Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-21T18:41:43.809Z Has data issue: false hasContentIssue false
  • English
  • Français

Experimental investigation of viscoplastic free-surface flows in a steady uniform regime

Published online by Cambridge University Press:  04 August 2014

Guillaume Chambon ,
A. Ghemmour  and
M. Naaim
Guillaume Chambon*
Affiliation:
IRSTEA, UR ETGR, Snow Avalanche and Torrent Control Research Unit, Domaine Universitaire, BP 76, Grenoble, France Université Grenoble Alpes, Grenoble, France
A. Ghemmour
Affiliation:
IRSTEA, UR ETGR, Snow Avalanche and Torrent Control Research Unit, Domaine Universitaire, BP 76, Grenoble, France Université Grenoble Alpes, Grenoble, France
M. Naaim
Affiliation:
IRSTEA, UR ETGR, Snow Avalanche and Torrent Control Research Unit, Domaine Universitaire, BP 76, Grenoble, France Université Grenoble Alpes, Grenoble, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We present experimental results focused on the hydraulic properties of free-surface flows of viscoplastic fluids. The objective is to investigate the possibility of predicting macroscopic flow properties on the base of conventional rheometrical characterization of the fluids. The experiments are performed in an inclined conveyor-belt channel allowing us to generate gravity-driven surges which remain stationary in the laboratory frame. Two different types of materials are studied: Kaolin slurries and Carbopol microgels. Global height–velocity relationships and local velocity profiles are measured in the uniform zone for different experimental conditions (slope angle, rheological parameters). These data are then compared to theoretical predictions based on the Herschel–Bulkley constitutive law and independent measurements of the rheological parameters. Great care has been devoted to the determination of experimental uncertainties, including those associated with the rheometrical characterization. For Kaolin, the experimental results show excellent agreement with theoretical predictions. With Carbopol, on the contrary, a systematic discrepancy between measured and theoretical flow heights is observed. The velocity profiles do nevertheless remain consistent with a Herschel–Bulkley rheology, and we show that all experimental data can be explained by increasing the rheological parameters (yield stress and consistency) by 10–20 % compared to the values measured in the rheometer. Potential interpretations for this discrepancy are discussed.

