Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T21:58:13.803Z Has data issue: false hasContentIssue false

Falling jet of dry granular material in water

Published online by Cambridge University Press:  14 April 2021

G. Saingier
Affiliation:
Surface du Verre et Interfaces, UMR 125, CNRS/Saint-Gobain, 39, quai Lucien Lefranc, F-93303Aubervilliers, France
A. Sauret
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA93106, USA
P. Jop*
Affiliation:
Surface du Verre et Interfaces, UMR 125, CNRS/Saint-Gobain, 39, quai Lucien Lefranc, F-93303Aubervilliers, France
*
Email address for correspondence: [email protected]

Abstract

Modelling the flow of dry granular materials entering water is crucial for optimizing blending processes in industry and for natural hazard assessment when describing tsunami waves induced by landslides. In this study, we experimentally investigate the case of a jet of grains entering from the air into a water bath. After an initial transient state, a stationary impregnation front appears between the dry and the wet grains. The wet grains are then dispersed in the liquid. To describe this dry-to-wet transition, we focus on the first step of the process, when the liquid invades the dense granular medium. In this regime, the granular jet is modelled as a translating porous material, and we systematically characterize the impregnation process using a combination of experiments, analytical modelling, and numerical tools. We then compare this process to the situation of a confined granular jet entering a water bath. Our approach is a first step toward describing the interplay between dry grains and a liquid and the resulting dispersion of particles.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by 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

