During his research into the 'ether', Lord Kelvin (above) proposed the following problem: What is the most economical way of partitioning space with equally sized cells?
Kelvin's solution, the tetrakaidecahedron, remained the best solution to this problem until 1993 when Denis Weaire and Robert Phelan found a structure with 0.3% less surface area than Kelvin's structure.
The Weaire–Phelan structure is based on a class of chemical compounds known as clathrates. It can also be found in liquid crystals. The above picture is an image of the Weaire–Phelan structure.
For more information please look up one of our publications on the subject.
From the 17th century onwards, up to the beginning of this century, materials were divided into solids, which behave according to the theory of linear elasticity (i.e. Hooke's law), and liquids which exhibit viscous flow, described by the Navier-Stokes equations.
But this simple division excludes an increasingly number of modern materials, whose properties lie between the above two extremes. Foams are examples of such viscoelastic materials.
The actual behaviour of the material depends on the circumstances and parameters under which an experiment (or application) is carried out (time scale, applied force etc.)
An example of a viscoelastic material is shaving foam, which sticks onto the face until being made to flow under the action of the razor. The foam exhibits a certain yield-stress below which it behaves as a solid (with a corresponding shear modulus) and above which it flows as a liquid.
We have developed a simple mechanical model of a 2-dimensional solid foam, which tells us how a foam buckles under stress. Here you can see one of our results on an eight-cell system:
Foam drainage plays an important part in the formation and evolution of liquid foams. A freshly formed foam is not in equilibrium under gravity, and liquid drains out of it until such an equilibrium is attained. This is free drainage. Forced drainage, on the other hand, is the steady flow through an otherwise static foam, which can be produced by continuous addition of liquid at the top.
We have observed forced drainage in simple experiments in which liquid is added steadily to the top of a column of soap froth, which has first been allowed to drain freely so that it is close to the dry limit over most of its height. These experiments revealed a striking effect: immediately after liquid is introduced at the top, or the flow rate is increased, a front travels down the tube at a constant velocity, like the bore on certain rivers. Theoretical investigation has shown that this is indeed an example of a solitary wave.
The experimental arrangement, with a steady flow rate Q, is illustrated below. The diagram on the right shows the solitary wave, with higher liquid fraction fl behind the wave front.