JFM classification

Waves/Free-surface Flows: Hydraulics Interfacial Flows (free surface): Interfacial Flows (free surface) Non-Newtonian Flows: Non-Newtonian Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 754 , 10 September 2014 , pp. 332 - 364
Copyright
© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alexandrou, A. N., McGilvreay, T. M. & Burgos, G. 2001 Steady Herschel–Bulkley fluid flow in three-dimensional expansions. J. Non-Newtonian Fluid Mech. 100, 77–96.Google Scholar
Ancey, C. 2007 Plasticity and geophysical flows: a review. J. Non-Newtonian Fluid Mech. 142, 4–35.Google Scholar
Ancey, C., Andreini, N. & Epely-Chauvin, G. 2012 Viscoplastic dambreak waves: review of simple computational approaches and comparison with experiments. Adv. Water Resour. 48, 79–91.Google Scholar
Ancey, C. & Cochard, S. 2009 The dam-break problem for Herschel–Bulkley viscoplastic fluids down steep flumes. J. Non-Newtonian Fluid Mech. 158 (1–3), 18–35.Google Scholar
Ancey, C., Coussot, P. & Evesque, P. 1996 Examination of the possibility of a fluid-mechanics treatment of dense granular flows. Mech. Cohes.-Frict. Mat. 1 (4), 385–403.Google Scholar
Andreini, N., Epely-Chauvin, G. & Ancey, C. 2012 Internal dynamics of Newtonian and viscoplastic fluid avalanches down a sloping bed. Phys. Fluids 24, 053101.Google Scholar
Balmforth, N. J. & Craster, R. V. 1999 A consistent thin-layer theory for Bingham plastics. J. Non-Newtonian Fluid Mech. 84, 65–81.Google Scholar
Balmforth, N. J., Craster, R. V., Rust, A. C. & Sassi, R. 2006 Viscoplastic flow over an inclined surface. J. Non-Newtonian Fluid Mech. 139 (1–2), 103–127.Google Scholar
Barnes, H. A. 1995 A review of the slip (wall depletion) of polymer solutions, emulsions and particle suspensions in viscosimeters: its cause, character, and cure. J. Non-Newtonian Fluid Mech. 56, 221–251.CrossRefGoogle Scholar
Barnes, H. A. 1999 The yield stress – a review or ‘ $\pi \alpha \nu \tau \alpha \rho \epsilon \iota $ ’ – everything flows? J. Non-Newtonian Fluid Mech. 81 (1–2), 133–178.Google Scholar
Baudez, J.-C., Ayol, A. & Coussot, P. 2004 Practical determination of the rheological behavior of pasty biosolids. J. Environ. Manage. 72, 181–188.Google Scholar
Baudonnet, L., Pere, D., Michaud, P., Grossiord, J.-L. & Rodriguez, F. 2002 Effect of dispersion stirring speed the particle size distribution and rheological properties of carbomer dispersions and gels. J. Disper. Sci. Technol. 23, 499–510.CrossRefGoogle Scholar
Beaulne, M. & Mitsoulis, E. 1997 Creeping motion of a sphere in tubes filled with Herschel–Bulkley fluids. J. Non-Newtonian Fluid Mech. 72 (1), 55–71.Google Scholar
Bird, R. B., Armstrong, R. C. & Hassager, O. 1987 Dynamics of Polymeric Liquids, 2nd edn. Fluid Mechanics, vol. 1. Wiley-Interscience.Google Scholar
Bird, R. B., Dai, G. C. & Yarusso, B. J. 1983 The rheology and flow of viscoplastic materials. Rev. Chem. Engng 1, 1–70.Google Scholar
Bossard, F., Moan, M. & Aubry, T. 2007 Linear and nonlinear viscoelastic behavior of very concentrated plate-like Kaolin suspensions. J. Rheol. 51 (6), 1253–1270.Google Scholar
Chambon, G., Ghemmour, A. & Laigle, D. 2009 Gravity-driven surges of a viscoplastic fluid: an experimental study. J. Non-Newtonian Fluid Mech. 158, 54–62.Google Scholar
Cheddadi, I., Saramito, P. & Graner, F. 2012 Steady Couette flow of elastoviscoplastic fluids are non-unique. J. Rheol. 56 (1), 213–239.Google Scholar
Coussot, P. 1994 Steady, laminar, flow of concentrated mud suspensions in open channel. J. Hydraul. Res. 32 (4), 535–559.Google Scholar
Coussot, P. 1995 Structural similarity and transition from Newtonian to Non-Newtonian behavior for clay-water suspensions. Phys. Rev. Lett. 74 (20), 3971–3974.Google Scholar
Coussot, P. 2005 Rheometry of Pastes, Suspensions, and Granular Materials. Applications in Industry and Environment. Wiley-Interscience.CrossRefGoogle Scholar
Coussot, P., Nguyen, Q. D., Huynh, H. T. & Bonn, D. 2002 Avalanche behavior in yield stress fluids. Phys. Rev. Lett. 88 (17), 175501.Google Scholar
Coussot, P., Tocquer, L., Lanos, C. & Ovarlez, G. 2009 Macroscopic vs. local rheology of yield stress fluids. J. Non-Newtonian Fluid Mech. 158 (1–3), 85–90.Google Scholar
Frigaard, I. A. & Nouar, C. 2005 On the usage of viscosity regularisation methods for visco-plastic fluid flow computation. J. Non-Newtonian Fluid Mech. 127 (1), 1–26.Google Scholar
Geraud, B., Bocquet, L. & Barentin, C. 2013 Confined flows of a polymer microgel. Eur. Phys. J. E 36, 30.CrossRefGoogle ScholarPubMed
Goyon, J., Colin, A., Ovarlez, G., Adjari, A. & Bocquet, L. 2008 Spatial cooperativity in soft glassy flows. Nature 454, 84–87.CrossRefGoogle ScholarPubMed
Jay, P., Magnin, A. & Piau, J. M. 2002 Numerical simulation of viscoplastic fluid flows through an axisymmetric contraction. Trans. ASME: J. Fluids Engng 124, 700–705.Google Scholar
