Abstract This paper presents a three-dimensional numerical simulation of water flow on an inclined plate using the software package OpenFOAM. We specifically investigate the influence of a heterogeneous surface on the flow pattern and the degree of wetting. By analyzing 400 simulation results a recently developed method for applying random contact angle inhomogeneities to surfaces is investigated. The simulations were carried out using the empirical contact angle model, which enables stable rivulet development. Part of the analysis is conducted with the help of the statistical software Dakota, which provides information about the probability distribution of the amount of wetted area when varying the two important influencing factors: the amplitude of the contact angle disturbance or the size of contiguous hydrophobic or hydrophilic areas. The results show that a variation of the two input parameters as desired leads to the introduction of a random component and thus to a change in the flow behavior. However, the changes remain within a narrow range around the mean value and produce only a few outliers, which occur mainly at large contact angle disturbance amplitudes and thus indicate the determining influence of the amplitude. The method has proven useful for performing several runs of the same simulation configuration for collecting statistics. Furthermore the inclination of the plate and the contact angle using a constant contact angle model are varied. Here, a clear dominance of the influence of the inclination also manifests over a wide contact angle range.

中文翻译：

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异质表面上小溪流动的不确定性——数值研究

摘要 本文介绍了使用OpenFOAM 软件包对倾斜板上的水流进行三维数值模拟。我们专门研究了异质表面对流动模式和润湿程度的影响。通过分析 400 个模拟结果，研究了最近开发的将随机接触角不均匀性应用于表面的方法。模拟是使用经验接触角模型进行的，这可以实现稳定的小溪发展。部分分析是在统计软件 Dakota 的帮助下进行的，该软件提供了有关在改变两个重要影响因素时润湿面积的概率分布的信息：接触角扰动的幅度或连续疏水性或疏水性的大小。亲水区。结果表明，根据需要改变两个输入参数会导致引入随机分量，从而导致流动行为发生变化。然而，变化保持在平均值附近的狭窄范围内，仅产生少数异常值，主要发生在大接触角扰动幅度下，因此表明幅度的决定性影响。该方法已被证明可用于执行相同模拟配置的多次运行以收集统计数据。此外，使用恒定接触角模型的板的倾斜度和接触角是变化的。在这里，倾斜影响的明显优势也表现在很宽的接触角范围内。