×

zbMATH — the first resource for mathematics

An efficient cellular flow model for cohesive particle flocculation in turbulence. (English) Zbl 1460.76866
Summary: We propose a one-way coupled model that tracks individual primary particles in a conceptually simple cellular flow set-up to predict flocculation in turbulence. This computationally efficient model accounts for Stokes drag, lubrication, cohesive and direct contact forces on the primary spherical particles, and allows for a systematic simulation campaign that yields the transient mean floc size as a function of the governing dimensionless parameters. The simulations reproduce the growth of the cohesive flocs with time, and the emergence of a log-normal equilibrium distribution governed by the balance of aggregation and breakage. Flocculation proceeds most rapidly when the Stokes number of the primary particles is \(O(1)\). Results from this simple computational model are consistent with experimental observations, thus allowing us to propose a new analytical flocculation model that yields improved agreement with experimental data, especially during the transient stages.

MSC:
76T20 Suspensions
76F65 Direct numerical and large eddy simulation of turbulence
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bergougnoux, L., Bouchet, G., Lopez, D. & Guazzelli, E.2014The motion of solid spherical particles falling in a cellular flow field at low Stokes number. Phys. Fluids26 (9), 093302.
[2] Biegert, E., Vowinckel, B. & Meiburg, E.2017aA collision model for grain-resolving simulations of flows over dense, mobile, polydisperse granular sediment beds. J. Comput. Phys.340, 105-127. · Zbl 1376.76069
[3] Biegert, E., Vowinckel, B., Ouillon, R. & Meiburg, E.2017bHigh-resolution simulations of turbidity currents. Prog. Earth Planet. Sci.4 (1), 33.
[4] Bouyer, D., Line, A. & Do-Quang, Z.2004Experimental analysis of floc size distribution under different hydrodynamics in a mixing tank. AIChE J.50, 2064-2081.
[5] Cox, R. G. & Brenner, H.1967The slow motion of a sphere through a viscous fluid towards a plane surface—II Small gap widths, including inertial effects. Chem. Engng Sci.22, 1753-1777.
[6] Hill, P. S., Boss, E., Newgard, J. P., Law, B. A. & Milligan, T. G.2011Observations of the sensitivity of beam attenuation to particle size in a coastal bottom boundary layer. J. Geophys. Res.116, C02023.
[7] Keyvani, A. & Strom, K.2014Influence of cycles of high and low turbulent shear on the growth rate and equilibrium size of mud flocs. Mar. Geol.354, 1-14.
[8] Khelifa, A. & Hill, P. S.2006aKinematic assessment of floc formation using a Monte Carlo model. J. Hydraul Res.44 (4), 548-559.
[9] Khelifa, A. & Hill, P. S.2006bModels for effective density and settling velocity of flocs. J. Hydraul Res.44 (3), 390-401.
[10] Kuprenas, R., Tran, D. & Strom, K.2018A shear-limited flocculation model for dynamically predicting average floc size. J. Geophys. Res.123, 6736-6752.
[11] Lee, J. B., Toorman, E., Molz, J. F. & Wang, J.2011A two-class population balance equation yielding bimodal flocculation of marine or estuarine sediments. Water Res.45, 2131-2145.
[12] Levich, V. G.1962Physicochemical Hydrodynamics. Prentice Hall.
[13] Maggi, F., Mietta, F. & Winterwerp, J. C.2007Effect of variable fractal dimension on the floc size distribution of suspended cohesive sediment. J. Hydrol.343, 43-55.
[14] Maxey, M. R.1987The motion of small spherical particles in a cellular flow field. Phys. Fluids30, 1915-1928.
[15] Shen, X., Lee, B. J., Fettweis, M. & Toorman, E. A.2018A tri-modal flocculation model coupled with TELEMAC for estuarine muds both in the laboratory and in the field. Water Res.145, 473-486.
[16] Sherwood, C. R., Aretxabaleta, A. L. & Harris, C. K.2018Cohesive and mixed sediment in the regional ocean modeling system implemented in the coupled ocean atmosphere wave sediment-transport modeling system. Geosci. Model Develop.11, 1849-1871.
[17] Shin, J. H., Son, M. & Lee, G.2015Stochastic flocculation model for cohesive sediment suspended in water. Water7, 2527-2541.
[18] Son, M. & Hsu, T. J.2008Flocculation model of cohesive sediment using variable fractal dimension. Environ. Fluid Mech.8 (1), 55-71.
[19] Son, M. & Hsu, T. J.2009The effect of variable yield strength and variable fractal dimension on flocculation of cohesive sediment. Water Res.43 (14), 3582-3592.
[20] Strom, K. & Keyvani, A.2016Flocculation in a decaying shear field and its implications for mud removal in near-field river mouth discharges. J. Geophys. Res.121, 2142-2162.
[21] Tran, D., Kuprenas, R. & Strom, K.2018How do changes in suspended sediment concentration alone influence the size of mud flocs under steady turbulent shearing?Cont. Shelf Res.158, 1-14.
[22] Verney, R., Lafite, R., Burn-Cottan, J. C. & Le Hir, P.2011Behaviour of floc population during a tidal cycle: laboratory experiments and numerical modeling. Cont. Shelf Res.31 (10), 64-83.
[23] Vowinckel, B., Withers, J., Luzzatto-Fegiz, P. & Meiburg, E.2019Settling of cohesive sediment: particle-resolved simulations. J. Fluid Mech.858, 5-44. · Zbl 1415.76700
[24] Wang, L. P. & Maxey, R. M.1993Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech.256, 27-68.
[25] Winterwerp, J. C.1998A simple model for turbulence induced flocculation of cohesive sediment. J. Hydraul Res.36 (3), 309-326.
[26] Winterwerp, J. C., Manning, A. J., Martens, C., De Mulder, T. & Vanlede, J.2006A heuristic formula for turbulence-induced flocculation of cohesive sediment. Estuar. Coast. Shelf Sci.68, 195-207.
[27] Yoshimasa, W.2017Flocculation and me. Water Res.114, 88-103.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.