The Surface Evolver

The Surface Evolver is a computer program that minimizes the energy of a surface subject to constraints. The surface is represented as a simplicial complex. The energy can include surface tension, gravity, and other forms. Constraints can be geometrical constraints on vertex positions or constraints on integrated quantities such as body volumes. The minimization is done by evolving the surface down the energy gradient. This paper describes the mathematical model used and the operations available to interactively modify the surface

Magnetic cylindrical colloids at liquid interfaces exhibit non-volatile switching of their orientation in an external field

We study the orientation of magnetic cylindrical particles adsorbed at a liquid interface in an external field using analytical theory and high resolution finite element simulations. Cylindrical particles are interesting since they possess multiple locally stable orientations at the liquid interface so that the orientational transitions induced by an external field will not disappear when the external field is removed, i.e., the switching effect is \emph{non-volatile}. We show that, in the absence of an external field, as we reduce the aspect ratio $\alpha$ of the cylinders below a critical value ($\alpha_c \approx 2$) the particles undergo spontaneous symmetry breaking from a stable side-on state to one of two equivalent stable tilted states, similar to the spontaneous magnetisation of a ferromagnet going through the Curie point. By tuning both the aspect ratio and contact angle of the cylinders, we show that it is possible to engineer particles that have one, two, three or four locally stable orientations. We also find that the magnetic responses of cylinders with one or two stable states are similar to that of paramagnets and ferromagnets respectively, while the magnetic response of systems with three or four stable states are even more complex and have no analogs in simple magnetic systems. Magnetic cylinders at liquid interfaces therefore provide a facile method for creating switchable functional monolayers where we can use an external field to induce multiple non-volatile changes in particle orientation and self-assembled structure

Wetting of anisotropic sinusoidal surfaces - experimental and numerical study of directional spreading

Directional wettability, i.e. variation of wetting properties depending on the surface orientation, can be achieved by anisotropic surface texturing. A new high precision process can produce homogeneous sinusoidal surfaces (in particular parallel grooves) at the micro-scale, with a nano-scale residual roughness five orders of magnitude smaller than the texture features. Static wetting experiments have shown that this pattern, even with a very small aspect ratio, can induce a strong variation of contact angle depending on the direction of observation. A comparison with numerical simulations (using Surface Evolver software) shows good agreement and could be used to predict the fluid-solid interaction and droplet behaviour on textured surfaces. Two primary mechanisms of directional spreading of water droplets on textured stainless steel surface have been identified. The first one is the mechanical barrier created by the textured surface peaks, this limits spreading in perpendicular direction to the surface anisotropy. The second one is the capillary action inside the sinusoidal grooves accelerating spreading along the grooves. Spreading has been shown to depend strongly on the history of wetting and internal drop dynamics

Gravity-Induced Shape Transformations of Vesicles

We theoretically study the behavior of vesicles filled with a liquid of higher density than the surrounding medium, a technique frequently used in experiments. In the presence of gravity, these vesicles sink to the bottom of the container, and eventually adhere even on non - attractive substrates. The strong size-dependence of the gravitational energy makes large parts of the phase diagram accessible to experiments even for small density differences. For relatively large volume, non-axisymmetric bound shapes are explicitly calculated and shown to be stable. Osmotic deflation of such a vesicle leads back to axisymmetric shapes, and, finally, to a collapsed state of the vesicle.Comment: 11 pages, RevTeX, 3 Postscript figures uuencode

Computation of equilibrium foam structure using the Surface Evolver

The Surface Evolver has been used to minimise the surface area of various ordered structures for monodisperse foam. Additional features have enabled its application to foams of arbitrary liquid fraction. Early results for the case of dry foam (negligible liquid fraction) produced a structure haveing lower surface area, or energy, than Kelvin\u27s 1887 minimal tetrakaidecahedron. The calculations reported here show that this remains the case when the liquid fraction is finite, up to about 11%, at which point an f.c.c arrangement of the cells becomes preferable

A Zador-Like Formula for Quantizers Based on Periodic Tilings

We consider Zador's asymptotic formula for the distortion-rate function for a variable-rate vector quantizer in the high-rate case. This formula involves the differential entropy of the source, the rate of the quantizer in bits per sample, and a coefficient G which depends on the geometry of the quantizer but is independent of the source. We give an explicit formula for G in the case when the quantizing regions form a periodic tiling of n-dimensional space, in terms of the volumes and second moments of the Voronoi cells. As an application we show, extending earlier work of Kashyap and Neuhoff, that even a variable-rate three-dimensional quantizer based on the ``A15'' structure is still inferior to a quantizer based on the body-centered cubic lattice. We also determine the smallest covering radius of such a structure.Comment: 8 page

Diffusive transport of light in three-dimensional disordered Voronoi structures

The origin of diffusive transport of light in dry foams is still under debate. In this paper, we consider the random walks of photons as they are reflected or transmitted by liquid films according to the rules of ray optics. The foams are approximately modeled by three-dimensional Voronoi tessellations with varying degree of disorder. We study two cases: a constant intensity reflectance and the reflectance of thin films. Especially in the second case, we find that in the experimentally important regime for the film thicknesses, the transport-mean-free path does not significantly depend on the topological and geometrical disorder of the Voronoi foams including the periodic Kelvin foam. This may indicate that the detailed structure of foams is not crucial for understanding the diffusive transport of light. Furthermore, our theoretical values for transport-mean-free path fall in the same range as the experimental values observed in dry foams. One can therefore argue that liquid films contribute substantially to the diffusive transport of light in {dry} foams.Comment: 8 pages, 8 figure