论文标题
用于润湿/脱水问题的正规模型：渐近分析和$γ$ - convergence
A regularized model for wetting/dewetting problems: asymptotic analysis and $Γ$-convergence
论文作者
论文摘要
通过引入表面能密度的高度依赖性，我们提出了一种新型的正则变分模型，以模拟润湿/脱水问题。正则化模型导致前体层的外观，该图层覆盖了裸露的基板，根据正则化参数$ \ varepsilon $，前体的高度。新模型在分析和模拟方面具有许多优势。借助前体层，正则化模型自然地扩展到比经典尖端模型的域更大的域，因此可以在固定域中求解。无需明确跟踪接触线运动，并且可以避免因自由边界问题而引起的困难。此外，可以自动捕获拓扑变更事件。在某些温和且身体有意义的条件下，我们显示了新模型最小化器的阳性性能。通过使用渐近分析和$γ$ - 范围，我们研究了新的正规化模型与经典尖锐间接模型之间的收敛关系。最后，提供数值结果来验证我们的理论分析，以及新的正规化模型的准确性和效率。
By introducing height dependency in the surface energy density, we propose a novel regularized variational model to simulate wetting/dewetting problems. The regularized model leads to the appearance of a precursor layer which covers the bare substrate, with the precursor height depending on the regularization parameter $\varepsilon$. The new model enjoys lots of advantages in analysis and imulations. With the help of the precursor layer, the regularized model is naturally extended to a larger domain than that of the classical sharp-interface model, and thus can be solved in a fixed domain. There is no need to explicitly track the contact line motion, and difficulties arising from free boundary problems can be avoided. In addition, topological change events can be automatically captured. Under some mild and physically meaningful conditions, we show the positivity-preserving property of the minimizers of the new model. By using asymptotic analysis and $Γ$-convergence, we investigate the convergence relations between the new regularized model and the classical sharp-interface model. Finally, numerical results are provided to validate our theoretical analysis, as well as the accuracy and efficiency of the new regularized model.
