Bingham plastics exhibit complex behaviors, depending on both geometrical and rheological factors, and are difficult to characterize systematically. This is particularly true in the case of transient flows, where solidlike and fluidlike behaviors coexist in an intermittent fashion. The aim of this contribution is to study the slump of Bingham columns under gravity, while varying systematically and independently both the geometry of the system and the rheological parameters. To do so, numerical experiments are carried out in two dimensions with a non-Newtonian Navier–Stokes code, the Gerris flow solver, using a volume-of-fluid approach. We are able to determine the slump height and the spreading of the column after motion ceased. These characteristics are related to the rheological properties and initial shape through scaling relationships. The results are compared with previous scalings and prediction from the literature. A discussion ensues on the importance of the normalization choice and of unambiguous discrimination between geometrical and material factors.
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July 2013
Research Article|
July 01 2013
Scaling laws for the slumping of a Bingham plastic fluid
Lydie Staron;
Lydie Staron
a)
CNRS–Université Pierre
et Marie Curie Paris 6, UMR 7190, Institut Le Rond d'Alembert, F-75252 Paris, France and School of Earth Sciences, University of Bristol
, Queens Road, Bristol BR8 1RJ, United Kingdom
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Pierre-Yves Lagrée;
Pierre-Yves Lagrée
CNRS–Université Pierre et Marie Curie Paris 6
, UMR 7190, Institut Jean Le Rond d'Alembert, F-75252 Paris, France
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Pascal Ray;
Pascal Ray
CNRS–Université Pierre et Marie Curie Paris 6
, UMR 7190, Institut Jean Le Rond d'Alembert, F-75252 Paris, France
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Stéphane Popinet
Stéphane Popinet
National Institute of Water and Atmospheric Research
, P.O. Box 14-901 Kilbirnie, Wellington, New Zealand
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a)
Author to whom correspondence should be addressed; electronic mail: lydie.staron@upmc.fr
J. Rheol. 57, 1265–1280 (2013)
Article history
Received:
May 30 2012
Citation
Lydie Staron, Pierre-Yves Lagrée, Pascal Ray, Stéphane Popinet; Scaling laws for the slumping of a Bingham plastic fluid. J. Rheol. 1 July 2013; 57 (4): 1265–1280. https://doi.org/10.1122/1.4802052
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