Foams, and by extension a whole class of random cellular materials are characterized by minimizing total interfacial area between the cells. Both structure and evolution of such materials by aging (coarsening) are ill-understood because of our lack of knowledge of the cell geometry. Combining Plateau's rules and certain symmetry requirements, we analytically determine the geometry of generic polyhedral cells we call Isotropic Plateau Polyhedra (IPPs). Their properties, such as surface area, edge length, or coarsening rate, are exactly known and very close approximations to the corresponding properties of average, random foam bubbles. Certain IPPs can also be found experimentally in soap foam. We show that measuring the coarsening rate of these bubbles allows for the simple computation of the soap film thickness, which is found to vary with foam age.
|Title of host publication||Mechanics of the 21st century: 21st International Congress of Theoretical and Applied Mechanics|
|Editors||Witold Gutkowski, Tomasz A. Kowalewski|
|Place of Publication||Berlin, Germany|
|Publication status||Published - 15 Aug 2004|
|Event||XXI International Congress of Theoretical and Applied Mechanics, ICTAM 2004 - Warsaw, Poland|
Duration: 15 Aug 2004 → 21 Aug 2004
Conference number: 21
|Conference||XXI International Congress of Theoretical and Applied Mechanics, ICTAM 2004|
|Period||15/08/04 → 21/08/04|
Hilgenfeldt, S., Kraynik, A. M., Reinelt, D. A., & Sullivan, J. M. (2004). Bubble shapes in foams: the importance of being isotropic. In W. Gutkowski, & T. A. Kowalewski (Eds.), Mechanics of the 21st century: 21st International Congress of Theoretical and Applied Mechanics (pp. -). Berlin, Germany: Springer.