The structure of foam cells: Isotropic Plateau polyhedra

Hilgenfeldt, Sascha; Kraynik, Andrew M.; Reinelt, Douglas A.; Sullivan, Jason M.

doi:10.1209/epl/i2003-10295-7

Cited by 60 publications

(70 citation statements)

References 30 publications

(47 reference statements)

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“…Here, its 3D counterpart, the S opt /V 2/3 versus F relation, is more complicated (in particular, unlike in 2D, it depends on the volume ratio) [21]: but it appears to have the same essential property as in 2D, namely to be a non-increasing function of F; we thus hope to extend to 3D this 2D result [27].…”

Section: Correlationsmentioning

confidence: 88%

Three-dimensional bubble clusters: Shape, packing, and growth rate

Cox

Graner²

2004

Phys. Rev. E

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We consider three-dimensional clusters of equal-volume bubbles packed around a central bubble and calculate their energy and optimal shape. We obtain the surface area and bubble pressures to improve on existing growth laws for three-dimensional bubble clusters. We discuss the possible number of bubbles that can be packed around a central one: the "kissing problem", here adapted to deformable objects.

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Section: Correlationsmentioning

confidence: 88%

Three-dimensional bubble clusters: Shape, packing, and growth rate

Cox

Graner²

2004

Phys. Rev. E

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“…Grains with less than six sides shrink, whereas grains with more than six sides grow. An expression analogous to von Neumann-Mullins, but valid in three spatial dimensions, has been sought for over fifty years 1,[13][14][15][16] . Such an expression may be obtained based on the assumption that a polycrystalline network can be represented, albeit abstractly, by ANHs.…”

Section: D Analogue Of Von Neumann-mullins Equationmentioning

confidence: 99%

Modeling polycrystals with regular polyhedra

Rios

Glicksman

2006

Mat. Res.

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Polycrystalline structure is of paramount importance to materials science and engineering. It provides an important example of a space-filling irregular network structure that also occurs in foams as well as in certain biological tissues. Therefore, seeking an accurate description of the characteristics of polycrystals is of fundamental importance. Recently, one of the authors (MEG) published a paper in which a method was devised of representation of irregular networks by regular polyhedra with curved faces. In Glicksman's method a whole class of irregular polyhedra with a given number of faces, N, is represented by a single symmetrical polyhedron with N curved faces. This paper briefly describes the topological and metric properties of these special polyhedra. They are then applied to two important problems of irregular networks: the dimensionless energy 'cost' of irregular networks, and the derivation of a 3D analogue of the von Neumann-Mullins equation for the growth rate of grains in a polycrystal.

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“…Coarsening in that limit has been investigated experimentally, numerically and theoretically in two (2D) [3][4][5][6][7] and later in three dimensions (3D) [8][9][10][11][12][13][14].…”

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confidence: 99%

Growth Laws and Self-Similar Growth Regimes of Coarsening Two-Dimensional Foams: Transition from Dry to Wet Limits

et al. 2012

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We study the topology and geometry of two dimensional coarsening foams with arbitrary liquid fraction. To interpolate between the dry limit described by von Neumann's law, and the wet limit described by Marqusee equation, the relevant bubble characteristics are the Plateau border radius and a new variable, the effective number of sides. We propose an equation for the individual bubble growth rate as the weighted sum of the growth through bubble-bubble interfaces and through bubble-Plateau borders interfaces. The resulting prediction is successfully tested, without adjustable parameter, using extensive bidimensional Potts model simulations. Simulations also show that a selfsimilar growth regime is observed at any liquid fraction and determine how the average size growth exponent, side number distribution and relative size distribution interpolate between the extreme limits. Applications include concentrated emulsions, grains in polycrystals and other domains with coarsening driven by curvature.

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The structure of foam cells: Isotropic Plateau polyhedra

Cited by 60 publications

References 30 publications

Three-dimensional bubble clusters: Shape, packing, and growth rate

Three-dimensional bubble clusters: Shape, packing, and growth rate

Modeling polycrystals with regular polyhedra

Growth Laws and Self-Similar Growth Regimes of Coarsening Two-Dimensional Foams: Transition from Dry to Wet Limits

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