Water scarcity has required constant water recycling, leading to a decline in water quality, further exacerbated by high concentrations of fine particles that reduce the efficiency of solid–liquid separation systems. Inclined settlers offer a viable secondary treatment option for high-turbidity water. Effective design requires understanding of operational conditions, geometry, and suspension properties. Using OpenFOAM, computational fluid dynamics simulations were performed for a continuous inclined countercurrent conduit to assess the influence of inlet particle concentration on efficiency, exploring various Surface Overflow Rates (SOR) and inclination angles. The results show that the steady state in which the flow settles is strongly dependent on the particle concentration. For very low particle concentrations, the flow is mostly stationary with little to no resuspension of particles. Increasingly unstable regimes are observed to emerge as the inlet concentration increases, leading to increased particle resuspension. Instabilities arise from overhanging zones at the tip of the suspension, generating recirculation zones that enlarge the resuspension region and induce entrainment within the bulk suspension. Shear instabilities become noticeable at large particle concentrations, further increasing resuspension. Different regimes were identified, influenced by the SOR and the inclination angles. Additionally, a Reynolds number characterizing these systems is proposed alongside a scale analysis. The findings highlight particle concentration as a critical parameter in inclined plate settler design.
REFERENCES
1.
D.
Connelly
, “High clay ores a mineral processing nightmare
,” Australian J. Min.
24
, 28
–29
(2011
).2.
M.
Gräfe
, C.
Klauber
, A. J.
McFarlane
, and D. J.
Robinson
, Clays in the Minerals Processing Value Chain
(Cambridge University Press
, 2017
).3.
S. E.
Clark
, C. D.
Roenning
, J. C.
Elligson
, and J.
Mikula
, “Inclined plate settlers to treat storm-water solids
,” J. Environ. Eng.
135
, 621
–626
(2009
).4.
J.
Edzwald
, Water Quality & Treatment: A Handbook on Drinking Water
(McGraw-Hill Education
, 2011
).5.
T. E.
Wilson
, “Introduction and overview water environment federation clarifier design, manual of practice no. fd-8
,” in WEFTEC 2005
(Water Environment Federation
, 2005
), pp. 4412
–4416
.6.
J. C.
Crittenden
, R. R.
Trussell
, D. W.
Hand
, K. J.
Howe
, and G.
Tchobanoglous
, MWH's Water Treatment: Principles and Design
(Wiley
, 2012
).7.
A.
Boycott
, “Sedimentation of blood corpuscles
,” Nature
104
, 532
–532
(1920
).8.
R.
Tarpagkou
and A.
Pantokratoras
, “The influence of lamellar settler in sedimentation tanks for potable water treatment—A computational fluid dynamic study
,” Powder Technol.
268
, 139
–149
(2014
).9.
A.
Salem
, G.
Okoth
, and J.
Thöming
, “An approach to improve the separation of solid–liquid suspensions in inclined plate settlers: CFD simulation and experimental validation
,” Water Res.
45
, 3541
–3549
(2011
).10.
C.
Reyes
, F.
Apaz
, Y.
Niño
, B.
Barraza
, C.
Arratia
, and C. F.
Ihle
, “A review on steeply inclined settlers for water clarification
,” Miner. Eng.
184
, 107639
(2022
).11.
K. M.
Yao
, “Theoretical study of high-rate sedimentation
,” J. Water Pollut. Control Federation
42
, 218
–228
(1970
).12.
R. D.
Letterman
, Water Quality and Treatment: A Handbook of Community Water Supplies
(McGraw-Hill Inc., 1999
).13.
A. A.
Fadel
and E. R.
Baumann
, “Tube settler modeling
,” J. Environ. Eng.
116
, 107
–124
(1990
).14.
15.
R. L.
Droste
and R. L.
Gehr
, Theory and Practice of Water and Wastewater Treatment
(Wiley
, 2018
).16.
E.
Ponder
, “On sedimentation and Rouleaux formation-I
,” Exp. Physiol.
15
, 235
–252
(1925
).17.
H.
Nakamura
and K.
Kuroda
, “La cause de l'acceleration de la vitesse de sedimentation des suspensions dans les recipients inclines
,” Keijo J. Med.
8
, 256
–296
(1937
).18.
A.
Acrivos
and E.