Jogun, S. M. & Zukoski, C. F. 1999 Rheology and microstructure of dense suspensions of plate-shaped colloidal particles. J. Rheol. 43 (4), 847–871.Google Scholar
Jossic, L. & Magnin, A. 2001 Drag and stability of objects in a yield stress fluid. AIChE J. 47 (12), 2666–2672.Google Scholar
Khaldoun, A., Moller, P., Fall, A., Wegdam, G., De Leeuw, B., Méheust, Y., Fossum, J. O. & Bonn, D. 2009 Quick clay and landslides of clayey soils. Phys. Rev. Lett. 103, 188301.Google Scholar
Laigle, D. & Coussot, P. 1997 Numerical modeling of mudflows. J. Hydraul. Engng 123 (7), 617–623.Google Scholar
Laigle, D., Lachamp, P. & Naaim, M. 2007 SPH-based numerical investigation of mudflow and other complex fluid flow interactions with structures. Comput. Geosci. 11 (4), 297–306.CrossRefGoogle Scholar
Lee, D., Gutowski, I. A., Bailey, A. E., Rubatat, L., de Bruyn, J. R. & Frisken, B. J. 2011 Investigating the microstructure of a yield-stress fluid by light scattering. Phys. Rev. E 83, 031401.Google Scholar
Luu, L. H. & Forterre, Y. 2009 Drop impact of yield-stress fluids. J. Fluid Mech. 632, 301–327.Google Scholar
Magnin, A. & Piau, J. M. 1987 Shear rheometry of fluids with a yield stress. J. Non-Newtonian Fluid Mech. 23, 91–106.Google Scholar
Magnin, A. & Piau, J. M. 1990 Cone-and-plate rheometry of yield stress fluids. Study of an aqueous gel. J. Non-Newtonian Fluid Mech. 36, 85–108.CrossRefGoogle Scholar
Malet, J. P., Laigle, D., Remaitre, A. & Maquaire, O. 2005 Triggering conditions and mobility of debris flows associated with complex earthflows. Geomorphology 66 (1–4), 215–235.Google Scholar
Meunier, P. & Leweke, T. 2003 Analysis and treatment of errors due to high velocity gradients in particle image velocimetry. Exp. Fluids 35, 408–421.Google Scholar
Mitsoulis, E. & Galazoulas, S. 2009 Simulation of viscoplastic flow past cylinders in tubes. J. Non-Newtonian Fluid Mech. 158 (1–3), 132–141.Google Scholar
Oppong, F. K. & de Bruyn, J. R. 2011 Microrheology and jamming in a yield stress fluid. Rheol. Acta 50, 317–326.Google Scholar
Ovarlez, G., Cohen-Addad, S., Krishan, K., Goyon, J. & Coussot, P. 2012 On the existence of a simple yield stress fluid behavior. J. Non-Newtonian Fluid Mech. 193, 68–79.CrossRefGoogle Scholar
Ovarlez, G., Mahaut, F., Bertrand, F. & Chateau, X. 2011 Flows and heterogeneities with a vane tool: magnetic resonance imaging measurements. J. Rheol. 55 (2), 197–223.Google Scholar
Ovarlez, G., Rodts, S., Chateau, X. & Coussot, P. 2009 Phenomenology and physical origin of shear localization and shear banding in complex fluids. Rheol. Acta 48, 831–844.Google Scholar
Peixinho, J., Nouar, C., Desaubry, C. & Théron, B. 2005 Laminar transitional and turbulent flow of yield stress fluid in a pipe. J. Non-Newtonian Fluid Mech. 128 (2–3), 172–184.Google Scholar
Piau, J.-M. 2007 Carbopol gels: elastoviscoplastic and slippery glasses made of individual swollen sponges. Meso- and macroscopic properties, constitutive equations and scaling laws. J. Non-Newtonian Fluid Mech. 144, 1–29.Google Scholar
Putz, A. M. V. & Burghelea, T. I. 2009 The solid–fluid transition in a yield stress shear thinning physical gel. Rheol. Acta 48, 673–689.Google Scholar
Putz, A. M. V., Burghelea, T. I., Frigaard, I. A. & Martinez, D. M. 2008 Settling of an isolated spherical particle in a yield stress shear thinning fluid. Phys. Fluids 20, 033102.CrossRefGoogle Scholar
Rickenmann, D., Laigle, D., McArdell, B. W. & Hubl, J. 2006 Comparison of 2D debris-flow simulation models with field events. Comput. Geosci. 10 (2), 241–264.CrossRefGoogle Scholar
Robert, G. P. & Barnes, H. A. 2001 New measurements of the flow-curves for Carbopol dispersions without slip artefacts. Rheol. Acta 40, 499–503.CrossRefGoogle Scholar
Saramito, P. & Roquet, N. 2001 An adaptive finite element method for viscoplastic fluid flows in pipes. Comput. Meth. Appl. Mech. 190 (40–41), 5391–5412.Google Scholar
Sikorski, D., Tabuteau, H. & de Bruyn, J. R. 2009 Motion and shape of bubbles rising through a yield-stress fluid. J. Non-Newtonian Fluid Mech. 159 (1–3), 10–16.Google Scholar
Souza Mendes, P. R. & Dutra, S. S. 2004 Viscosity function for yield-stress liquids. Appl. Rheol. 14 (6), 296–302.Google Scholar
de Souza Mendes, P. R., Naccache, M. F., Varges, P. R. & Marchesini, F. H. 2007 Flow of viscoplastic liquids through axisymmetric expansions-contractions. J. Non-Newtonian Fluid Mech. 142, 207–217.Google Scholar
Tabuteau, H., Coussot, P. & de Bruyn, J. R. 2007 Drag force on a sphere in steady motion through a yield-stress fluid. J. Rheol. 51 (1), 125–137.Google Scholar
Vola, D., Babik, F. & Latché, J. C. 2004 On a numerical strategy to compute gravity currents of non-Newtonian fluids. J. Comput. Phys. 201 (2), 397–420.CrossRefGoogle Scholar
Wachs, A. 2007 Numerical simulation of steady Bingham flow through an eccentric annular cross-section by distributed Lagrange multiplier/fictitious domain and augmented Lagrangian methods. J. Non-Newtonian Fluid Mech. 142 (1–3), 183–198.Google Scholar