Application of Onsager's variational principle to the dynamics of a solid toroidal island on a substrate

Wei Jiang; Quan Zhao; Tiezheng Qian; David J Srolovitz; Weizhu Bao

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arXiv · 1806.08272

Application of Onsager's variational principle to the dynamics of a solid toroidal island on a substrate

Wei Jiang·Quan Zhao·Tiezheng Qian·David J Srolovitz·Weizhu Bao

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Abstract

In this paper, we consider the capillarity-driven evolution of a solid toroidal island on a flat rigid substrate, where mass transport is controlled by surface diffusion. This problem is representative of the geometrical complexity associated with the solid-state dewetting of thin films on substrates. We apply Onsager's variational principle to develop a general approach for describing surface diffusion-controlled problems. Based on this approach, we derive a simple, reduced-order model and obtain an analytical expression for the rate of island shrinking and validate this prediction by numerical simulations based on a full, sharp-interface model. We find that the rate of island shrinking is proportional to the material constants $B$ and the surface energy density $\gamma_0$, and is inversely proportional to the island volume $V_0$. This approach represents a general tool for modeling interface diffusion-controlled morphology evolution.

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Wei Jiang, Quan Zhao, Tiezheng Qian, David J Srolovitz, Weizhu Bao. 2018-06-21. Application of Onsager's variational principle to the dynamics of a solid toroidal island on a substrate. https://arxiv.org/abs/1806.08272

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