Cahn and Hilliard fluid on an oscillating boundary. (English) Zbl 0807.76081

Bouchitté, G.; Seppecher, P.

Buttazzo, Giuseppe (ed.) et al., Motion by mean curvature and related topics: proceedings of the international conference held at Trento, Italy, July 20-24, 1992. Berlin: de Gruyter. 23-42 (1994).

Summary: A Cahn and Hilliard fluid is in equilibrium in a solid container. The rugosity of the boundaries is taken into account through the assumption of an oscillating boundary whose period and amplitude are of the same order of magnitude as the thickness of the interface. We study the \(\Gamma\)-limit of this problem when this length tends to zero. We obtain a homogenized boundary energy and we show that rugosity may modify the wetting property of the wall until it is completely wet.
For the entire collection see [Zbl 0794.00019].

MSC:

76T99	Multiphase and multicomponent flows
35Q35	PDEs in connection with fluid mechanics
35B27	Homogenization in context of PDEs; PDEs in media with periodic structure

Keywords:

\(\Gamma\)-limit; homogenized boundary energy; rugosity; wetting