We study steady-state thin films on chemically heterogeneous substrates of finite size, subject to no-flux boundary conditions. Based on the structure of the bifurcation diagram, we classify the 1D steady-state solutions that exist on such substrates into six different branches and develop asymptotic estimates for the steady states on each branch. Using perturbation expansions, we show that leading-order solutions provide good predictions of the steady-state thin films on stepwise-patterned substrates. We show how the analysis in one dimension can be extended to axisymmetric solutions. We also examine the influence of the wettability contrast of the substrate pattern on the linear stability of droplets and the time evolution for dewetting on small domains. Results are also applied to describe 2D droplets on hydrophilic square patches and striped regions used in microfluidic applications.

中文翻译：

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化学非均质基材上薄膜液滴的稳态

我们研究有限通量的化学异质衬底上的稳态薄膜，并受无磁通边界条件的影响。基于分叉图的结构，我们将存在于此类衬底上的一维稳态解分为六个不同的分支，并为每个分支上的稳态建立渐近估计。使用扰动展开，我们证明了前导解为逐步图案化衬底上的稳态薄膜提供了良好的预测。我们展示了如何将一维分析扩展到轴对称解。我们还检查了底物图案的可湿性对比对液滴的线性稳定性的影响以及在小区域上进行去湿的时间演变。