Herbolzheimer
, “Enhanced sedimentation in settling tanks with inclined walls
,” J. Fluid Mech.
92
, 435
–457
(1979
).19.
E.
Herbolzheimer
, “Stability of the flow during sedimentation in inclined channels
,” Phys. Fluids
26
, 2043
–2054
(1983
).20.
R. H.
Davis
, E.
Herbolzheimer
, and A.
Acrivos
, “Wave formation and growth during sedimentation in narrow tilted channels
,” Phys. Fluids
26
, 2055
–2064
(1983
).21.
E. S. G.
Shaqfeh
and A.
Acrivos
, “The effects of inertia on the buoyancy-driven convection flow in settling vessels having inclined walls
,” Phys. Fluids
29
, 3935
–3948
(1986
).22.
A.
Borhan
and A.
Acrivos
, “The sedimentation of nondilute suspensions in inclined settlers
,” Phys. Fluids
31
, 3488
–3501
(1988
).23.
H.
Laux
and T.
Ytrehus
, “Computer simulation and experiments on two-phase flow in an inclined sedimentation vessel
,” Powder Technol.
94
, 35
–49
(1997
).24.
N.
Patankar
and D.
Joseph
, “Modeling and numerical simulation of particulate flows by the Eulerian–Lagrangian approach
,” Int. J. Multiphase Flow
27
, 1659
–1684
(2001
).25.
Y.-C.
Chang
, T.-Y.
Chiu
, C.-Y.
Hung
, and Y.-J.
Chou
, “Three-dimensional Eulerian-Lagrangian simulation of particle settling in inclined water columns
,” Powder Technol.
348
, 80
–92
(2019
).26.
Z.
Zhang
, D.
Legendre
, and R.
Zamansky
, “Fluid inertia effects on the motion of small spherical bubbles or solid spheres in turbulent flows
,” J. Fluid Mech.
921
, A4
(2021
).27.
D.
Esipov
and D.
Kuranakov
, “2D CFD-DEM numerical simulation of the sedimentation of circular particles in the rectangular inclined vessel
,” in AIP Conference Proceedings
(AIP Publishing
, 2023
), Vol. 2504
.28.
C. F.
Ihle
and C.
Reyes
, “A new criterion to estimate the capacity of steeply inclined settlers of arbitrary cross-sectional shape
,” Powder Technol.
397
, 117004
(2022
).29.
R. H.
Davis
and A.
Acrivos
, “Sedimentation of noncolloidal particles at low Reynolds numbers
,” Annu. Rev. Fluid Mech.
17
, 91
–118
(1985
).30.
31.
W. F.
Leung
and R. F.
Probstein
, “Lamella and tube settlers. 1. Model and operation
,” Ind. Eng. Chem. Proc. Des. Dev.
22
, 58
–67
(1983
).32.
C.
Reyes
, C.
Ihle
, and C.
Arratia
, “Stability and nonlinear dynamics of a settling fresh water particle laden fluid below a salt water layer
,” in International Symposium on Stratified Flows
, San Diego, USA, 2016
.33.
C.
Reyes
, C. F.
Ihle
, F.
Apaz
, and L. A.
Cisternas
, “Heat-assisted batch settling of mineral suspensions in inclined containers
,” Minerals
9
, 228
(2019
).34.
C. M.
Rhie
and W.-L.
Chow
, “Numerical study of the turbulent flow past an airfoil with trailing edge separation
,” AIAA J.
21
, 1525
–1532
(1983
).35.
H.
Rusche
, “Computational fluid dynamics of dispersed two-phase flow at high phase fractions
,” Ph. D. thesis (University of London
, 2002
).36.
H. G.
Weller
, “Derivation, modelling and solution of the conditionally averaged two-phase flow equations
,” Nabla Ltd., No Tech. Rep. TR/HGW
(2002
).37.
J. H.
Ferziger
, M.
Perić
, and R. L.
Street
, Computational Methods for Fluid Dynamics
(Springer
, 2019
).38.
H.
Versteeg
and W.
Malalasekera
, “The finite volume method
,” in An Introduction to Computational Fluid Dynamics
(Pearson
, 1995
), Vol. 102
.39.
D.
Gidaspow
, Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions
(Academic Press
, 1994
).40.
L.
Mortimer
, M.
Fairweather
, and D.
