Hostname: page-component-84b7d79bbc-tsvsl Total loading time: 0 Render date: 2024-07-25T20:04:52.400Z Has data issue: false hasContentIssue false
  • English
  • Français

Settling of cohesive sediment: particle-resolved simulations

Published online by Cambridge University Press:  31 October 2018

B. Vowinckel Open the ORCID record for B. Vowinckel [Opens in a new window] ,
J. Withers ,
Paolo Luzzatto-Fegiz  and
E. Meiburg Open the ORCID record for E. Meiburg [Opens in a new window]
B. Vowinckel*
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93116, USA
J. Withers
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93116, USA The University of Queensland, School of Mechanical and Mining Engineering, Brisbane, Queensland 4072, Australia
Paolo Luzzatto-Fegiz
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93116, USA
E. Meiburg
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93116, USA
*
†Email address for correspondence: vowinckel@engineering.ucsb.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We develop a physical and computational model for performing fully coupled, grain-resolved direct numerical simulations of cohesive sediment, based on the immersed boundary method. The model distributes the cohesive forces over a thin shell surrounding each particle, thereby allowing for the spatial and temporal resolution of the cohesive forces during particle–particle interactions. The influence of the cohesive forces is captured by a single dimensionless parameter in the form of a cohesion number, which represents the ratio of cohesive and gravitational forces acting on a particle. We test and validate the cohesive force model for binary particle interactions in the drafting–kissing–tumbling (DKT) configuration. Cohesive sediment grains can remain attached to each other during the tumbling phase following the initial collision, thereby giving rise to the formation of flocs. The DKT simulations demonstrate that cohesive particle pairs settle in a preferred orientation, with particles of very different sizes preferentially aligning themselves in the vertical direction, so that the smaller particle is drafted in the wake of the larger one. This preferred orientation of cohesive particle pairs is found to remain influential for systems of higher complexity. To this end, we perform large simulations of 1261 polydisperse settling particles starting from rest. These simulations reproduce several earlier experimental observations by other authors, such as the accelerated settling of sand and silt particles due to particle bonding, the stratification of cohesive sediment deposits, and the consolidation process of the deposit. They identify three characteristic phases of the polydisperse settling process, viz. (i) initial stir-up phase with limited flocculation, (ii) enhanced settling phase characterized by increased flocculation, and (iii) consolidation phase. The simulations demonstrate that cohesive forces accelerate the overall settling process primarily because smaller grains attach to larger ones and settle in their wakes. For the present cohesive number values, we observe that settling can be accelerated by up to 29 %. We propose physically based parametrization of classical hindered settling functions introduced by earlier authors, in order to account for cohesive forces. An investigation of the energy budget shows that, even though the work of the collision forces is much smaller than that of the hydrodynamic drag forces, it can substantially modify the relevant energy conversion processes.

JFM classification

Complex Fluids: Colloids Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Sediment transport
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 858 , 10 January 2019 , pp. 5 - 44
Check for updates
Copyright
© 2018 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