REFERENCES

Bán, S., Wolfram, E. & Rohrsetzer, S. 1987 The condition of starting of liquid imbibition in powders. Colloids Surf. 22, 291300.CrossRefGoogle Scholar
Bear, J. 1988 Dynamics of Fluids in Porous Media. Dover.Google Scholar
Benner, E.M. & Petsev, D.N. 2013 Potential flow in the presence of a sudden expansion: application to capillary driven transport in porous media. Phys. Rev. E 87, 033008.CrossRefGoogle Scholar
Blake, T.D. & Ruschak, K.J. 1979 A maximum speed of wetting. Nature 282 (5738), 489491.CrossRefGoogle Scholar
Bougouin, A., Lacaze, L. & Bonometti, T. 2017 Collapse of a neutrally buoyant suspension column: from newtonian to apparent non-newtonian flow regimes. J. Fluid Mech. 826, 918941.CrossRefGoogle Scholar
Campos, J. & De Carvalho, J. 1992 Drag force on the particles at the upstream end of a packed bed and the stability of the roof of bubbles in fluidised beds. Chem. Engng Sci. 47 (15–16), 40574062.CrossRefGoogle Scholar
Carman, P.C. 1937 Fluid flow through granular beds. Trans. Inst. Chem. Engrs 15, 150166.Google Scholar
Cazacliu, B. & Roquet, N. 2009 Concrete mixing kinetics by means of power measurement. Cem. Concr. Res. 39 (3), 182194.CrossRefGoogle Scholar
Cervantes-Álvarez, A.M., Escobar-Ortega, Y.Y., Sauret, A. & Pacheco-Vázquez, F. 2020 Air entrainment and granular bubbles generated by a jet of grains entering water. J. Colloid Interface Sci. 574, 285292.CrossRefGoogle ScholarPubMed
Cheng, X., Varas, G., Citron, D., Jaeger, H.M. & Nagel, S.R. 2007 Collective behavior in a granular jet: emergence of a liquid with zero surface tension. Phys. Rev. Lett. 99 (18), 188001.CrossRefGoogle Scholar
Chopin, J. & Kudrolli, A. 2011 Building designed granular towers one drop at a time. Phys. Rev. Lett. 107, 208304.CrossRefGoogle ScholarPubMed
Clarke, A. 2002 Coating on a rough surface. AIChE J. 48 (10), 21492156.CrossRefGoogle Scholar
Collet, R., Oulahna, D., De Ryck, A., Henri, P. & Martin, M. 2010 Mixing of a wet granular medium : effect of the particle size, the liquid and the granular compacity on the intensity consumption. Chem. Engng J. 164 (2–3), 299304.CrossRefGoogle Scholar
Courrech du Pont, S., Gondret, P., Perrin, B. & Rabaud, M. 2003 Granular avalanches in fluids. Phys. Rev. Lett. 90, 044301.CrossRefGoogle ScholarPubMed
Delker, T., Pengra, D.B. & Wong, P.Z. 1996 Interface pinning and the dynamics of capillary rise in porous media. Phys. Rev. Lett. 76 (16), 29022905.CrossRefGoogle ScholarPubMed
Doppler, D., Gondret, P., Loiseleux, T., Meyer, S. & Rabaud, M. 2007 Relaxation dynamics of water-immersed granular avalanches. J. Fluid Mech. 577, 161181.CrossRefGoogle Scholar
Forny, L., Marabi, A. & Palzer, S. 2011 Wetting, disintegration and dissolution of agglomerated water soluble powders. Powder Technol. 206 (1–2), 7278.CrossRefGoogle Scholar
Fritz, H.M., Hager, W.H. & Minor, H. 2003 Landslide generated impulse waves. 1. Instantaneous flow fields. Exp. Fluids 35, 505519.CrossRefGoogle Scholar
González Gutiérrez, J., Carrillo Estrada, J.L. & Ruiz Suárez, J.C. 2014 Penetration of granular projectiles into a water target. Sci. Rep. 4, 6762.CrossRefGoogle ScholarPubMed
Guérin, A., Devauchelle, O. & Lajeunesse, E. 2014 Response of a laboratory aquifer to rainfall. J. Fluid Mech. 759, 111.CrossRefGoogle Scholar
He, M. & Nagel, S.R. 2019 Characteristic interfacial structure behind a rapidly moving contact line. Phys. Rev. Lett. 122 (1), 018001.CrossRefGoogle ScholarPubMed
Heller, V., Hager, W.H. & Minor, H. 2008 Scale effects in subaerial landslide generated impulse waves. Exp. Fluids 44, 691703.CrossRefGoogle Scholar
Herminghaus, S. 2005 Dynamics of wet granular matter. Adv. Phys. 54 (3), 221261.CrossRefGoogle Scholar
Horton, R.E. 1945 Erosional development of streams and their drainage basins; hydrophysical approach to quantitative morphology. Geol. Soc. Am. Bull. 56 (3), 275370.CrossRefGoogle Scholar
Hyväluoma, J., Raiskinmäki, P., Jäsberg, A., Koponen, A., Kataja, M. & Timonen, J. 2006 Simulation of liquid penetration in paper. Phys. Rev. E 73, 036705.CrossRefGoogle ScholarPubMed
Janssen, H.A. 1895 Versuche uber getreidedruck in silozellen. Z. Ver. Dtsch. Ing. 39 (35), 10451049.Google Scholar
Jerome, J.J.S., Vandenberghe, N. & Forterre, Y. 2016 Unifying impacts in granular matter from quicksand to cornstarch. Phys. Rev. Lett. 117, 098003.CrossRefGoogle ScholarPubMed
Kiesgen de Richter, S., Hanotin, C., Marchal, P., Leclerc, S., Demeurie, F. & Louvet, N. 2015 Vibration-induced compaction of granular suspensions. Eur. Phys. J. E 38 (7), 74.CrossRefGoogle ScholarPubMed
Kirchner, J.W., Feng, X. & Neal, C. 2000 Fractal stream chemistry and its implications for contaminant transport in catchments. Nature 403 (6769), 524527.CrossRefGoogle ScholarPubMed
Knight, J.B., Fandrich, C.G., Lau, C.N., Jaeger, H.M. & Nagel, S.R. 1995 Density relaxation in a vibrated granular material. Phys. Rev. E 51, 39573963.CrossRefGoogle Scholar
Lago, M. & Araujo, M. 2001 Capillary rise in porous media. J. Colloid Interface Sci. 234 (1), 3543.CrossRefGoogle ScholarPubMed
