Equilibrium states and ground state of two-dimensional fluid foams

Graner, François; Jiang, Yi; Janiaud, E.; Flament, C.

doi:10.1103/physreve.63.011402

Cited by 78 publications

(99 citation statements)

References 26 publications

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“…(A3) of Ref. [57], except that our definition includes a factor of √ 4π ; it approaches E = π/3 = 1.047 in the limit n → ∞. For n 3 our expression for the circularity is within 0.5% of C = (π 2 /12) 1/4 (1 − n/6) = 0.95(1 − n/6), the linear expansion around n = 6.…”

Section: Shapementioning

confidence: 75%

“…While the quantity 1/E 2 is commonly known as compactness, we follow Ref. [57] in referring to E as elongation. The term in parentheses in Eq.…”

Section: Shapementioning

confidence: 99%

“…These are like regular polygons but with edges replaced by circular arcs, all of radius R, that meet at 120 • as required by Plateau's laws. Isotropic bubbles have been used to model both two- [57] and three-dimensional [58][59][60][61] foams. We find…”

Section: Shapementioning

confidence: 99%

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Bubble statistics and coarsening dynamics for quasi-two-dimensional foams with increasing liquid content

2013

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. (2013). Bubble statistics and coarsening dynamics for quasi-two-dimensional foams with increasing liquid content. Physical Review E, 87(4) Bubble statistics and coarsening dynamics for quasi-two-dimensional foams with increasing liquid content AbstractWe report on the statistics of bubble size, topology, and shape and on their role in the coarsening dynamics for foams consisting of bubbles compressed between two parallel plates. The design of the sample cell permits control of the liquid content, through a constant pressure condition set by the height of the foam above a liquid reservoir. We find that in the scaling regime, all bubble distributions are independent not only of time, but also of liquid content. For coarsening, the average rate decreases with liquid content due to the blocking of gas diffusion by Plateau borders inflated with liquid; we achieve a factor of 4 reduction from the dry limit. By observing the growth rate of individual bubbles, we find that von Neumann's law becomes progressively violated with increasing wetness and decreasing bubble size. We successfully model this behavior by explicitly incorporating the border-blocking effect into the von Neumann argument. Two dimensionless bubble shape parameters naturally arise, one of which is primarily responsible for the violation of von Neumann's law for foams that are not perfectly dry. We report on the statistics of bubble size, topology, and shape and on their role in the coarsening dynamics for foams consisting of bubbles compressed between two parallel plates. The design of the sample cell permits control of the liquid content, through a constant pressure condition set by the height of the foam above a liquid reservoir. We find that in the scaling regime, all bubble distributions are independent not only of time, but also of liquid content. For coarsening, the average rate decreases with liquid content due to the blocking of gas diffusion by Plateau borders inflated with liquid; we achieve a factor of 4 reduction from the dry limit. By observing the growth rate of individual bubbles, we find that von Neumann's law becomes progressively violated with increasing wetness and decreasing bubble size. We successfully model this behavior by explicitly incorporating the border-blocking effect into the von Neumann argument. Two dimensionless bubble shape parameters naturally arise, one of which is primarily responsible for the violation of von Neumann's law for foams that are not perfectly dry. Disciplines Physical Sciences and Mathematics | Physics

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Section: Shapementioning

confidence: 75%

“…While the quantity 1/E 2 is commonly known as compactness, we follow Ref. [57] in referring to E as elongation. The term in parentheses in Eq.…”

Section: Shapementioning

confidence: 99%

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Bubble statistics and coarsening dynamics for quasi-two-dimensional foams with increasing liquid content

2013

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“…Otherwise, the edges on the boundary must be counted only once in n N = 2E − E boundary , implying a additional boundary term in (1) [21]. E is the total number of edges, internal and on the boundary.…”

Section: Two Cells Correlationsmentioning

confidence: 99%

“…The present analysis is mostly devoted to bi-dimensional foams, subject to extensive theoretical and experimental investigations [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21] and where the progresses are ahead of those on 3D foams.…”

