Hostname: page-component-7c8c6479df-xxrs7 Total loading time: 0 Render date: 2024-03-29T00:24:05.371Z Has data issue: false hasContentIssue false

The dam-break problem for concentrated suspensions of neutrally buoyant particles

Published online by Cambridge University Press:  29 April 2013

C. Ancey*
Affiliation:
Environmental Hydraulics Laboratory, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
N. Andreini
Affiliation:
Environmental Hydraulics Laboratory, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
G. Epely-Chauvin
Affiliation:
Environmental Hydraulics Laboratory, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
*
Email address for correspondence: christophe.ancey@epfl.ch

Abstract

This paper addresses the dam-break problem for particle suspensions, that is, the flow of a finite volume of suspension released suddenly down an inclined flume. We were concerned with concentrated suspensions made up of neutrally buoyant non-colloidal particles within a Newtonian fluid. Experiments were conducted over wide ranges of slope, concentration and mass. The major contributions of our experimental study are the simultaneous measurement of local flow properties far from the sidewalls (velocity profile and, with lower accuracy, particle concentration) and macroscopic features (front position, flow depth profile). To that end, the refractive index of the fluid was adapted to closely match that of the particles, enabling data acquisition up to particle volume fractions of 60 %. Particle migration resulted in the blunting of the velocity profile, in contrast to the parabolic profile observed in homogeneous Newtonian fluids. The experimental results were compared with predictions from lubrication theory and particle migration theory. For solids fractions as large as 45 %, the flow behaviour did not differ much from that of a homogeneous Newtonian fluid. More specifically, we observed that the velocity profiles were closely approximated by a parabolic form and there was little evidence of particle migration throughout the depth. For particle concentrations in the 52–56 % range, the flow depth and front position were fairly well predicted by lubrication theory, but taking a closer look at the velocity profiles revealed that particle migration had noticeable effects on the shape of the velocity profile (blunting), but had little impact on its strength, which explained why lubrication theory performed well. Particle migration theories (such as the shear-induced diffusion model) successfully captured the slow evolution of the velocity profiles. For particle concentrations in excess of 56 %, the macroscopic flow features were grossly predicted by lubrication theory (to within 20 % for the flow depth, 50 % for the front position). The flows seemed to reach a steady state, i.e. the shape of the velocity profile showed little time dependence.

Type
Papers
Copyright
©2013 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.)

Footnotes

Sadly, Gaël Epely-Chauvin died in a diving accident during the writing of this paper.