Lorenceau, E., Restagno, F. & Quéré, D. 2003 Fracture of a viscous liquid. Phys. Rev. Lett. 90, 184501.CrossRefGoogle ScholarPubMed
Lucas, V.R. 1918 Ueber das zeitgesetz des kapillaren aufstiegs von ussigkeiten. Kolloid Z. 23, 15.CrossRefGoogle Scholar
Lyle, S., Huppert, H.E., Hallworth, M.A., Bickle, M. & Chadwick, A. 2005 Axisymmetric gravity currents in a porous medium. J. Fluid Mech. 543, 293302.CrossRefGoogle Scholar
Mensire, R., Ault, J.T., Lorenceau, E. & Stone, H.A. 2016 Point-source imbibition into dry aqueous foams. Europhys. Lett. 113 (7), 44002.CrossRefGoogle Scholar
Müller, P., Formella, A. & Pöschel, T. 2014 Granular jet impact: probing the ideal fluid description. J. Fluid Mech. 751, 601626.CrossRefGoogle Scholar
Mulligan, R.P. & Take, W.A. 2017 On the transfer of momentum from a granular landslide to a water wave. Coast. Engng 125, 1622.CrossRefGoogle Scholar
Mullins, B.J. & Braddock, R.D. 2012 Capillary rise in porous, fibrous media during liquid immersion. Intl J. Heat Mass Transfer 55 (21–22), 62226230.CrossRefGoogle Scholar
Nasto, A., Regli, M., Brun, P.-T., Alvarado, J., Clanet, C. & Hosoi, A.E. 2016 Air entrainment in hairy surfaces. Phys. Rev. Fluids 1, 033905.CrossRefGoogle Scholar
Nicolas, M., Duru, P. & Pouliquen, O. 2000 Compaction of a granular material under cyclic shear. Eur. Phys. J. E 3 (4), 309314.CrossRefGoogle Scholar
Philippe, P. & Richard, T. 2008 Start and stop of an avalanche in a granular medium subjected to an inner water flow. Phys. Rev. E 77 (4), 041306.CrossRefGoogle Scholar
Podgorski, T., Flesselles, J.-M. & Limat, L. 2001 Corners, cusps, and pearls in running drops. Phys. Rev. Lett. 87 (3), 036102.CrossRefGoogle ScholarPubMed
Quéré, D. 1999 Fluid coating on a fiber. Annu. Rev. Fluid Mech. 31 (1), 347384.CrossRefGoogle Scholar
Raux, P.S., Cockenpot, H., Ramaioli, M., Quéré, D. & Clanet, C. 2013 Wicking in a powder. Langmuir 29 (11), 3636–44.CrossRefGoogle ScholarPubMed
Reyssat, M., Sangne, L.Y., van Nierop, E.A. & Stone, H.A. 2009 Imbibition in layered systems of packed beads. Europhys. Lett. 86 (5), 56002.CrossRefGoogle Scholar
Richard, P., Nicodemi, M., Delannay, R., Ribiére, R. & Bideau, D. 2005 Slow relaxation and compaction of granular systems. Nat. Mater. 4, 121128.CrossRefGoogle ScholarPubMed
Robbe-Saule, M., Morize, C., Henaff, R., Bertho, Y., Sauret, A. & Gondret, P. 2021 Experimental investigation of tsunami waves generated by granular collapse into water. J. Fluid Mech. 907, A11.CrossRefGoogle Scholar
Saingier, G., Sauret, A. & Jop, P. 2017 Accretion dynamics on wet granular materials. Phys. Rev. Lett. 118, 208001.CrossRefGoogle ScholarPubMed
Seiwert, J., Clanet, C. & Quéré, D. 2011 Coating of a textured solid. J. Fluid Mech. 699, 5563.CrossRefGoogle Scholar
Shirtcliffe, N.J., McHale, G., Newton, M.I., Pyatt, F.B. & Doerr, S.H. 2006 Critical conditions for the wetting of soils. Appl. Phys. Lett. 89, 094101.CrossRefGoogle Scholar
Shojaaee, Z., Brendel, L., Török, J. & Wolf, D.E. 2012 Shear flow of dense granular materials near smooth walls. II. Block formation and suppression of slip by rolling friction. Phys. Rev. E 86 (1), 011302.CrossRefGoogle ScholarPubMed
Timounay, Y., Lorenceau, E. & Rouyer, F. 2015 Opening and retraction of particulate soap films. EPL 111 (2), 26001.CrossRefGoogle Scholar
Topin, V., Monerie, Y., Perales, F. & Radjaï, F. 2012 Collapse dynamics and runout of dense granular materials in a fluid. Phys. Rev. Lett. 109, 188001.CrossRefGoogle Scholar
Vanel, L. & Clément, E. 1999 Pressure screening and fluctuations at the bottom of a granular column. Eur. Phys. J. B-Condens. Matter Complex Syst. 11 (3), 525533.CrossRefGoogle Scholar
Vella, D. & Huppert, H.E. 2006 Gravity currents in a porous medium at an inclined plane. J. Fluid Mech. 555, 353362.CrossRefGoogle Scholar
Vinningland, J.L., Toussaint, R., Niebling, M., Flekkøy, E.G. & Måløy, K.J. 2012 Family-vicsek scaling of detachment fronts in granular Rayleigh–Taylor instabilities during sedimentating granular/fluid flows. Eur. Phys. J. Spec. Topics 204 (1), 2740.CrossRefGoogle Scholar
Viroulet, S., Sauret, A. & Kimmoun, O. 2014 Tsunami generated by a granular collapse down a rough inclined plane. Europhys. Lett. 105 (3), 34004.CrossRefGoogle Scholar
Washburn, E.W. 1921 The dynamics of capillary flow. Phys. Rev. 17 (3), 273283.CrossRefGoogle Scholar
Xiao, J., Stone, H.A. & Attinger, D. 2012 Source-like solution for radial imbibition into a homogeneous semi-infinite porous medium. Langmuir 28 (9), 4208–12.CrossRefGoogle ScholarPubMed
Zitti, G., Ancey, C., Postacchini, M. & Brocchini, M. 2016 Impulse waves generated by snow avalanches: momentum and energy transfer to a water body. J. Geophys. Res. Earth Surf. 121, 23992423.CrossRefGoogle Scholar

Saingier et al. supplementary movie

See pdf file for movie caption

Download Saingier et al. supplementary movie(Video)
Video 2 MB
Supplementary material: PDF

Saingier et al. supplementary material

Caption for movie

Download Saingier et al. supplementary material(PDF)
PDF 28.2 KB