Computation of constant mean curvature surfaces: Application to the gas-liquid interface of a pressurized fluid on a superhydrophobic surface

The interface shape separating a gas layer within a superhydrophobic surface consisting of a square lattice of posts from a pressurized liquid above the surface is computed numerically. The interface shape is described by a constant mean curvature surface that satisfies the Young-Laplace equation with the three-phase gas-liquid-solid contact line assumed pinned at the post outer edge. The numerical method predicts the existence of constant mean curvature solutions from the planar, zero curvature solution up to a maximum curvature that is dependent on the post shape, size and pitch. An overall force balance between surface tension and pressure forces acting on the interface yields predictions for the maximum curvature that agree with the numerical simulations to within one percent for convex shapes such as circular and square posts, but significantly over predicts the maximum curvature for non-convex shapes such as a circular post with a sinusoidal surface perturbation. Changing the post shape to increase the contact line length, while maintaining constant post area, results in increases of 2 to 12% in the maximum computable curvature for contact line length increases of 11 to 77%. Comparisons are made to several experimental studies for interface shape and pressure stability.     

Nanonails: a simple geometrical approach to electrically tunable superlyophobic surfaces

In this work, dynamically tunable, superlyophobic surfaces capable of undergoing a transition from profound superlyophobic behavior to almost complete wetting have been demonstrated for the first time. In the initial state, with no voltage applied, these surfaces exhibit contact angles as high as 150 degrees for a wide variety of liquids with surface tensions ranging from 21.8 mN/m (ethanol) to 72.0 mN/m (water). Upon application of an electrical voltage, a transition from the superlyophobic state to wetting is observed. We have examined experimentally and theoretically the nature of these transitions. The reported results provide novel methods of manipulating liquids on the microscale.     

On <Emphasis Type="Italic">g</Emphasis>-functions for Laguerre function expansions of Hermite type

We examine weighted L ^p boundedness of g-functions based on semigroups related to multi-dimensional Laguerre function expansions of Hermite type. A technique of vector-valued Calderón–Zygmund operators is used.