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

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