Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-26T11:39:24.108Z Has data issue: false hasContentIssue false
  • English
  • Français

Collapse of a neutrally buoyant suspension column: from Newtonian to apparent non-Newtonian flow regimes

Published online by Cambridge University Press:  15 August 2017

A. Bougouin Open the ORCID record for A. Bougouin [Opens in a new window] ,
L. Lacaze  and
T. Bonometti
A. Bougouin*
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT) - Université de Toulouse, CNRS-INPT-UPS, Toulouse, France
L. Lacaze
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT) - Université de Toulouse, CNRS-INPT-UPS, Toulouse, France
T. Bonometti
Affiliation:
Institut de Mécanique des Fluides de Toulouse (IMFT) - Université de Toulouse, CNRS-INPT-UPS, Toulouse, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Experiments on the collapse of non-colloidal and neutrally buoyant particles suspended in a Newtonian fluid column are presented, in which the initial volume fraction of the suspension $\unicode[STIX]{x1D719}$ , the viscosity of the interstitial fluid $\unicode[STIX]{x1D707}_{f}$ , the diameter of the particles $d$ and the mixing protocol, i.e. the initial preparation of the suspension, are varied. The temporal evolution of the slumping current highlights two main regimes: (i) an inertial-dominated regime followed by (ii) a viscous-dominated regime. The inertial regime is characterized by a constant-speed slumping which is shown to scale as in the case of a classical inertial dam-break. The viscous-dominated regime is observed as a decreasing-speed phase of the front evolution. Lubrication models for Newtonian and power-law fluids describe most of situations encountered in this regime, which strongly depends on the suspension parameters. The temporal evolution of the propagating front is used to extract the rheological parameters of the fluid models. At the early stages of the viscous-dominated regime, a constant effective shear viscosity, referred to as an apparent Newtonian viscous regime, is found to depend only on $\unicode[STIX]{x1D719}$ and $\unicode[STIX]{x1D707}_{f}$ for each mixing protocol. The obtained values are shown to be well fitted by the Krieger–Dougherty model whose parameters involved, say a critical volume fraction $\unicode[STIX]{x1D719}_{m}$ and the exponent of divergence, depend on the mixing protocol, i.e. the microscale interaction between particles. On a longer time scale which depends on $\unicode[STIX]{x1D719}$ , the front evolution is shown to slightly deviate from the apparent Newtonian model. In this apparent non-Newtonian viscous regime, the power-law model, indicating both shear-thinning and shear-thickening behaviours, is shown to be more appropriate to describe the front evolution. The present experiments indicate that the mixing protocol plays a crucial role in the selection of a shear-thinning or shear-thickening type of collapse, while the particle diameter $d$ and volume fraction $\unicode[STIX]{x1D719}$ play a significant role in the shear-thickening case. In all cases, the normalized effective consistency of the power-law fluid model is found to be a unique function of $\unicode[STIX]{x1D719}$ . Finally, an apparent viscoplastic regime, characterized by a finite length spreading reached at finite time, is observed at high $\unicode[STIX]{x1D719}$ . This regime is mostly observed for volume fractions larger than $\unicode[STIX]{x1D719}_{m}$ and up to a volume fraction $\unicode[STIX]{x1D719}_{M}$ close to the random close packing fraction at which the initial column remains undeformed on opening the gate.

JFM classification

Geophysical and Geological Flows: Gravity currents Non-Newtonian Flows: Rheology Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 826 , 10 September 2017 , pp. 918 - 941
Check for updates
Copyright
© 2017 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

