Capillary drops on a rough surface

  • Antoine Mellet

    University of Maryland, College Park, USA
  • James Nolen

    Duke University, Durham, USA


We study liquid drops lying on a rough planar surface. The drops are minimizers of an energy functional that includes a random adhesion energy. We prove the existence of minimizers and the regularity of the free boundary. When the length scale of the randomly varying surface is small, we show that minimizers are close to spherical caps which are minimizers of an averaged energy functional. In particular, we give an error estimate that is algebraic in the scale parameter and holds with high probability.

Cite this article

Antoine Mellet, James Nolen, Capillary drops on a rough surface. Interfaces Free Bound. 14 (2012), no. 2, pp. 167–184

DOI 10.4171/IFB/278