Weaire D, Barry JD and Hutzler S, The continuum theory of shear localization in two-dimensional foam, Journal of Physics: Condensed Matter, 22, 2010, 193101 - (22pp)
Journal of Physics: Condensed Matter; 22;
We review some recent advances in the rheology of two-dimensional
liquid foams, which should have implications for three-dimensional foams, as well
as other mechanical systems that have a yield stress. We focus primarily on shear
localization under steady shear, an effect first highlighted in an experiment by
Debr´egeas et al. A continuum theory which incorporates wall drag has reproduced
the effect. Its further refinements are successful in matching results of more
extensive observations and make interesting predictions regarding experiments for
low strain rates, and non-steady shear. Despite these successes, puzzles remain,
particularly in relation to quasistatic simulations. The continuum model is semiempirical:
the meaning of its parameters may be sought in comparison with more
detailed simulations and other experiments. The question of the origin of the
Herschel-Bulkley relation is particularly interesting.
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