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By introducing height dependency in the surface energy density, we propose anovel regularized variational model to simulate wetting/dewetting problems. Theregularized model leads to the appearance of a precursor layer which covers thebare substrate, with the precursor height depending on the regularizationparameter $\varepsilon$. The new model enjoys lots of advantages in analysisand imulations. With the help of the precursor layer, the regularized model isnaturally extended to a larger domain than that of the classicalsharp-interface model, and thus can be solved in a fixed domain. There is noneed to explicitly track the contact line motion, and difficulties arising fromfree boundary problems can be avoided. In addition, topological change eventscan be automatically captured. Under some mild and physically meaningfulconditions, we show the positivity-preserving property of the minimizers of thenew model. By using asymptotic analysis and $\Gamma$-convergence, weinvestigate the convergence relations between the new regularized model and theclassical sharp-interface model. Finally, numerical results are provided tovalidate our theoretical analysis, as well as the accuracy and efficiency ofthe new regularized model.

A regularized model for wetting/dewetting problems: asymptotic analysis and $\Gamma$-convergence