Deformed foam structure and transitions in a tube

The "staircase" (2,1.1) foam structure in an ordered foam under expansion i n a cylindrical tube and the structural transition to the "bamboo" (1,1,0) structure are studied experimentally, analytically, and numerically using t he Surface Evolver minimization program. An analytical expression of the ob lique interface ill the (2,1,1) structure, a minimal surface, but curved by stretching of the foam, is given as a classic example of singular perturba tion (boundary layer) theory. The structural transition from staircase stru cture to bamboo structure takes place at a considerable dilation. The trans ition is not due to an edge length tending to zero continuously with dilati on, but results from the equilibrium (2,1,1) solution losing its stability due to a saddle node bifurcation.