The effects of Plateau borders in the two-dimensional soap froth I. Decoration lemma and diffusion theorem

Bolton, F.; Weaire, D.

doi:10.1080/13642819108205538

Cited by 75 publications

(67 citation statements)

References 14 publications

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“…In the wet limit, the shear modulus goes to zero (smoothly in the case of disordered foams with polydisperse bubble sizes), as was first confirmed from experiments by Princen and Kiss [4] and tentatively identified in the early two-dimensional (2D) PLAT simulation of Bolton and Weaire [5,6,7,8] as well as in the 2D Bubble Model of Durian [9]. Also, the yield stress goes to zero.…”

Section: Introductionmentioning

confidence: 54%

“…Before proceeding to the analysis of rearrangements we shall present results for various basic quantities of interest, complementing and completing previously published data from PLAT [8,5,6,11,17].…”

Section: The Plat Softwarementioning

confidence: 99%

“…PLAT [5,6,7,8], as the name suggests, is a software package for the simulation of a foam in 2D based on the direct implementation of Plateau's Laws, rather than an energy minimisation routine.…”

Section: The Plat Softwarementioning

confidence: 99%

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Statistics and topological changes in 2D foam from the dry to the wet limit

Dunne

Bolton²,

Weaire

et al. 2017

Philosophical Magazine

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Section: Introductionmentioning

confidence: 54%

Section: The Plat Softwarementioning

confidence: 99%

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Statistics and topological changes in 2D foam from the dry to the wet limit

Dunne

Bolton²,

Weaire

et al. 2017

Philosophical Magazine

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“…Other studies on coarsening in three-dimensional wet foams have found empirically that the coarsening rate is reduced by a factor of 1/ √ ε [33,35]. In two dimensions, there has been theoretical [36][37][38][39] and simulation [36,40] work on the effects of liquid fraction on coarsening. Recently, a theoretical approach was proposed, and tested by Potts model simulations, based on an effective number of sides that depends on the fraction of the perimeter occupied by wet versus dry interfaces [41].…”

Section: Introductionmentioning

confidence: 99%

“…To this end we construct a border-blocking model, with the same assumptions used in the models of Refs. [26,32,36]. Namely, the Plateau borders swell with liquid and totally block gas diffusion, reducing the film area and hence slowing the rate of coarsening.…”

Section: B Border-blocking Modelmentioning

confidence: 99%

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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