Aberle, J., Nikora, V. & Walters, R. 2004 Effects of bed material properties on cohesive sediment erosion. Mar. Geol. 207 (1), 83–93.Google Scholar
Balachandar, S. & Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111–133.Google Scholar
Been, K. & Sills, G. C. 1981 Self-weight consolidation of soft soils: an experimental and theoretical study. Geotechnique 31 (4), 519–535.Google Scholar
Berg, J. C. 2010 An Introduction to Interfaces & Colloids: the Bridge to Nanoscience. World Scientific.Google Scholar
Bergström, L. 1997 Hamaker constants of inorganic materials. Adv. Colloid Interface Sci. 70, 125–169.Google Scholar
Biegert, E., Vowinckel, B. & Meiburg, E. 2017a A collision model for grain-resolving simulations of flows over dense, mobile, polydisperse granular sediment beds. J. Comput. Phys. 340, 105–127.Google Scholar
Biegert, E., Vowinckel, B., Ouillon, R. & Meiburg, E. 2017b High-resolution simulations of turbidity currents. Prog. Earth Planet. Sci. 4 (1), 33.Google Scholar
Breuer, M. & Almohammed, N. 2015 Modeling and simulation of particle agglomeration in turbulent flows using a hard-sphere model with deterministic collision detection and enhanced structure models. Intl J. Multiphase Flow 73, 171–206.Google Scholar
Capart, H. & Fraccarollo, L. 2011 Transport layer structure in intense bed-load. Geophys. Res. Lett. 38 (20), L20402.Google Scholar
Clift, R., Grace, J. R. & Weber, M. E. 2005 Bubbles, Drops, and Particles. Courier Corporation.Google Scholar
Cox, R. G. & Brenner, H. 1967 The slow motion of a sphere through a viscous fluid towards a plane surface. Small gap widths, including inertial effects. Chem. Engng Sci. 22, 1753–1777.Google Scholar
Dankers, P. J. T. & Winterwerp, J. C. 2007 Hindered settling of mud flocs: theory and validation. Cont. Shelf Res. 27 (14), 1893–1907.Google Scholar
De Swart, H. E. & Zimmerman, J. T. F. 2009 Morphodynamics of tidal inlet systems. Annu. Rev. Fluid Mech. 41, 203–229.Google Scholar
Debnath, K. & Chaudhuri, S. 2010 Cohesive sediment erosion threshold: a review. ISH J. Hydraul. Engng 16 (1), 36–56.Google Scholar
Delenne, J.-Y., El Youssoufi, M. S., Cherblanc, F. & Bénet, J.-C. 2004 Mechanical behaviour and failure of cohesive granular materials. Intl J. Numer. Anal. Meth. Geomech. 28 (15), 1577–1594.Google Scholar
Derjaguin, B. V. & Landau, L. 1941 Theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solutions of electrolytes. Acta Phys. USSR 14, 633–662.Google Scholar
Derksen, J. J. 2014 Simulations of hindered settling of flocculating spherical particles. Intl J. Multiphase Flow 58, 127–138.Google Scholar
Desmond, K. W. & Weeks, E. R. 2014 Influence of particle size distribution on random close packing of spheres. Phys. Rev. E 90 (2), 022204.Google Scholar
Fortes, A. F., Joseph, D. D. & Lundgren, T. S. 1987 Nonlinear mechanics of fluidization of beds of spherical particles. J. Fluid Mech. 177, 467–483.Google Scholar
Francisco, E. P., Espath, L. F. R., Laizet, S. & Silvestrini, J. H. 2018 Reynolds number and settling velocity influence for finite-release particle-laden gravity currents in a basin. Comput. Geosci. 110, 1–9.Google Scholar
Glowinski, R., Pan, T. W., Hesla, T. I., Joseph, D. D. & Priaux, J. 2001 A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow. J. Comput. Phys. 169, 363–426.Google Scholar
Gondret, P., Lance, M. & Petit, L. 2002 Bouncing motion of spherical particles in fluids. Phys. Fluids 14 (2), 643–652.Google Scholar
Grabowski, R. C., Droppo, I. G. & Wharton, G. 2011 Erodibility of cohesive sediment: the importance of sediment properties. Earth-Sci. Rev. 105 (3), 101–120.Google Scholar
Gu, Y., Ozel, A. & Sundaresan, S. 2016 A modified cohesion model for CFD–DEM simulations of fluidization. Powder Technol. 296, 17–28.Google Scholar
Hamaker, H. C. 1937 The London van der Waals attraction between spherical particles. Physica 4 (10), 1058–1072.Google Scholar
Ho, C. A. & Sommerfeld, M. 2002 Modelling of micro-particle agglomeration in turbulent flows. Chem. Engng Sci. 57 (15), 3073–3084.Google Scholar
