Eur. Phys. J. E 4, 299-304
Deformed foam structure and transitions in a tube
D. Reinelt1, P. Boltenhagen2 and N. Rivier21 Department of Mathematics, Southern Methodist University, Dallas, TX 75275, USA
2 Laboratoire de Dynamique des Fluides Complexes, UMR 7506, 3 rue de l'Université, F-67084, Strasbourg Cedex, France
(Received 3 August 2000)
Abstract
The "staircase"(2,1,1) foam structure in an ordered foam under expansion
in a cylindrical tube and the structural transition to the "bamboo"
(1,1,0) structure
are studied experimentally, analytically, and numerically using
the Surface Evolver minimization program. An analytical expression of
the oblique interface in the (2,1,1) structure, a minimal surface, but
curved by stretching of the foam, is given as a classic example of
singular perturbation (boundary layer) theory. The structural transition
from staircase structure to bamboo
structure takes place at a considerable
dilation. The transition is not due to an edge length tending to zero
continuously with dilation, but results from
the equilibrium (2,1,1) solution losing its stability due to a saddle
node bifurcation.
61.72.-y - Defects and impurities in crystals; microstructure.
63.70.+h - Statistical mechanics of lattice vibrations and displacive phase transitions.
02.30.Mv - Approximations and expansions.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2001