Amy, L. A., Hogg, A. J., Peakall, J. & Talling, P. J. 2005 Abrupt transitions in gravity currents. J. Geophys. Res. Earth Surf. 110 (F3).CrossRefGoogle Scholar
Ancey, C., Andreini, N. & Epely-Chauvin, G. 2013a The dam-break problem for concentrated suspensions of neutrally buoyant particles. J. Fluid Mech. 724, 95–122.Google Scholar
Ancey, C., Andreini, N. & Epely-Chauvin, G. 2013b Granular suspension avalanches. I. Macro-viscous behavior. Phys. Fluids 25, 033301.CrossRefGoogle Scholar
Andreini, N., Ancey, C. & Epely-Chauvin, G. 2013 Granular suspension avalanches. II. Plastic regime. Phys. Fluids 25, 033302.Google Scholar
Bagnold, R. A. 1954 Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. R. Soc. Lond. A 225 (1160), 49–63.Google Scholar
Balmforth, N. J., Craster, R. V., Perona, P., Rust, A. C. & Sassi, R. 2007 Viscoplastic dam breaks and the Bostwick consistometer. J. Non-Newtonian Fluid Mech. 142, 63–78.Google Scholar
Batchelor, G. K. & Green, J. T. 1972 The determination of the bulk stress in a suspension of spherical particles to order c 2 . J. Fluid Mech. 56, 401–427.Google Scholar
Benjamin, T. B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31, 209–248.Google Scholar
Bonnoit, C., Darnige, D., Clement, E. & Lindner, A. 2010 Inclined plane rheometry of a dense granular suspension. J. Rheol. 54, 65–79.Google Scholar
Bonometti, T., Balachandar, S. & Magnaudet, J. 2008 Wall effects in non-Boussinesq density currents. J. Fluid Mech. 616, 445–475.Google Scholar
Boyer, F., Guazzelli, E. & Pouliquen, O. 2011 Unifying suspension and granular rheology. Phys. Rev. Lett. 107, 188301.Google Scholar
Castruccio, A., Rust, A. C. & Sparks, R. S. J. 2010 Rheology and flow of crystal-bearing lavas: insights from analogue gravity currents. Earth Planet. Sci. Lett. 297, 471–480.CrossRefGoogle Scholar
Cohen-Addad, S., Höhler, R. & Pitois, O. 2013 Flow in foams and flowing foams. Annu. Rev. Fluid Mech. 45, 241–267.Google Scholar
Dbouk, T., Lobry, L. & Lemaire, E. 2013 Normal stresses in concentrated non-Brownian suspensions. J. Fluid Mech. 715, 239–272.Google Scholar
Di Federico, V., Malavasi, S. & Cintoli, S. 2006 Viscous spreading of non-Newtonian gravity currents on a plane. Meccanica 41, 207–217.Google Scholar
Dressler, R. F. 1952 Hydraulic resistance effect upon the dam-break functions. J. Res. Natl Bur. Stand. 49, 217–225.CrossRefGoogle Scholar
Dressler, R. F. 1954 Comparison of theories and experiments for the hydraulic dam-break wave. Intl Assoc. Sci. Hydrol. 3, 319–328.Google Scholar
Einstein, A. 1906 Eine neue Bestimmung der Moleküldimensionen. Ann. Phys. 19, 289–306.Google Scholar
Espín, L. & Kumar, S. 2014a Forced spreading of films and droplets of colloidal suspensions. J. Fluid Mech. 742, 495–519.CrossRefGoogle Scholar
Espín, L. & Kumar, S. 2014b Sagging of evaporating droplets of colloidal suspensions on inclined substrates. Langmuir 30, 11966–11974.CrossRefGoogle ScholarPubMed
Fall, A., Bertrand, F., Ovarlez, G. & Bonn, D. 2009 Yield stress and shear banding in granular suspensions. Phys. Rev. Lett. 103, 178301.Google Scholar
Fall, A., Lemaitre, A., Bertrand, F., Bonn, D. & Ovarlez, G. 2010 Shear thickening and migration in granular suspensions. Phys. Rev. Lett. 105, 268303.Google Scholar
Gadala-Maria, F. & Acrivos, A. 1980 Shear-induced structure in a concentrated suspension of solid spheres. J. Rheol. 24, 799–814.CrossRefGoogle Scholar
Gallier, S., Lemaire, E., Peters, F. & Lobry, L. 2014 Rheology of sheared suspensions of rough frictional particles. J. Fluid Mech. 757, 514–549.Google Scholar
Gratton, J., Minotti, F. & Mahajan, S. M. 1999 Theory of creeping gravity currents of a non-Newtonian liquid. Phys. Rev. E 60, 6960–6967.Google ScholarPubMed
Hager, W. H. 1988 Abflussformeln für turbulente Strömungen. Wasserwirtschaft 78, 79–84.Google Scholar
Hallworth, M. A. & Huppert, H. E. 1998 Abrupt transitions in high-concentration, particle-driven gravity currents. Phys. Fluids 10, 1083–1087.Google Scholar
Hogg, A. J. 2006 Lock-release gravity currents and dam-break flows. J. Fluid Mech. 569, 61–87.CrossRefGoogle Scholar
Hogg, A. J. & Pritchard, D. 2004 The effects of hydraulic resistance on dam-break and other shallow inertial flows. J. Fluid Mech. 501, 179–212.Google Scholar
Hogg, A. J. & Woods, A. w. 2001 The transition from inertia- to bottom-drag-dominated motion of turbulent gravity currents. J. Fluid Mech. 449, 201–224.Google Scholar
Hoult, D. P. 1972 Oil spreading on the sea. Annu. Rev. Fluid Mech. 4, 341–368.Google Scholar
Huang, N. & Bonn, D. 2007 Viscosity of dense suspension in Couette flow. J. Fluid Mech. 590, 497–507.Google Scholar