References

Abbott, J. R., Tetlow, N., Graham, A. L., Altobelli, S. A., Fukushima, E., Mondy, L. A. & Stephens, T. S. 1991 Experimental observations of particle migration in concentrated suspensions: Couette flow. J. Rheol. 35, 773795.Google Scholar
Ancey, C. 2012 Gravity flow on steep slope. In Buoyancy Driven Flows (ed. Chassignet, E., Cenedese, C. & Verron, J.), Cambridge University Press.Google Scholar
Ancey, C., Andreini, N. & Epely-Chauvin, G. 2013 Granular suspensions I. Macro-viscous behaviour. Phys. Fluids 25, 033301.Google Scholar
Ancey, C., Cochard, S. & Andreini, N. 2009 The dam-break problem for viscous fluids in the high-capillary-number limit. J. Fluid Mech. 624, 122.Google Scholar
Andreini, N. 2012 Dam break of Newtonian fluids and granular suspensions: internal dynamics measurements. PhD thesis, École Polytechnique Fédérale de Lausanne.Google Scholar
Andreini, N., Ancey, C. & Epely-Chauvin, G. 2013 Granular suspensions. II. Plastic regime. Phys. Fluids 25, 033302.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
Bonnoit, C., Darnige, T., Clément, E. & Lindner, A. 2010 Inclined plane rheometry of a dense granular suspension. J. Rheol. 54, 6579.CrossRefGoogle Scholar
Boyer, F., Guazzelli, E. & Pouliquen, O. 2011 Unifying suspension and granular rheology. Phys. Rev. Lett. 107, 188301.Google Scholar
Chang, C. & Powell, R. L. 1994 Effect of particle size distributions on the rheology of concentrated bimodal suspensions. J. Rheol. 38, 8598.CrossRefGoogle Scholar
Cheng, D. C. H. 1984 Further observations on the rheological behaviour of dense suspensions. Powder Technol. 37, 255273.Google Scholar
Cook, P. E., Bertozzi, A. L. & Hosoi, A. E. 2008 Shock solutions for particle-laden thin films. SIAM J. Appl. Maths 68, 760783.Google Scholar
Gondret, P. & Petit, L. 1997 Dynamic viscosity of macroscopic suspensions of bimodal sized solid spheres. J. Rheol. 41, 12611274.Google Scholar
Gray, J. M. N. T. 2010 Particle size segregation in granular avalanches: a brief review of recent progress. In AIP Conference Proceedings, vol. 1227 (ed. Goddard, J. D., Jenkins, J. T. & Giovine, P.). pp. 343362. American Institute of Physics.Google Scholar
Gray, J. M. N. T. & Ancey, C. 2009 Segregation, recirculation and deposition of coarse particles near two-dimensional avalanche fronts. J. Fluid Mech. 629, 387423.Google Scholar
Hansen, F. K. & Rødsrud, G. 1991 Surface tension by pendant drop: I. A fast standard instrument using computer image analysis. J. Colloid Interface Sci. 141, 19.Google Scholar
Hsiao, S. C., Christensen, D., Ingber, M. S., Mondy, L. A. & Altobelli, S. A. 2005 Particle migration rates in a Couette apparatus. J. Mech. 21, 7175.Google Scholar
Huppert, H. E. 1982a Flow and instability of a viscous current down a slope. Nature 300, 427429.Google Scholar
Huppert, H. E. 1982b The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech. 121, 4358.CrossRefGoogle Scholar
Koh, C. J., Hookham, P. & Leal, L. G. 1994 An experimental investigation of concentrated suspension flows in a rectangular channel. J. Fluid Mech. 266, 132.Google Scholar
Krieger, I. M. & Dougherty, T. J. 1959 A mechanism for non-Newtonian flow in suspensions of rigid spheres. Trans. Soc. Rheol. 3, 137152.Google Scholar
Krishnan, G. P., Beimfohr, S. & Leighton, D. T. 1996 Shear-induced radial segregations in bidisperse suspensions. J. Fluid Mech. 321, 371393.CrossRefGoogle Scholar
Leighton, D. & Acrivos, A. 1987 The shear-induced migration of particles in concentrated suspensions. J. Fluid Mech. 181, 415439.Google Scholar
Lhuillier, D. 2009 Migration of rigid particles in non-Brownian viscous suspensions. Phys. Fluids 21, 023302.Google Scholar
Lyon, M. K. & Leal, L. G. 1998a An experimental study of the motion of concentrated suspensions in two-dimensional channel flow. Part 1. Monodisperse systems. J. Fluid Mech. 363, 2556.Google Scholar
Lyon, M. K. & Leal, L. G. 1998b An experimental study of the motion of concentrated suspensions in two-dimensional channel flow. Part 2. Bidisperse systems. J. Fluid Mech. 363, 5777.Google Scholar
Medhi, B. J., Kumar, A. & Singh, A. 2011 Apparent wall slip velocity measurements in free surface flow of concentrated suspensions. Intl J. Multiphase Flow 37, 609619.Google Scholar
Morris, J. F. 2009 A review of microstructure in concentrated suspensions and its implications for rheology and bulk flow. Rheol. Acta 48, 909923.Google Scholar
Morris, J. F. & Boulay, F. 1999 Curvilinear flows of noncolloidal suspensions: the role of normal stresses. J. Rheol. 43, 12131238.CrossRefGoogle Scholar
Morris, J. F. & Brady, J. F. 1998 Pressure-driven flow of a suspension: buoyancy effects. Intl J. Multiphase Flow 24, 105130.Google Scholar
Norman, J. T., Nayak, H. V. & Bonnecaze, R. T. 2005 Migration of buoyant particles in low-Reynolds-number pressure-driven flows. J. Fluid Mech. 523, 135.Google Scholar
Nott, P. R. & Brady, J. F 1994 Pressure-driven flow of suspensions: simulation and theory. J. Fluid Mech. 275, 157199.Google Scholar
Nott, P. R., Guazzelli, E. & Pouliquen, O. 2011 The suspension balance model revisited. Phys. Fluids 23, 043304.Google Scholar
Nsom, B. 2000 The dam break problem for a hyperconcentrated suspension. Appl. Rheol. 10, 224230.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, 259292.Google Scholar
Phillips, R. J., Armstrong, R. C., Brown, R. A., Graham, A. L. & Abbott, J. R. 1992 A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration. Phys. Fluids A 4, 3039.CrossRefGoogle Scholar
Raffel, M., Willert, C. E., Wereley, S. T. & Kompenhans, J. 2007 Particle Image Velocimetry. Springer.Google Scholar
Reardon, P. T., Feng, S., Graham, A. L., Chawla, V., Admuthe, R. S. & Abbott, J. R. 2008 Shear-thinning of polydisperse suspensions. J. Phys. D: Appl. Phys. 41, 115408.Google Scholar
Stickel, J. J. & Powell, R. L. 2005 Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129149.Google Scholar
Sveen, J. K. 2004 An introduction to MatPIV. In Mechanics and Applied Mathematics. Tech Rep. eprint series No. 2. Department of Mathematics, University of Oslo.Google Scholar
Tetlow, N., Graham, A. L., Ingber, M. S., Subia, S. R., Mondy, L. A. & Altobelli, S. A. 1998 Particle migration in a Couette apparatus: experiment and modelling. J. Rheol. 42, 307328.CrossRefGoogle Scholar
Timberlake, B. D. & Morris, J. F. 2005 Particle migration and free-surface topography in inclined plane flow of a suspension. J. Fluid Mech. 538, 309341.Google Scholar
Ward, T., Wey, C., Gidden, 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
Wiederseiner, S., Andreini, N., Epely-Chauvin, G. & Ancey, C. 2011 Refractive index matching in concentrated particle suspensions: a review. Exp. Fluids 50, 11831206.Google Scholar
Zarraga, I. E., Hill, D. A. & Leighton, D. T. 2000 The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids. J. Rheol. 44, 185221.Google Scholar

Ancey et al. supplementary movie

This movie shows the flowing suspension from above. Note the parabolic shape of the contact line.

Download Ancey et al. supplementary movie(Video)
Video 41.7 MB
Supplementary material: PDF

Ancey et al. supplementary material

Supplement

Download Ancey et al. supplementary material(PDF)
PDF 14.5 MB

Ancey et al. supplementary movie

This movie shows a view of the flowing suspension taken from the sidewall, 2.5 m downstream of the flume inlet. Flow from right to left. Suspension: solids fraction of 0.52; flume inclination 25°. The black dots are the PMMA particles whereas the white area is produced by the rhodamine contained in the fluid and whose fluorescence is excited by the laser.

Download Ancey et al. supplementary movie(Video)
Video 13.3 MB