Abstract
Hindered settling, the process by which the settling of sediment particles becomes impeded due to the proximity of other sediment particles, can be an important process for the coastal modeller, especially in highly muddy environments. It is also a significant process in other disciplines such as chemical engineering, the modelling of debris flow, the study of turbidites, piping of slurries and the understanding of processes occurring within a dredger hopper. This study first examines the hindered settling behaviour of monodisperse suspensions in order to create a framework for polydisperse hindered settling that works for both non-cohesive and cohesive suspensions. The Richardson–Zaki equation is adapted to make it compatible with the changes with viscosity that occur near the point at which suspensions become solid. The modified monodisperse settling equation is then compared to data for hindered settling of cohesive suspensions and shown to be consistent with the transition between hindered settling and the initial permeability phase of consolidation. Based on the monodisperse framework developed initially, this paper proposes a hindered settling model for sand/mud mixtures which is based on a modification of the Masliyah (1979) and Lockett and Bassoon (1979) hindered settling equation. The model is shown to reproduce the hindered settling of a variety of different sediment mixtures whilst reducing the extent of empiricism often associated with the modelling of polydisperse hindered settling of mud/sand mixtures.
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References
Al-Naafa MA, Selim MS (1989) Sedimentation of polydisperse concentrated suspensions. Can J Chem Eng 67:253–264
Amy, L.A., Talling, P.J., Edmonds, V.O., Sumner, E.J. and Lesueur, A. (2006). An experimental investigation of sand–mud suspension settling behaviour: implications for bimodal mud contents of submarine flow deposits
Baldock T, Tomkins MR, Nielsen P, Hughes MG (2004) Settling velocity of sediments at high concentrations. Coast Eng 51:91–100
Batchelor GK (1982) Sedimentation in a batch of dilute polydisperse system of interacting spheres, Part 1: General Theory. Journal of Fluid Mechanics 119:379–408
Batchelor GK, Wen CS (1982) Sedimentation in a dilute polydisperse system of interacting spheres:Part 2. Numerical results, Journal Fluid Mechanics 124:495–528
Baugh JV, Manning AJ (2007) An assessment of a new settling velocity parameterisation for cohesive sediment transport modelling. Cont Shelf Res. doi:10.1016/j.csr.2007.03.003
Bergougnoux L, Ghicini S, Guazzelli E, Hinch J (2002) Spreading fronts and fluctuations in sedimentation. Physical Fluids 15:1875–1887
Berres S, Burger E, Tory EM (2005) Applications of polydisperse sedimentation models. Chem Eng J 111:105–117
Bürger R, García A, Karlsen KH, Towers JD (2008) A family of numerical schemes for kinematic flows with discontinuous flows. Journal of Engineering Mathematics 60(3):387–425
Burger R, Karlsen KH, Tory EM, Wendland WL (2002) Model equations and instability regions for the sedimentation of polydisperse suspensions of spheres. ZAMM Z Angew Math Mech 82(10):699–722
Camenen B (2008) Settling velocity of sediments at high concentration. In: Kusada T, Yamanishi H, Spearman J, Gailani J (eds) Sediment and Ecohydraulics, INTERCOH 2005. Elsevier, Amsterdam, pp 211–226
Camenen B, Pham Van Bang D (2011) Modelling the settling of suspended sediments for concentrations close to the gelling concentration. Cont Shelf Res 31:106–111