Houssais, M., Ortiz, C. P., Durian, D. J. & Jerolmack, D. J. 2016 Rheology of sediment transported by a laminar flow. Phys. Rev. E 94 (6), 062609.Google Scholar
Huang, I. B.2017 Cohesive sediment flocculation in a partially-stratified estuary. PhD thesis, Stanford University, USA.Google Scholar
Israelachvili, J. N. 1992 Adhesion forces between surfaces in liquids and condensable vapours. Surf. Sci. Rep. 14 (3), 109–159.Google Scholar
Joseph, G. G. & Hunt, M. L. 2004 Oblique particle–wall collisions in a liquid. J. Fluid Mech. 510, 71–93.Google Scholar
Joseph, G. G., Zenit, R., Hunt, M. L. & Rosenwinkel, A. M. 2001 Particle–wall collisions in a viscous fluid. J. Fluid Mech. 433, 329–346.Google Scholar
Kempe, T. & Fröhlich, J. 2012a Collision modelling for the interface-resolved simulation of spherical particles in viscous fluids. J. Fluid Mech. 709, 445–489.Google Scholar
Kempe, T. & Fröhlich, J. 2012b An improved immersed boundary method with direct forcing for the simulation of particle laden flows. J. Comput. Phys. 231 (9), 3663–3684.Google Scholar
Konopliv, N. & Meiburg, E. 2016 Double-diffusive lock-exchange gravity currents. J. Fluid Mech. 797, 729–764.Google Scholar
Kosinski, P. & Hoffmann, A. C. 2010 An extension of the hard-sphere particle–particle collision model to study agglomeration. Chem. Engng Sci. 65 (10), 3231–3239.Google Scholar
Krieger, I. M. & Dougherty, T. J. 1959 A mechanism for non-Newtonian flow in suspensions of rigid spheres. Trans. Soc. Rheol. 3 (1), 137–152.Google Scholar
Leong, Y. K. & Ong, B. C. 2003 Critical zeta potential and the Hamaker constant of oxides in water. Powder Technol. 134 (3), 249–254.Google Scholar
Liang, Y., Hilal, N., Langston, P. & Starov, V. 2007 Interaction forces between colloidal particles in liquid: theory and experiment. Adv. Colloid Interface Sci. 134, 151–166.Google Scholar
Liao, C.-C., Hsiao, W.-W., Lin, T.-Y. & Lin, C.-A. 2015 Simulations of two sedimenting-interacting spheres with different sizes and initial configurations using immersed boundary method. Comput. Mech. 55 (6), 1191–1200.Google Scholar
Lick, W., Jin, L. & Gailani, J. 2004 Initiation of movement of quartz particles. J. Hydraul. Engng 130 (8), 755–761.Google Scholar
Loth, E. 2000 Numerical approaches for motion of dispersed particles, droplets and bubbles. Prog. Energy Combust. Sci. 26 (3), 161–223.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 (6), 1693–1724.Google Scholar
Mehta, A. J., Hayter, E. J., Parker, W. R., Krone, R. B. & Teeter, A. M. 1989 Cohesive sediment transport. I. process description. J. Hydraul. Engng 115 (8), 1076–1093.Google Scholar
Metcalfe, G., Speetjens, M. F. M., Lester, D. R. & Clercx, H. J. H. 2012 Beyond passive: chaotic transport in stirred fluids. In Advances in Applied Mechanics, vol. 45, pp. 109–188. Elsevier.Google Scholar
Mordant, N. & Pinton, J. F. 2000 Velocity measurement of a settling sphere. Eur. Phys. J. B 18 (2), 343–352.Google Scholar
Necker, F., Härtel, C., Kleiser, L. & Meiburg, E. 2005 Mixing and dissipation in particle-driven gravity currents. J. Fluid Mech. 545, 339–372.Google Scholar
Pandit, J. K., Wang, X. S. & Rhodes, M. J. 2005 Study of Geldart’s group A behaviour using the discrete element method simulation. Powder Technol. 160 (1), 7–14.Google Scholar
Parsons, D. F., Walsh, R. B. & Craig, V. S. J. 2014 Surface forces: surface roughness in theory and experiment. J. Chem. Phys. 140 (16), 164701.Google Scholar
Pednekar, S., Chun, J. & Morris, J. F. 2017 Simulation of shear thickening in attractive colloidal suspensions. Soft Matt. 13 (9), 1773–1779.Google Scholar
Rhoads, D. C. 1974 Organism–sediment relations on the muddy sea floor. Mar. Biol. Annu. Rev. 12, 263–300.Google Scholar
Richardson, J. F. & Zaki, W. N. 1954 The sedimentation of a suspension of uniform spheres under conditions of viscous flow. Chem. Engng Sci. 3 (2), 65–73.Google Scholar
Righetti, M. & Lucarelli, C. 2007 May the Shields theory be extended to cohesive and adhesive benthic sediments? J. Geophys. Res. 112 (C5), C05039.Google Scholar
Seminara, G. 2010 Fluvial sedimentary patterns. Annu. Rev. Fluid Mech. 42, 43–66.Google Scholar
