Capillary drops on a rough surface | Zendy

Antoine Mellet | Zendy; James Nolen | Zendy

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Capillary drops on a rough surface

Author(s) -

Antoine Mellet,

James Nolen

Publication year - 2012

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/278

Subject(s) - planar , surface (topology) , capillary action , energy (signal processing) , surface energy , mathematics , scale (ratio) , algebraic number , boundary (topology) , rough surface , length scale , specific surface energy , adhesion , mathematical analysis , drop (telecommunication) , geometry , physics , mechanics , materials science , thermodynamics , computer science , statistics , quantum mechanics , telecommunications , computer graphics (images) , composite material

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.

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