Capillary drops on a rough surface

Journal Article

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. © European Mathematical Society 2012.

Full Text

Duke Authors

Cited Authors

  • Mellet, A; Nolen, J

Published Date

  • 2012

Published In

Volume / Issue

  • 14 / 2

Start / End Page

  • 167 - 184

International Standard Serial Number (ISSN)

  • 1463-9963

Digital Object Identifier (DOI)

  • 10.4171/IFB/278