Chesher TJ, Ockenden MC (1997) Numerical modelling of mud and sand mixtures. In: Burt N, Parker R, Watts J (eds) Cohesive Sediments – Proc. of INTERCOH Conf. Wiley, (Wallingford, England), Chichester, pp 395–406
Chong JS, Christiansen EB, Baer AD (1971) Rheology of concentrated suspensions. J Appl Polym Sci 15:2007–2021
Coulson JM, Richardson JF (1955) Chemical engineering, vol 2. Pergamon press, London
Cuthbertson A, Dong P, King S, Davies P (2008) Hindered settling velocity of cohesive/noncohesive sediment mixtures. Coastal Engineering 55(12):1197–1208
Dankers PJT (2006) On the hindered settlling of suspensions of mud and mud-sand mixtures. Doctoral Thesis for the Technical University of Delft, Netherlands
Davies R (1968) The experimental study of the differential settling of particles in suspension at high concentrations, Proceedings of the International Conference on Powder Technology, Chicago, May 20-23, 1968, Powder technology. Elsivier, Netherlands
Davis RH, Gecol H (1994) Hindered settling function with no empirical parameters for polydisperse suspensions. AIChE Journal 40(3):570–575
Davies R, Kaye BH (1971) Experimental investigation into the settling behaviour of suspensions, Proceedings of PowTech, 71: International Powder Technology and Bulk Grabular Solids Conference, 1971
Dorrell R, Hogg AJ (2010) Sedimentation of bidisperse dispersion. Int J Multiphase Flow 36:481–490
Dorrell RM, Hogg AJ, Sumner EJ, Talling PJ (2011) The structure of the deposit produced by sedimentation of polydisperse suspensions. J Geophys Res Earth Surf 116(1):F01024
Dumbser M, Enaux C, Toro EF (2008) Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws. J Comp Phys 227:3971–4001
Faas RW (1984) Time and density-dependent properties of fluid mud suspensions in NE Brazilian Continental Shelf. Geo-Mar Lett 4:147–152
Garside J, Al-Dibouni MR (1977) Velocity-voidage relationship for fluidization and sedimentation in solid-liquid systems. Ind. Eng. Chem., process Des Dev 16:206–214
Gratiot N, Manning AJ (2007) A laboratory study of dilute suspension mud floc characteristics in an oscillatory diffusive turbulent flow. J Coast Res SI 50:1142–1146
Ha Z, Liu S (2002) Settling Velocities of Polydisperse Concentrated Suspensions. The Canadian Journal of Chemical Engineering 80(5):783–790
Harper MA, Harper JF (1967) Measurements of diatom adhesion and their relationship with movement. Br Phycological Bull 3:195–207
Koch DL, Shaqfeh ESG (1991) Screening in sedimenting suspensions. J Fluid Mech 224:275–230
Kothari AC (1981) Sedimentation of Multisized Particles, MS Thesis. Texas Technology University, Lubbock
Kranck K (1984) The role of flocculation in the filtering of particulate matter in estuaries. In: Kennedy V (ed) The Estuary as a Filter. Academic Press, Orlando Inc, pp 159–175
Kranenburg C (1992) Hindered settlign and consolidation of mud - analytical results, Report number 11-92. Delft University of Technology, Netherlands
Krieger IM, Dougherty TJ (1959) A mechanism for non-Newtonian flow in suspension of rigid spheres. Trans Soc Rheol 3:137–152
Krone RB (1963) A study of rheological properties of estuarial sediments. Report No. 63-68, Hyd. Eng. Lab. and Sanitary Eng. Lab. University of California, Berkeley, pp 63–68
Leng, D.E., Katti, S.S. and Atiemo-Obeng V. (2009). Industrial mixing technology, In: L.F. Albright (ed), Albrights Chemical Engineering Handbook, CRC Press, Boca Raton, pp615–707.
