THE LINEAR ELASTIC BEHAVIOR OF A BIDISPERSE WEAIRE-PHELAN SOAP FOAM

Abstract

The linear elastic constants for a dry Weaire-Phelan foam with bidisperse cell-size distribution are computed. This highly ordered structure has eight polyhedral bubbles in the unit cell: two pentagonal dodecahedra and six tetrakaidecahedra with twelve pentagonal faces and two hexagonal faces. Both dodecahedra have equal volume and all of the tetrakaidecahedra have equal volume, but these volumes are different for the bidisperse structures considered here. These volume constraints preserve the cubic symmetry of the Weaire-Phelan structure so that the elastic response is completely characterized by a bulk modulus k for volume compression and two shear moduli μ₁ and μ ₂. The shear moduli can be combined to obtain an effective isotropic shear modulus μ¯, which represents the shear response averaged over all orientations of the foam. For the monodisperse case, μ¯ = 0.8684 TV¯,^-1/3 where TT is surface tension and V is the average bubble volume. For bidisperse structures, p. never differs from the monodisperse case by more than 0.5% and the at always lie within 4% of ft. The pressure inside the dodecahedra is always greater than the pressure inside the tetrakaidecahedra even when the dodecahedra are larger.

KEYWORDS:

• Elastic
• Bidisperse
• Weaire-Phelan
• Soap foam

Notes

*This manuscript has been submitted to the Festschrift volume of Chemical Engineering Communications to honor Professor Howard Brenner on the occasion of his 65th birthday

*We dedicate this manuscript to Professor Howard Brenner a true scholar and inspiration.

Additional information

Notes on contributors

ANDREW M. KRAYNIK

To whom correspondence should be sent