Foams : Linking Geometry and Physics
Sascha Hilgenfeldt (Northwestern University, Illinois)

Jeudi 1er décembre 2005

When a liquid is frothed up and left to drain, the result is a unique material called a dry foam, a collection of polyhedra filling space in an intricate way. Dry foam exists at the boundary between liquids and solids : it flows under external forces once a yield stress has been overcome, it possesses a well-defined average structure as well as a special kind of disorder, and it is a dynamically evolving substance in which both liquid and gas flows alter its physical properties.

In describing a foam, a knowledge of its structure and of the geometry of the bubbles is of prime importance. We highlight the link between foam geometry and foam physics and observe that the specific connectivity of the continuous phase in foams discovered by Plateau in the 19th century is crucial for the understanding of foam coarsening, the exchange of gas between bubbles. A set of bubbles called Isotropic Plateau Polyhedra is defined for which geometrical properties and coarsening rates can be computed analytically, allowing for specific and accurate predictions.

We will also touch upon the flow of a foam between parallel plates to illustrate its use as a model for atomistic processes in solids, up to and including material failure. Foams thus emerge as well-controlled versatile systems for modeling the behavior of materials ranging from soft matter and complex fluids all the way to hard condensed matter. The unique benefit of foams is the accessibility of the microscopic scale in the system, i.e. that of a single bubble.