Equilibrium states and ground state of two-dimensional fluid foams

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 63, Issue 1, 2001, Pages

  Graner, F ^a   Jiang, Y ^b   Janiaud, E ^c,d   Flament, C ^c,d  

^a UNIV GRENOBLE ALPES   (France)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

^c SORBONNE UNIVERSITÉ   (France)

^d CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 18644374348     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.63.011402     Document Type: Article

References (51)

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25. If energy H is a strictly increasing function of the total perimeter (Formula presented) then the mechanical equilibrium (energy is extremal with respect to infinitesimal displacements, (Formula presented) still follows as the Laplace law, with an effective surface tension (Formula presented) In most foams, the amount of edge fluid is fixed: when the perimeter varies, the edge thickness varies too. Even if this variation changes (Formula presented) the geometry of the pattern remains the same.
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35. The total perimeter of a set of hexagons, possibly irregular, depends only on the sum of their areas, not on their detailed area distribution, as long as they have straight edges and (Formula presented) contact angles. See, for instance, I. M. Lipschitz, Zh. Éksp. Teor. Fiz. 42, 1354 (1962) [Sov. Phys. JETP 15, 939 (1962)] or
36. S. A. Safran, Phys. Rev. Lett. 46, 1581 (1981).In our notation, when the area polydispersity is increased at constant total area (Formula presented) decreases, (Formula presented) increases, and (Formula presented) is roughly constant if the edges remain nearly straight.
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38. This is usually derived from the Euler theorem 1214, applied here to a non-simply-convex foam (e.g., on a torus).
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45. Except, of course, in the trivial case of a single bubble where (Formula presented)
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