Computation of Equilibrium Foam Structures Using the Surface Evolver

Phelan, Robert J.; Weaire, D.; Brakke, Kenneth A.

doi:10.1080/10586458.1995.10504320

Cited by 73 publications

(44 citation statements)

References 10 publications

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“…The shape of the pore is assumed to be spherical and spheres of equal volume are arranged according to the following three lattice structures: (i) BCC, body-centered cubic, (ii) FCC, face-centered cubic, and (iii) A15 lattice, which is similar to the Weaire-Phelan (WP) structure [16,17]. The periodic foam unit-cell geometry is obtained by subtracting the spheres at the various lattice points from the unit cell cube as shown in Figure 1a.…”

Section: Geometric Modelmentioning

confidence: 99%

Permeability and Thermal Transport in Compressed Open-Celled Foams

Annapragada

Murthy

Garimella

2008

Heat Transfer: Volume 1

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Section: Geometric Modelmentioning

confidence: 99%

Permeability and Thermal Transport in Compressed Open-Celled Foams

Annapragada

Murthy

Garimella

2008

Heat Transfer: Volume 1

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“…for several years [15][16][17], so we can rely on it safely. Just as an exercise, we have tested it for the equilibrium condition of a perfect sphere with a given target volume evolved from a cube in the SC model.…”

Section: The Model the Software And The Proceduresmentioning

confidence: 99%

Numerical observation of nonaxisymmetric vesicles in fluid membranes

Yan

Liu

et al. 1998

Phys. Rev. E

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By means of Surface Evolver (Exp. Math,1,141 1992), a software package of bruteforce energy minimization over a triangulated surface developed by the geometry center of University of Minnesota, we have numerically searched the non-axisymmetric shapes under the Helfrich spontaneous curvature (SC) energy model. We show for the first time there are abundant mechanically stable non-axisymmetric vesicles in SC model, including regular ones with intrinsic geometric symmetry and complex irregular ones. We report in this paper several interesting shapes including a corniculate shape with six corns, a quadri-concave shape, a shape resembling sickle cells, and a shape resembling acanthocytes. As far as we know, these shapes have not been theoretically obtained by any curvature model before. In addition, the role of the spontaneous curvature in the formation of irregular crenated vesicles has been studied. The results shows a positive spontaneous curvature may be a necessary condition to keep an irregular crenated shape being mechanically stable.

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“…The result is an equilibrium foam. 40 This approach can be used to study the well-known Kelvin problem, described as,"finding the minimal surface area partition of three-dimensional space into cells of equal volume." Sir William Thomson 41 , Lord Kelvin, proposed a tiling by truncated octahedra with slightly curved faces, i.e.…”

Section: B Cell Representation and Characteristic Dimensionsmentioning

confidence: 99%

An experimentally validated and parameterized periodic unit-cell reconstruction of open-cell foams

Jaeger

T’Joen

Huisseune

et al. 2011

Journal of Applied Physics

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The physical behavior of open-cell foams depends on their microscopic structure. An open-cell geometrical model is proposed, which can serve as the basis for a future macroscopic analysis. The strut geometry is of particular interest, as it is reported to have substantial influence on the occurring thermo-hydraulic and mechanical phenomena. Axial strut size variation, as well as the porosity dependence of shape is quantified and included in a geometrical model. The foam is generated by placing the struts on an elongated tetrakaidecahedron. The required input parameters for the model are two cell dimensions, corresponding to the mean transverse and conjugate diameters of the ellipse encompassing a cell, and the strut cross-sectional surface area at its midpoint between two nodes. The foam geometry is generated iteratively, as porosity is used as validation. A high resolution micro-computed tomography scan is performed to measure the three parameters, the resulting porosity and surface-to-volume ratio. This allows to validate the model. The predictions are found to be within measurement accuracy. A numerical implementation of the model in the preprocessor of a commercial CFD package is demonstrated.

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Computation of Equilibrium Foam Structures Using the Surface Evolver

Cited by 73 publications

References 10 publications

Permeability and Thermal Transport in Compressed Open-Celled Foams

Permeability and Thermal Transport in Compressed Open-Celled Foams

Numerical observation of nonaxisymmetric vesicles in fluid membranes

An experimentally validated and parameterized periodic unit-cell reconstruction of open-cell foams

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