Shao, X.-M., Liu, Y. & Yu, Z.-S. 2005 Interactions between two sedimenting particles with different sizes. Appl. Math. Mech. 26 (3), 407–414.Google Scholar
te Slaa, S., van Maren, D. S., He, Q. & Winterwerp, J. C. 2015 Hindered settling of silt. J. Hydraul. Engng 141 (9), 04015020.Google Scholar
Sohn, H. Y. & Moreland, C. 1968 The effect of particle size distribution on packing density. Can. J. Chem. Engng 46 (3), 162–167.Google Scholar
Sun, R., Xiao, H. & Sun, H. 2018 Investigating the settling dynamics of cohesive silt particles with particle-resolving simulations. Adv. Water Resour. 111, 406–422.Google Scholar
Sutherland, B. R., Barrett, K. J. & Gingras, M. K. 2015 Clay settling in fresh and salt water. Environ. Fluid Mech. 15 (1), 147–160.Google Scholar
Ten Cate, A., Nieuwstad, C. H., Derksen, J. J. & Van den Akker, H. E. A. 2002 Particle imaging velocimetry experiments and lattice-Boltzmann simulations on a single sphere settling under gravity. Phys. Fluids 14 (11), 4012–4025.Google Scholar
Thornton, C., Cummins, S. J. & Cleary, P. W. 2013 An investigation of the comparative behaviour of alternative contact force models during inelastic collisions. Powder Technol. 233, 30–46.Google Scholar
Thornton, C., Cummins, S. J. & Cleary, P. W. 2017 On elastic-plastic normal contact force models, with and without adhesion. Powder Technol. 315, 339–346.Google Scholar
Toner, J., Tu, Y. & Ramaswamy, S. 2005 Hydrodynamics and phases of flocks. Ann. Phys. 318 (1), 170–244.Google Scholar
Uhlmann, M. 2005 An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 209 (2), 448–476.Google Scholar
Verwey, E. J. W. & Overbeek, J. T. G. 1948 Theory of the Stability of Lyophobic Colloids: The Interaction of Sol Particles Having an Electric Double Layer. Courier Corporation.Google Scholar
Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I. & Shochet, O. 1995 Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75 (6), 1226–1229.Google Scholar
Visser, J. 1972 On Hamaker constants: a comparison between Hamaker constants and Lifshitz–van der Waals constants. Adv. Colloid Interface Sci. 3 (4), 331–363.Google Scholar
Visser, J. 1989 Van der Waals and other cohesive forces affecting powder fluidization. Powder Technol. 58 (1), 1–10.Google Scholar
Vowinckel, B., Kempe, T. & Fröhlich, J. 2014 Fluid–particle interaction in turbulent open channel flow with fully-resolved mobile beds. Adv. Water Resour. 72, 32–44.Google Scholar
Vowinckel, B., Nikora, V., Kempe, T. & Fröhlich, J. 2017a Momentum balance in flows over mobile granular beds: application of double-averaging methodology to DNS data. J. Hydraul. Res. 55 (2), 190–207.Google Scholar
Vowinckel, B., Nikora, V., Kempe, T. & Fröhlich, J. 2017b Spatially-averaged momentum fluxes and stresses in flows over mobile granular beds: a DNS-based study. J. Hydraul. Res. 55 (2), 208–223.Google Scholar
Wang, L., Guo, Z. L. & Mi, J. C. 2014 Drafting, kissing and tumbling process of two particles with different sizes. Comput. Fluids 96, 20–34.Google Scholar
Winterwerp, J. C. 2001 Stratification effects by cohesive and noncohesive sediment. J. Geophys. Res. 106 (C10), 22559–22574.Google Scholar
Winterwerp, J. C. 2002 On the flocculation and settling velocity of estuarine mud. Cont. Shelf Res. 22 (9), 1339–1360.Google Scholar
Wu, L., Ortiz, C. P. & Jerolmack, D. J. 2017 Aggregation of elongated colloids in water. Langmuir 33 (2), 622–629.Google Scholar
Ye, M., van der Hoef, M. A. & Kuipers, J. A. M. 2004 A numerical study of fluidization behavior of Geldart A particles using a discrete particle model. Powder Technol. 139 (2), 129–139.Google Scholar
Zinchenko, A. Z. & Davis, R. H. 2014 Growth of multiparticle aggregates in sedimenting suspensions. J. Fluid Mech. 742, 577–617.Google Scholar

Vowinckel et al. supplementary movie

Particles settling over time. From left to right: Co = 0 (cohesionless), Co = 1, and Co = 5. The cohesive sediment is seen to settle more rapidly than its noncohesive counterpart.

Download Vowinckel et al. supplementary movie(Video)
Video 32.7 MB