Layering and wetting transitions for an SOS interface

We study the solid-on-solid interface model above a horizontal wall in three dimensional space, with an attractive interaction when the interface is in contact with the wall, at low temperatures. There is no bulk external field. The system presents a sequence of layering transitions, whose levels increase with the temperature, before reaching the wetting transition.Comment: 61 pages, 6 figures. Miscellaneous corrections and changes, primarily in Section 4. Figure 5 added

Rigorous generalization of Young's law for heterogeneous and rough substrates

We consider a SOS type model of interfaces on a substrate which is both heterogeneous and rough. We first show that, for appropriate values of the parameters, the differential wall tension that governs wetting on such a substrate satisfies a generalized law which combines both Cassie and Wenzel laws. Then in the case of an homogeneous substrate, we show that this differential wall tension satisfies either the Wenzel's law or the Cassie's law, according to the values of the parameter

Wetting of Heterogeneous Surfaces at the Mesoscopic Scale

International audienceWe consider the problem of wetting on a heterogeneous wall with mesoscopic defects: i.e.\ defects of order $L^{\varepsilon}$, $0<\varepsilon<1$, where $L$ is some typical length--scale of the system. In this framework, we extend several former rigorous results which were shown for walls with microscopic defects \cite{DMR,DMR2}. Namely, using statistical techniques applied to a suitably defined semi-infinite Ising-model, we derive a generalization of Young's law for rough and heterogeneous surfaces, which is known as the generalized Cassie-Wenzel's equation. In the homogeneous case, we also show that for a particular geometry of the wall, the model can exhibit a surface phase transition between two regimes which are either governed by Wenzel's or by Cassie's law

Layering in the Ising model

We consider the three-dimensional Ising model in a half-space with a boundary field (no bulk field). We compute the low-temperature expansion of layering transition lines

A lattice model for the line tension of a sessile drop

Within a semi--infinite thre--dimensional lattice gas model describing the coexistence of two phases on a substrate, we study, by cluster expansion techniques, the free energy (line tension) associated with the contact line between the two phases and the substrate. We show that this line tension, is given at low temperature by a convergent series whose leading term is negative, and equals 0 at zero temperature

Wulff shape of crystals

Article in a peer-reviewed open-access encyclopedia.International audienceWulff shape of crystals. The shape of an equilibrium crystal is obtained, according to the Gibbs thermodynamic principle, by minimizing the total surface free energy associated to the crystal-medium interface. To study the solution to this problem, known as the Wulff construction, is the object of the article