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In geometry, the Weaire–Phelan structure is a three-dimensional structure representing an idealised foam of equal-sized bubbles, with two different shapes. In 1993, Denis Weaire and Robert Phelan found that this structure was a better solution of the Kelvin problem of tiling space by equal volume cells of minimum surface area than the previous best-known solution, the Kelvin structure.
The Kelvin foam and the Weaire–Phelan foam are more stable, having smaller interfacial energy in the limit of a very small liquid content. [9] There are two types of interstitial holes left by hcp and fcc conformations; tetrahedral and octahedral void. Four spheres surround the tetrahedral hole with three spheres being in one layer and one ...
The mathematical topics described in the book include sphere packing (including the Tammes problem, the Kepler conjecture, and higher-dimensional sphere packing), the Honeycomb conjecture and the Weaire–Phelan structure, Voronoi diagrams and Delaunay triangulations, Apollonian gaskets, random sequential adsorption, and the physical ...
Using the Weaire–Phelan geometry, the Water Cube's exterior cladding is made of 4,000 ETFE bubbles, some as large as 9.14 meters (30 ft) across, with seven different sizes for the roof and 15 for the walls. [15] The structure had a capacity of 17,000 during the games. [11]
A foam pump, or squeeze foamer and dispensing device is a non- aerosol way of dispensing liquid materials. [1] The foam pump outputs the liquid in the form of foam and it is operated by squeezing. The parts of the foam pump, mostly made from polypropylene (PP), are similar to those of other pump devices. The foaming pump often comes with a ...
What is the most efficient foam in 3 dimensions? This was conjectured to be solved by the Kelvin structure, and this was widely believed for over 100 years, until disproved in 1993 by the discovery of the Weaire–Phelan structure. The surprising discovery of the Weaire–Phelan structure and disproof of the Kelvin conjecture is one reason for ...
A network model of a primitive cubic system. The primitive and cubic close-packed (also known as face-centered cubic) unit cells. In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals.
Peristaltic pump in motion. A peristaltic pump, also commonly known as a roller pump, is a type of positive displacement pump used for pumping a variety of fluids. The fluid is contained in a flexible tube fitted inside a circular pump casing. Most peristaltic pumps work through rotary motion, though linear peristaltic pumps have also been made.