Little C (2000) The biology of soft shores and estuaries. Oxford University Press, UK 252p
Liu S (2000) Suspension flow in pipeline. Recent Res. Devel. Chemical Engg. 4:161–233
Lockett MJ, Al-Habbooby HM (1974) Relative particle velocities in two-species settling. Powder technology 10:67–71
Lockett MJ, Bassoon KS (1979) Sedimentation of binary particle maixtures. Powder Technology 24:1–7
Manning AJ, Baugh JV, Spearman J, Whitehouse RJS (2010) Flocculation settling characteristics of mud:sand mixtures. Ocean Dyn 60:237–253. doi:10.1007/s10236-009-0251-0
Manning AJ, Baugh JV, Soulsby RL, Spearman JR, Whitehouse RJS (2011a) Cohesive sediment flocculation and the application to settling flux modelling. In: SS Ginsberg (ed) ‘Sediment Transport’, Publisher: InTech (Vienna), Chapter 5, pp. 91–116. doi:10.5772/16055
Manning AJ, Baugh JV, Spearman J, Pidduck EL, Whitehouse RJS (2011b) The settling dynamics of flocculating mud-sand mixtures: part 1—empirical algorithm development. Ocean Dyn 61(2–3):311–350. doi:10.1007/s10236-011-0394-7
Manning AJ, Whitehouse RJS, Soulsby RL (2012) Methods for predicting suspensions of mud. Technical Report, HR Wallingford Ltd http://eprints.hrwallingford.co.uk/661/1/TR104.pdf
Masliyah JH (1979) Hindered settling in a multi-species particle system. Chem Eng Sci 34(1979):1166–1168
Maude AD and Whitmore RL (1958) A generalized theory of sedimentation. Brit J Appl Phys 9:477–482
Mehta, A.J., Jaeger, J.M., Valle-Levinson, A., Hayter, E.J., Wolanski, E. and Manning, A.J. (2009). Resuspension Dynamics in Lake Apopka, Florida. Final Synopsis Report, submitted to St. Johns River Water Management District, Palatka, Florida, June 2009, Report No. UFL/COEL-2009/00, 158p
Merckelbach LM and Kranenburg C (2004) New constitutive equations for soft mud-sand mixtures. Géotechnique 54(4):235–243
Merckelbach L (2000) Consolidation and strength evolution of soft mud layers, Communications on Hydraulic and Geotechnical Engineering, PhD thesis for Delft University of Technology. Geotechnical Engineering, report 00-2, Delft University of Technology
Mirza S, Richardson JF (1979) Sedimentation of suspensions of particles of two or more sizes. Chemical Engineering Science 34(4):447–454
Mucha PJ, Brenner MP (2003) Diffusivities and front propagation in sedimentation. Phys Fluids 15(5):1305–1313
Nguyen QD (2008) Etude expérimentale et numérique du début de consolidation de sols de très forte teneur en eau. PhD. thesis. Université de Nantes, France In French
Nguyen NQ, Ladd AJC (2005) Sedimentation of hard-sphere suspensions at low Reynolds number. J Fluid Mech 525:73–104
Paterson, D.M. and Hagerthey, S.E. (2001). Microphytobenthos in contrasting coastal ecosystems: Biology and dynamics. In: Ecological comparisons of sedimentary shores (K. Reise, Ed.), Ecological studies, pp. 105–125
Quemada D (1977) Rheology of concentrated disperse systems and minimum energy dissipation principle. Rheol Acta 16:82–94
Richardson JF, Zaki WN (1954) Sedimentation and fluidization: part I. Trans Instn Chem Engrs 32:35–53
Ross MA (1988) Vertical structure of estuarine fine sediment suspensions. Ph.D. thesis. University of Florida, Gainesville
Rowe PN (1987) A convenient empirical equation for estimation of the Richardson-Zaki exponent. Chem.Eng.Sci. 43:2795–2796
Schiller, L. and Naumann, A. (1933). Uber die grundlegenden Berechnungen bei der Schwerkrauftbereitung, Z.,VDI, volume 77. (In German)
Siwiec T (2007) The experimental verification of Richardson-Zaki law on example of selected beds used in water treatment. J Polish Agric Univ 10(2):5
Smith SJ, Freidrichs CT (2011) Size and settling velocities of cohesive flocs and suspended sediment aggregates in a trailing suction hopper dredge plume. Cont Shelf Res 31:S50–S63
Soulsby RL (1997) Dynamics of marine sands. Thomas Telford Publications, London
Soulsby RL, Manning AJ, Spearman J, Whitehouse RJS (2013) Settling velocity and mass settling flux of flocculated estuarine sediments. Mar Geol. doi:10.1016/j.margeo.2013.04.006
Spearman J, Manning AJ, Whitehouse RJS (2011) The settling dynamics of flocculating mud-sand mixtures: part 2—numerical modelling. Ocean Dyn 60(2):237–253
