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

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences (Impact Factor: 2.19). 06/2009; 465(2108). DOI: 10.1098/rspa.2009.0057
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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. 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.

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