Section: Introductionmentioning

confidence: 99%

Topological correlations and asymptotic freedom in cellular aggregates

Miri¹,

Oguey²

2007

Colloids and Surfaces A: Physicochemical and Engineering Aspect

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In random cellular systems, both observation and maximum entropy inference give a specific form to the topological pair correlation: it is bi-affine in the cells number of edges with coefficients depending on the distance between the two cells of the pair. Assuming this form for the pair correlations, we make explicit the conditions of statistical independence at large distance. When, on average, the defects do not contribute, the layer population and the enclosed topological charge both increase polynomially with distance. In dimension 2, the exponent of the leading terms depend on sum rules satisfied, or not, by the maximum entropy coefficients.

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Two‐Dimensional Tiling by Rubrene Molecules Self‐Assembled in Supramolecular Pentagons, Hexagons, and Heptagons on a Au(111) Surface

et al. 2008

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Surface nanostructuring by molecular self-organization is a relevant process in the growing field of nanotechnology. Depending on the characteristics of the molecules and on the type of interactions among them and with the substrate, a variety of surface patterns have been observed by means of scanning tunneling microscopy (STM).[1] Indeed, two-dimensional (2D) tiling constitutes a fundamental issue in topology, [2] with fascinating examples in nature and art, and applications in many domains such as cellular biology, [3] foam physics, [4] and crystal growth.[5] Herein we present the first observation of surface tiling with both nonperiodic and periodic arrangements of slightly distorted pentagons, hexagons, and heptagons formed by rubrene molecules adsorbed on a Au(111) surface. On adjacent regions of the sample, ordered honeycomb and hexagonal close-packed patterns are found. The existence of manifold arrangements in the supramolecular self-assembly of rubrene on gold originates from the three-dimensional nonplanar flexible structure of the molecule, as well as from the nature of the intermolecular bonds.Rubrene (5,6,11,12-tetraphenylnaphthacene, C 42 H 28 ) is a nonplanar chiral aromatic hydrocarbon constituted of a twisted tetracene backbone flanked by four out-of-plane phenyl groups as shown in the inset of Figure 1. The survey STM image (Figure 1) shows a Au(111) surface covered by a single layer of rubrene molecules. Three terraces separated by monatomic steps are visible, as well as the Au(111) herringbone reconstruction underlying the molecular layer. This overview shows areas with variable packing densities and different degrees of supramolecular order, denoted by A, B, and C. Regions A and C appear as ordered arrangements: the porous domain A reveals a honeycomb pattern, while region C displays a hexagonal close-packed structure. In contrast, the inhomogeneous area B presents no translational symmetry.A detail of the latter nonperiodic phase is shown in Figure 2 a. The dashed blue circle surrounds a single rubrene molecule; the submolecular contrast reveals three lobes and a quite regular threefold symmetry.[6] The self-assembled pattern is composed of supramolecular pentagons, hexagons, and filled heptagons, which appear to be randomly distributed over the surface. There exist 11 distinct tilings by regular polygons; [2] however, a combination of regular pentagons, hexagons, and heptagons generates empty gaps and overlapping regions, as inferred from the consideration of the angles at the corners of a regular pentagon (1088), hexagon (1208), and heptagon ( % 1298). Only when three hexagons joined and share a common corner is the angular sum exactly 3608. Nevertheless, three configurations exist that yield an angular sum close to 3608 (Figure 2 b): pentagon-hexagonheptagon ( % 3578), pentagon-heptagon-heptagon ( % 3668), and hexagon-hexagon-heptagon ( % 3698). The introduction of a slight distortion of the polygons allows a plane-filling tessellation. These three configurations are the most frequently...

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Equilibrium states and ground state of two-dimensional fluid foams

Cited by 78 publications

References 26 publications

Bubble statistics and coarsening dynamics for quasi-two-dimensional foams with increasing liquid content

Bubble statistics and coarsening dynamics for quasi-two-dimensional foams with increasing liquid content

Topological correlations and asymptotic freedom in cellular aggregates

Two‐Dimensional Tiling by Rubrene Molecules Self‐Assembled in Supramolecular Pentagons, Hexagons, and Heptagons on a Au(111) Surface

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