Dynamics of small solid particles on substrates of arbitrary topography

We study the dynamics of a small solid particle arising from the dewetting of a thin film on a curved substrate driven by capillarity, where mass transport is controlled by surface diffusion. We consider the case when the size of the deposited particle is much smaller than the local radius of curvature of the substrate surface. The application of the Onsager variational principle leads to a reduced-order model for the dynamic behaviour of particles on arbitrarily curved substrates. We demonstrate that particles move toward region of the substrate surface with lower mean curvature with a determined velocity. In particular, the velocity is proportional to the substrate curvature gradient and inversely proportional to the size of the particle, with a coefficient that depends on material properties that include the surface energy, surface diffusivity, density, and Young's (wetting) angle. The reduced model is validated by comparing with numerical results for the full, sharp-interface model in both two and three dimensions.