有相似几何和物理特性的短丝的形成使我们能够同时进行准相同的实验来研究随后的断裂。我们开发了一个简单的流体动力学模型来预测由给定初始长度和宽度的细丝产生的液滴数量。该模型能够产生对应于少量液滴的长度间隔，并且其预测成功地与实验数据以及完整 Navier-Stokes 方程的数值模拟进行了比较，该方程提供了去湿运动的详细时间演变直到分解成液滴。最后，对有限长丝的预测与对无限长丝的现有理论进行了对比。