Math @ Duke

Publications [#349994] of Thomas P. Witelski
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 Witelski, TP, Nonlinear dynamics of dewetting thin films,
Aims Mathematics, vol. 5 no. 5
(January, 2020),
pp. 42294259 [doi]
(last updated on 2020/11/25)
Abstract: © 2020 the Author(s), licensee AIMS Press. Fluid films spreading on hydrophobic solid surfaces exhibit complicated dynamics that describe transitions leading the films to break up into droplets. For viscous fluids coating hydrophobic solids this process is called “dewetting”. These dynamics can be represented by a lubrication model consisting of a fourthorder nonlinear degenerate parabolic partial differential equation (PDE) for the evolution of the film height. Analysis of the PDE model and its regimes of dynamics have yielded rich and interesting research bringing together a wide array of different mathematical approaches. The early stages of dewetting involve stability analysis and pattern formation from small perturbations and selfsimilar dynamics for finitetime rupture from larger amplitude perturbations. The intermediate dynamics describes further instabilities yielding topological transitions in the solutions producing sets of slowlyevolving nearequilibrium droplets. The longtime behavior can be reduced to a finitedimensional dynamical system for the evolution of the droplets as interacting quasisteady localized structures. This system yields coarsening, the successive rearrangement and merging of smaller drops into fewer larger drops. To describe macroscale applications, meanfield models can be constructed for the evolution of the number of droplets and the distribution of droplet sizes. We present an overview of the mathematical challenges and open questions that arise from the stages of dewetting and how they relate to issues in multiscale modeling and singularity formation that could be applied to other problems in PDEs and materials science.


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