The Viscous Froth Model: steady states and the high-velocity limit

Simon John Cox; Gennady Mishuris; Denis Weaire

doi:10.1098/rspa.2009.0057

The Viscous Froth Model: steady states and the high-velocity limit

Department of Physics

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Abstract

The steady-state solutions of the viscous froth model for foam dynamics are analysed and shown to be of finite extent or to asymptote to straight lines. In the high-velocity limit, the solutions consist of straight lines with isolated points of infinite curvature. This analysis is helpful in the interpretation of observations of anomalous features of mobile two-dimensional foams in channels. Further physical effects need to be adduced in order to fully account for these.

Original language	English
Pages (from-to)	2391-2405
Number of pages	15
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	465
Issue number	2108
DOIs	https://doi.org/10.1098/rspa.2009.0057
Publication status	Published - 08 Aug 2009

Keywords

foams
discrete microfluidics
interface motion

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10.1098/rspa.2009.0057

high_vel_rev2.pdf

http://hdl.handle.net/2160/2527

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title = "The Viscous Froth Model: steady states and the high-velocity limit",

abstract = "The steady-state solutions of the viscous froth model for foam dynamics are analysed and shown to be of finite extent or to asymptote to straight lines. In the high-velocity limit, the solutions consist of straight lines with isolated points of infinite curvature. This analysis is helpful in the interpretation of observations of anomalous features of mobile two-dimensional foams in channels. Further physical effects need to be adduced in order to fully account for these.",

keywords = "foams, discrete microfluidics, interface motion",

author = "Cox, \{Simon John\} and Gennady Mishuris and Denis Weaire",

note = "S.J. Cox, D. Weaire and G. Mishuris (2009) The Viscous Froth Model: steady states and the high-velocity limit. Proc. R. Soc. A 465:2391-2405 Sponsorship: Financial support from (D.W.) the European Space Agency (MAP AO-99-108: C14914/02/NL/SH, MAP AO-99-075: C14308/00/NL/SH) (G.M.), the Wales Institute of Mathematical and Computational Sciences and (S.J.C.) EPSRC (EP/D048397/1, EP/D071127/1) is gratefully acknowledged. specialissue: 2391 journalsupplement: 2405 ",

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doi = "10.1098/rspa.2009.0057",

language = "English",

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AU - Mishuris, Gennady

AU - Weaire, Denis

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N2 - The steady-state solutions of the viscous froth model for foam dynamics are analysed and shown to be of finite extent or to asymptote to straight lines. In the high-velocity limit, the solutions consist of straight lines with isolated points of infinite curvature. This analysis is helpful in the interpretation of observations of anomalous features of mobile two-dimensional foams in channels. Further physical effects need to be adduced in order to fully account for these.

AB - The steady-state solutions of the viscous froth model for foam dynamics are analysed and shown to be of finite extent or to asymptote to straight lines. In the high-velocity limit, the solutions consist of straight lines with isolated points of infinite curvature. This analysis is helpful in the interpretation of observations of anomalous features of mobile two-dimensional foams in channels. Further physical effects need to be adduced in order to fully account for these.

KW - foams

KW - discrete microfluidics

KW - interface motion

U2 - 10.1098/rspa.2009.0057

DO - 10.1098/rspa.2009.0057

M3 - Article

SN - 1364-5021

VL - 465

SP - 2391

EP - 2405

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 2108

ER -

The Viscous Froth Model: steady states and the high-velocity limit

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