Two-dimensional magnetic liquid froth: Coarsening and topological correlations

Elias, Florence; Flament, C.; Bacri, Jean‐Claude; Cardoso, Olivier; Graner, François

doi:10.1103/physreve.56.3310

Cited by 35 publications

(20 citation statements)

References 15 publications

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“…This leads to a correction term that in part depends on the variance of the distribution. We note, for later, that this form of m(n) decreases monotonically with increasing n. This relationship has been used to analyze biological tissue [39,40], soap foams [41,42], and other cellular structures [43][44][45].…”

Section: Aboav-weaire Relationmentioning

confidence: 99%

Statistical topology of three-dimensional Poisson-Voronoi cells and cell boundary networks

et al. 2013

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Voronoi tessellations of Poisson point processes are widely used for modeling many types of physical and biological systems. In this paper, we analyze simulated Poisson-Voronoi structures containing a total of 250,000,000 cells to provide topological and geometrical statistics of this important class of networks. We also report correlations between some of these topological and geometrical measures. Using these results, we are able to corroborate several conjectures regarding the properties of three-dimensional Poisson-Voronoi networks and refute others. In many cases, we provide accurate fits to these data to aid further analysis. We also demonstrate that topological measures represent powerful tools for describing cellular networks and for distinguishing among different types of networks.

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Section: Aboav-weaire Relationmentioning

confidence: 99%

Statistical topology of three-dimensional Poisson-Voronoi cells and cell boundary networks

et al. 2013

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“…For instance, in a soap froth between two parallel plates of glass, each line has an energy proportional to its length, 3D effects such as the curvature in the vertical plane appearing only in the value of the proportionality constant. Some 2D foams are stabilised by dipolar interactions without amphiphilic molecules [29]: in Langmuir monolayers [4], magnetic garnets [37], oil/ferrofluid emulsions [7]; they are acceptable model of 2D foams if and only if the dipolar energy is small enough not to affect their behaviour.…”

Section: Two-dimensional (2d) Foamsmentioning

confidence: 99%

“…The same oil as that fills the bubbles surrounds them. For details see [7]. Annealing procedure: We tilt the Plexiglas plates from the horizontal plane to an angle of 0.1 • , inducing a low effective gravity field.…”

Section: Relation Between Pressure and Energymentioning

confidence: 99%

Two-Dimensional Fluid Foams at Equilibrium

Graner

2002

Morphology of Condensed Matter

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“…Examples include polycrystalline solids [1], magnetic garnet films [2], twophase ferrofluidic mixtures [3], superconducting magnetic froths [4], foams [5,6] or emulsions [7]. In such systems, the positive energy associated with the interfaces is the driving force of a characteristic grain growth or "coarsening" process by which smaller grains tend to disappear while larger grains grow, leading to a progressive reduction of the overall interfacial energy and to characteristic asymptotic grain size distributions.…”

Section: Introductionmentioning

confidence: 99%

Arresting bubble coarsening: A two-bubble experiment to investigate grain growth in the presence of surface elasticity

Salonen

Maestro

Drenckhan

et al. 2016

EPL

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Many two-phase materials suffer from grain-growth due to the energy cost which is associated with the interface that separates both phases. While our understanding of the driving forces and the dynamics of grain growth in different materials is well advanced by now, current research efforts address the question of how this process may be slowed down, or, ideally, arrested. We use a model system of two bubbles to explore how the presence of a finite surface elasticity may interfere with the coarsening process and the final grain size distribution. Combining experiments and modelling in the analysis of the evolution of two bubbles, we show that clear relationships can be predicted between the surface tension, the surface elasticity and the initial/final size ratio of the bubbles. We rationalise these relationships by the introduction of a modified Gibbs criterion. Besides their general interest, the present results have direct implications for our understanding of foam stability.

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Two-dimensional magnetic liquid froth: Coarsening and topological correlations

Cited by 35 publications

References 15 publications

Statistical topology of three-dimensional Poisson-Voronoi cells and cell boundary networks

Statistical topology of three-dimensional Poisson-Voronoi cells and cell boundary networks

Two-Dimensional Fluid Foams at Equilibrium

Arresting bubble coarsening: A two-bubble experiment to investigate grain growth in the presence of surface elasticity

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