Foam as a soft granular material
Seminar Room 1, Newton Institute
AbstractWhen considered as an assembly of bubbles rather than as a structure of films and vertices, a foam or an emulsion is analogous to a granular material. Hard grains experiencing solid friction are replaced by soft bubbles interacting elastically and through viscous forces . Several experiments have recently been applied to two-dimensional flows of bubbles, and they have raised many questions: -what is the atress-strain-strain rate relation? -when does flow localisation occur? -how do disorder, polydispersity and liquid fraction influence rheology and localisation? -when does size segregation occur? These questions are addressed by a growing body of theory and simulations, based on several different models, with fascinating results, not yet fully reconciled. In particular, we have performed numerical simulations based on an elementary discrete element method developed by Durian , whose early results have been seen to be misleading. We show that this numerical approach is successful in reproducing the Herschel-Bulkley rheology observed in foams (and many other systems), therefore clarifying the problem of its explanation, and providing a link between local and continuum descriptions. Our simulations also account for the occurrence of localisation when friction along a wall is added (consistent with the predictions of continuum models, and attributable to wall drag), and predict the existence of a dynamic dilatancy effect . Finally, we show how the model can be successfully applied to reproduce bubbles flows in various geometries, such as a rotating drum, a silo (constriction) or around an obstacle. References:  D. Weaire, V. Langlois, M. Saadatfar, S. Hutzler. Foam as granular matter, in Lecture notes in complex systems: Granular and complex materials, eds. T. Aste, T. Di Matteo, A. Tordesillas, World Scientific Publishing (2007).  D. Durian. Foam mechanics at the bubble scale, Phys. Rev. Lett., 75, 4780 - 4783 (1995).  V.J. Langlois, S. Hutzler, D. Weaire. Rheological properties of the soft-disk model for 2D foams, Phys. Rev. E, 78, 021401(2008).
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