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

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Original languageEnglish
Pages (from-to)154-160
Journal / PublicationActa Materialia
Online published11 Oct 2018
Publication statusPublished - 15 Jan 2019


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 γ0, and is inversely proportional to the island volume γ0. This approach represents a general tool for modeling interface diffusion-controlled morphology evolution.

Research Area(s)

  • Moving contact line, Onsager's variational principle, Shrinking instability, Solid-state dewetting, Surface diffusion