The foam drainage equation

Verbist, G.; Weaire, D.; Kraynik, Andrew M.

doi:10.1088/0953-8984/8/21/002

Cited by 250 publications

(225 citation statements)

References 15 publications

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“…Because the viscous resistance in this case of immobile interfaces is dominated by the PB (channels), this has been called the channel-dominated foam drainage equation. It was first derived by Gol'dfarb et al (1988) and was further analysed by Verbist et al (1996). Other classes of surfactants (in particular small, soap-like molecules) do not provide great resistance to in-plane motion of the interface.…”

Section: (B ) Interfacial Rheologymentioning

confidence: 99%

Foam: a multiphase system with many facets

Hilgenfeldt

Arif

Tsai

2008

Phil. Trans. R. Soc. A.

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Liquid foams are an extreme case of multiphase flow systems: capable of flow despite a very high dispersed phase volume fraction, yet exhibiting many characteristics of not only viscoelastic materials but also elastic solids. The non-trivial, well-defined geometry of foam bubbles is at the heart of a plethora of dynamical processes on widely varying length and time scales. We highlight recent developments in foam drainage (liquid dynamics) and foam rheology (flow of the entire gas-liquid system), emphasizing that many poorly understood features of other materials have precisely defined and quantifiable analogues in aqueous foams, where the only ingredients are well-known material parameters of Newtonian fluids and bubble geometry, together with subtle but important information on the surface mobility of the foam. Not only does this make foams an ideal model system for the theorist, but also an exciting object for experimental studies, in which dynamical processes span length scales from nanometres (thin films) to metres (foam continuum flows) and time scales from microseconds (film rupture) to minutes (foam rheology).

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Section: (B ) Interfacial Rheologymentioning

confidence: 99%

Foam: a multiphase system with many facets

Hilgenfeldt

Arif

Tsai

2008

Phil. Trans. R. Soc. A.

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“…Other solutions and comparisons to drop tower low gravity experiments have been reported by Weislogel and Lichter. 22,23 Modifications of the governing equation to account for a gravity force opposing spreading have been discussed by Verbist et al 24 and Kovscek and Radke. 25 Ma et al 26 first tried to account for a liquid-gas frictional interaction in their analysis of the flow in triangular microgrooves, a work that was continued and applied to the analysis of the heat transfer in microheat pipes in Refs.…”

Section: Introductionmentioning

confidence: 99%

Capillary rise of a liquid between two vertical plates making a small angle

Higuera¹,

Medina

Liñán³

2008

Physics of Fluids

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The penetration of a wetting liquid in the narrow gap between two vertical plates making a small angle is analyzed in the framework of the lubrication approximation. At the beginning of the process, the liquid rises independently at different distances from the line of intersection of the plates except in a small region around this line where the effect of the gravity is negligible. The maximum height of the liquid initially increases as the cubic root of time and is attained at a point that reaches the line of intersection only after a certain time. At later times, the motion of the liquid is confined to a thin layer around the line of intersection whose height increases as the cubic root of time and whose thickness decreases as the inverse of the cubic root of time. The evolution of the liquid surface is computed numerically and compared with the results of a simple experiment.

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“…Foams are viscoelastic "soft condensed matter" systems, with intriguing rheology [2] and drainage behavior [3]. They have numerous applications as detergents, lightweight structural materials, and in oil recovery [1].…”

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confidence: 99%

An Accurate von Neumann's Law for Three-Dimensional Foams

et al. 2001

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The diffusive coarsening of 2D soap froths is governed by von Neumann's law. A statistical version of this law for dry 3D foams has long been conjectured. A new derivation, based on a theorem by Minkowski, yields an explicit analytical von Neumann's law in 3D which is in very good agreement with detailed simulations and experiments. The average growth rate of a bubble with F faces is shown to be proportional to F 1͞2 for large F, in contrast to the conjectured linear dependence. Accounting for foam disorder in the model further improves the agreement with data.

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The foam drainage equation

Cited by 250 publications

References 15 publications

Foam: a multiphase system with many facets

Foam: a multiphase system with many facets

Capillary rise of a liquid between two vertical plates making a small angle

An Accurate von Neumann's Law for Three-Dimensional Foams

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