Te Slaa S, He Q, van Maren DS, Winterwerp JC (2013) Sediment processes in silt rich sediment systems. Ocean Dyn 63:399–421
Tolhurst TJ, Gust G, Paterson DM (2002) The influence on an extra-cellular polymeric substance (EPS) on cohesive sediment stability. In: Winterwerp JC, Kranenburg C (eds) Fine sediment dynamics in the marine environment - proceedings in marine science 5. Elsevier, Amsterdam, pp 409–425
Toorman E (1996) Sedimentation and self-weight consolidation: general unifying theory. Géotechnique 46(1):103–113
Toorman E (1997) Modelling the thixotropic behaviour of dense cohesive sediment suspensions. Rheol Acta 36:56–65
Toorman EA (1999) Sedimentation and self-weight consolidation: constitutive equations and numerical modelling. Geotechnique 49(6):709–726
Van LA, Pham Van Bang D (2013) Hindered settling of sand/mud flocs mixtures: from model formulation to numerical validation. Adv Water Resour 53:1–11
van Ledden M (2002) A process-based sand-mud model. In: Winterwerp JC, Kranenburg C (eds) Fine Sediment Dynamics in the Marine Environment - Proc. in Mar. Science 5. Elsevier, Amsterdam, pp 577–594
van Olphen H (1977) An introduction to clay colloid chemistry, 2nd edn. Wiley, London 318 p
Van Rijn LC (1993) Principles of sediment transport in rivers, estuaries and coastal seas. Aqua Publications, Amsterdam
van Rijn LC (2007) Unified view of sediment transport by currents and waves. II: Suspended Transport, Journal of Hydraulic Engineering 133(6):668–689
Waeles B, Le Hir P, Lesueur P (2008) A 3D morphodynamic process-based modelling of a mixed sand/mud coastal environment : the seine estuary, France. In: Kudusa T, Yamanishi H, Spearman J, Galiani JZ (eds) Sediment and Ecohydraulics - Proc. in Marine Science 9. Elsevier, Amsterdam, pp 477–498
HR Wallingford (1990) Fluid mud in estuaries, Field measurements, HR Wallingford Report EX2076, January 1990
Wang, Z.Y., Larsen, P. and Xiang, W. (1994). Rheological properties of sediment suspensions and their implications, Journal of Hydraulic Research, IAHR,495–516
Wang Z, Nestmann F, Dittrich A (1995) Fall velocity of sediment in clay suspensions, Procedings of the Sixth International Syposium on River sedimentation. Central Board of Irrigation and Power, New Delhi published by A.A. Balkema
Whitehouse RJS, Soulsby RL, Roberts W, Mitchener HJ (2000) Dynamics of estuarine muds. Thomas Telford, London, 210 pp
Winterwerp JC (1999) On the dynamics of high-concentrated mud suspensions. Ph.D. Thesis. Delft University of Technology, Faculty of Civil Engineering and Geosciences, The Netherlands 172 p
Winterwerp JC (2002) On the flocculation and settling velocity of estuarine mud. Cont Shelf Res 22(9):1339–1360
Winterwerp JC, Van Kesteren WGM (2004) Introduction to the physics of cohesive sediment dynamics in the marine environment. In: van Loon T (ed) Developments in sedimentology, 56. Elsevier, Amsterdam, 466p
Winterwerp JC, Manning AJ, Martens C, de Mulder T, Vanlede J (2006) A heuristic formula for turbulence-induced flocculation of cohesive sediment. Estuar Coast Shelf Sci 68:195–207
Wu W, Wang SY (2006) Formulas for sediment porosity and settling velocity. J Hydrual Eng 132(8):858–862
Yin X, Koch DL (2008) Velocity fluctuations and hydrodynamic diffusion in finite-Reynolds-number sedimenting suspensions. Phys Fluids 20:043305
Acknowledgements
Professor Manning’s contribution to this manuscript was partly funded by HR Wallingford Company Research project ‘FineScale - Dynamics of Fine-grained Cohesive Sediments at Varying Spatial and Temporal Scales’ (DDY0523).
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Responsible Editor: Erik A Toorman
This article is part of the Topical Collection on the 13th International Conference on Cohesive Sediment Transport in Leuven, Belgium 7-11 September 2015
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Spearman, J., Manning, A.J. On the hindered settling of sand-mud suspensions. Ocean Dynamics 67, 465–483 (2017). https://doi.org/10.1007/s10236-017-1034-7
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DOI: https://doi.org/10.1007/s10236-017-1034-7