Huang, N., Ovarlez, G., Bertrand, F., Rodts, S., Coussot, P. & Bonn, D. 2005 Flow of wet granular materials. Phys. Rev. Lett. 94, 028301.Google Scholar
Hunt, M. L., Zenit, R., Campbell, C. S. & Brennen, C. E. 2002 Revisiting the 1954 suspension experiments of R. A. Bagnold. J. Fluid Mech. 452, 1–24.Google Scholar
Huppert, H. E. 1982 The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech. 121, 43–58.Google Scholar
Huppert, H. E. & Simpson, J. E. 1980 The slumping of gravity currents. J. Fluid Mech. 99, 785–799.Google Scholar
Krieger, I. M. & Dougherty, T. J. 1959 A mechanism for non-Newtonian flow in suspensions of rigid spheres. Trans. Soc. Rheol. 3, 137–152.CrossRefGoogle Scholar
Kulkarni, S. D., Metzger, B. & Morris, J. F. 2010 Particle-pressure-induced self-filtration in concentrated suspensions. Phys. Rev. E 82, 010402.Google Scholar
Lajeunesse, E., Monnier, J. B. & Homsy, G. M. 2005 Granular slumping on a horizontal surface. Phys. Fluids 17, 103302.Google Scholar
Leal, J. G., Ferreira, R. M. & Cardoso, A. H. 2006 Dam-break wave-front velocity. J. Hydraul. Res. 132, 69–76.Google Scholar
Leighton, D. & Acrivos, A. 1987 The shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 181, 415–439.Google Scholar
Lhuillier, D. 2009 Migration of rigid particles in non-Brownian viscous suspensions. Phys. Fluids 21, 023302.Google Scholar
Lube, G., Huppert, H. E., Sparks, R. S. J. & Freundt, A. 2005 Collapses of two-dimensional granular columns. Phys. Rev. E 72, 041301.Google Scholar
Lyon, M. K. & Leal, L. G. 1998 An experimental study of the motion of concentrated suspensions in two-dimensional channel flow. Part 1. Monodisperse systems. J. Fluid Mech. 363, 25–56.Google Scholar
Mari, R., Seto, R., Morris, J. F. & Denn, M. M. 2014 Shear thickening, frictionless and frictional rheologies in non-Brownian suspensions. J. Rheol. 58, 1693–1724.Google Scholar
Matson, G. P. & Hogg, A. J. 2007 Two-dimensional dam break flows of Herschel–Bulkley fluids: the approach to the arrested state. J. Non-Newtonian Fluid Mech. 142, 79–94.CrossRefGoogle Scholar
Meiburg, E. & Kneller, B. 2010 Turbidity currents and their deposits. Annu. Rev. Fluid Mech. 42, 135–156.Google Scholar
Mueller, S., Llewellin, E. W. & Mader, H. M. 2010 The rheology of suspensions of solid particles. Proc. R. Soc. Lond. A 466, 1201–1228.Google Scholar
Nsom, B. 2000 The dam break problem for a hyperconcentrated suspension. Appl. Rheol. 10, 224–230.CrossRefGoogle Scholar
Ovarlez, G., Bertrand, F. & Rodts, S. 2006 Local determination of the constitutive law of a dense suspension of noncolloidal particles through magnetic resonance imaging. J. Rheol. 50, 259–292.Google Scholar
Piau, J. M. & Debiane, K. 2005 Consistometers rheometry of power-law viscous fluids. J. Non-Newtonian Fluid Mech. 127, 213–224.Google Scholar
Ritter, A. 1892 Die Fortpflanzung der Wasserwellen. Z. Verein Deutch. Ing. 36, 947–954.Google Scholar
Roche, O., Montserrat, S., Niño, Y. & Tamburrino, A. 2008 Experimental observations of water-like behavior of initially fluidized, dam-break granular flows and their relevance for the propagation of ash-rich pyroclastic flows. J. Geophys. Res. Solid Earth 113 (B12).CrossRefGoogle Scholar
Rottman, J. W. & Simpson, J. E. 1983 Gravity currents produced by instantaneous release of a heavy fluid in a rectangular channel. J. Fluid Mech. 135, 95–110.Google Scholar
Snabre, P. & Pouligny, B. 2008 Size segregation in a fluid-like or gel-like suspension settling under gravity or in a centrifuge. Langmuir 24, 13338–13347.Google Scholar
Stansby, P. K., Chegini, A. & Barnes, T. C. D. 1998 The initial stages of dam-break flow. J. Fluid Mech. 370, 203–220.Google Scholar
Stickel, J. J. & Powell, R. L. 2005 Fluids mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129–149.Google Scholar
Trulsson, M., Andreotti, B. & Claudin, P. 2012 Transition from the viscous to inertial regime in dense suspensions. Phys. Rev. Lett. 109, 118305.Google Scholar
Ward, T., Wey, C., Glidden, R., Hosoi, A. E. & Bertozzi, A. L. 2009 Experimental study of gravitation effects in the flow of a particle-laden thin film on an inclined plane. Phys. Fluids 21, 083305.Google Scholar

Bougouin et al. supplementary movie 1

Collapse of a neutrally buoyant suspension column in the inertial-dominated regime for particles TS140, \mu_f=0.049\:$Pa.s, $\phi=13.1\:$\% and protocol I.

Download Bougouin et al. supplementary movie 1(Video)
Video 8.5 MB

Bougouin et al. supplementary movie 2

Collapse of a neutrally buoyant suspension column in the viscous-dominated regime for particles TS140, \mu_f=0.049\:$Pa.s, $\phi=51.3\:$\% and protocol I.

Download Bougouin et al. supplementary movie 2(Video)
Video 16.8 MB