A single sagging Plateau border

B. Embley, P. Grassia

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The loading of foams with liquid weight, contributed primarily by the Plateau borders, results in an external force which may often be important to structure and drainage, especially in foams of a higher liquid content; loading induces deformations in structures. A Plateau border in a three-dimensional foam is supported by three films, which are assumed to sag under loading, initially with linear elasticity in these numerical simulations. The weight of a Plateau border is allowed to vary along its length, in accordance with the foam drainage equation for a single channel (balancing gravity and capillarity for a given channel size and orientation). The surface area of the deformed structure is subsequently minimized in the Surface Evolver, and it is found that only for sufficiently dry borders, the films have linear elasticity. For wet foams, the true distortion due to loading is larger than the linear model predicts; an iterative approach, based on the solution of the drainage equation and a direct application of gravitational forces in the Surface Evolver, is developed for wetter Plateau borders. The implications for forced-drainage experiments and continuum-level drainage models are discussed.
LanguageEnglish
Pages20-29
Number of pages10
JournalColloids and Surfaces A: Physicochemical and Engineering Aspects
Volume309
Issue number1-3
Early online date15 Nov 2006
DOIs
Publication statusPublished - 1 Nov 2007
Event6th Eufoam Conference - Potsdam, Germany
Duration: 2 Jul 20066 Jul 2006

Fingerprint

drainage
borders
foams
Drainage
Foams
plateaus
Elasticity
elastic properties
Capillarity
Liquids
liquids
Gravitation
gravitation
continuums
Computer simulation
simulation
Experiments

Keywords

  • foam drainage
  • foam structure
  • non-linear elasticity
  • surface evolver

Cite this

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title = "A single sagging Plateau border",
abstract = "The loading of foams with liquid weight, contributed primarily by the Plateau borders, results in an external force which may often be important to structure and drainage, especially in foams of a higher liquid content; loading induces deformations in structures. A Plateau border in a three-dimensional foam is supported by three films, which are assumed to sag under loading, initially with linear elasticity in these numerical simulations. The weight of a Plateau border is allowed to vary along its length, in accordance with the foam drainage equation for a single channel (balancing gravity and capillarity for a given channel size and orientation). The surface area of the deformed structure is subsequently minimized in the Surface Evolver, and it is found that only for sufficiently dry borders, the films have linear elasticity. For wet foams, the true distortion due to loading is larger than the linear model predicts; an iterative approach, based on the solution of the drainage equation and a direct application of gravitational forces in the Surface Evolver, is developed for wetter Plateau borders. The implications for forced-drainage experiments and continuum-level drainage models are discussed.",
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A single sagging Plateau border. / Embley, B.; Grassia, P.

In: Colloids and Surfaces A: Physicochemical and Engineering Aspects, Vol. 309, No. 1-3, 01.11.2007, p. 20-29.

Research output: Contribution to journalArticle

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AU - Embley, B.

AU - Grassia, P.

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AB - The loading of foams with liquid weight, contributed primarily by the Plateau borders, results in an external force which may often be important to structure and drainage, especially in foams of a higher liquid content; loading induces deformations in structures. A Plateau border in a three-dimensional foam is supported by three films, which are assumed to sag under loading, initially with linear elasticity in these numerical simulations. The weight of a Plateau border is allowed to vary along its length, in accordance with the foam drainage equation for a single channel (balancing gravity and capillarity for a given channel size and orientation). The surface area of the deformed structure is subsequently minimized in the Surface Evolver, and it is found that only for sufficiently dry borders, the films have linear elasticity. For wet foams, the true distortion due to loading is larger than the linear model predicts; an iterative approach, based on the solution of the drainage equation and a direct application of gravitational forces in the Surface Evolver, is developed for wetter Plateau borders. The implications for forced-drainage experiments and continuum-level drainage models are discussed.

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