Uniform Flow of Modified Bingham Fluids in Narrow Cross Sections
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Abstract
A model of modified Bingham fluid is used to investigate uniform mudflows in narrow cross sections of the kind typical of hillslope incisions. The problem is tackled both numerically and experimentally. Experiments were performed using carboxymethylcellulose, a shear thinning fluid whose rheological behavior can be interpreted by a modified Bingham fluid model. For narrow rectangular, trapezoidal, and triangular cross sections, the capability to flow has been expressed by a general relationship that defines a dimensionless coefficient as a function of two dimensionless parameters: the Bingham number and an aspect ratio of the channel. We also derive plots for the critical Bingham number for incipient flow of modified Bingham fluids as a function of the aspect ratio of the channel. The present calculations and the experimental results demonstrate that the narrow character of the channel as well as its shape strongly affect the flow conductance and the critical value of the Bingham number.
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Acknowledgments
The present work has been funded by Fondazione Cassa di Risparmio di Verona, Vicenza, Belluno ed Ancona under the project RIMOF. The writer would like to thank the reviewers, Dr. Stocchino and Mr. Guala for providing the numerical code of particle tracking. Special thanks to Professor Giovanni Seminara for his fundamental help and to Professor Jasim Imran and Dr. Pietro Valsecchi for the extensive discussions related to this topic.
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Published In
Journal of Hydraulic Engineering
Volume 135 • Issue 8 • August 2009
Pages: 640 - 650
Copyright
© 2009 ASCE.
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Received: Feb 15, 2008
Accepted: Jan 30, 2009
Published online: Jul 15, 2009
Published in print: Aug 2009
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