Njobuenwu
, “Particle concentration and stokes number effects in multi-phase turbulent channel flows
,” in Particles 2017: V International Conference on Particle-based Methods. Fundamentals and Applications
(International Center for Numerical Methods in Engineering
, 2017
), pp. 859
–869
.41.
A.
Volpe
, C.
Gaudiuso
, and A.
Ancona
, “Sorting of particles using inertial focusing and laminar vortex technology: A review
,” Micromachines
10
, 594
(2019
).42.
I. M.
Krieger
and T. J.
Dougherty
, “A mechanism for non-Newtonian flow in suspensions of rigid spheres
,” Trans. Soc. Rheol.
3
, 137
–152
(1959
).43.
S. M.
Damián
and N. M.
Nigro
, “An extended mixture model for the simultaneous treatment of small-scale and large-scale interfaces
,” Int. J. Numer. Methods Fluids
75
, 547
–574
(2014
).44.
R.
Warming
and R. M.
Beam
, “Upwind second-order difference schemes and applications in aerodynamic flows
,” AIAA J.
14
, 1241
–1249
(1976
).45.
C. J.
Greenshields
and H. G.
Weller
, Notes on Computational Fluid Dynamics: General Principles
(CFD Direct Limited
, 2022
).46.
J.
Crank
and P.
Nicolson
, “A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type
,” in Mathematical Proceedings of the Cambridge Philosophical Society
(Cambridge University Press
, 1947
), Vol. 43
, pp. 50
–67
.47.
S.
Benyahia
, M.
Syamlal
, and T. J.
O'Brien
, “Evaluation of boundary conditions used to model dilute, turbulent gas/solids flows in a pipe
,” Powder Technol.
156
, 62
–72
(2005
).48.
P. C.
Johnson
and R.
Jackson
, “Frictional–collisional constitutive relations for granular materials, with application to plane shearing
,” J. Fluid Mech.
176
, 67
–93
(1987
).49.
Y.
Liu
, J.
Li
, and A. J.
Smits
, “Roughness effects in laminar channel flow
,” J. Fluid Mech.
876
, 1129
–1145
(2019
).50.
B.
Milici
and M.
De Marchis
, “On the influence of wall roughness in particle-laden flows
,” in AIP Conference Proceedings
(AIP Publishing
, 2015
), Vol. 1648
.51.
K.
Luo
, Q.
Dai
, X.
Liu
, and J.
Fan
, “Effects of wall roughness on particle dynamics in a spatially developing turbulent boundary layer
,” Int. J. Multiphase Flow
111
, 140
–157
(2019
).52.
E. S. G.
Shaqfeh
and A.
Acrivos
, “The effects of inertia on the stability of the convective flow in inclined particle settlers
,” Phys. Fluids
30
, 960
–973
(1987
).53.
D.
Ahmet
, “Determination of settling efficiency and optimum plate angle for plated settling tanks
,” Water Res.
29
, 611
–616
(1995
).54.
A.
Borhan
, “An experimental study of the effect of suspension concentration on the stability and efficiency of inclined settlers
,” Phys. Fluids A: Fluid Dyn.
1
, 108
–123
(1989
).55.
W. F.
Leung
, “Lamella and tube settlers. 2. Flow stability
,” Ind. Eng. Chem. Proc. Des. Dev.
22
, 68
–73
(1983
).56.
R. F.
Probstein
, D.
Yung
, and R. E.
Hicks
, “A model for lamella settlers
,” in Theory, Practice, and Process Principles for Physical Separations', Engng Foundation Conf.
, Asilomar, California, 1977
.57.
D. J.
Brown
, “Design of lamella separators
,” Part 2, Ph.D. thesis (Loughborough University of Technology
, 1986
).58.
K.
Kinosita
, “Sedimentation in tilted vessels (1)
,” J. Colloid Sci.
4
, 525
–536
(1949
).59.
U.
Frisch
, Turbulence: The legacy of A. N. Kolmogorov
(Cambridge University Press
, 1995
).60.
Y.-J.
Chang
, R.-L.
Chern
, and Y.-J.
Chou
, “Transient instability in long, tilted water columns with fast-settling, particle-laden layers
,” J. Fluid Mech.
929
, A42
(2021
).61.
J.
Richardson
and W.
Zaki
, “Sedimentation and fluidisation: Part I
,” Chem. Eng. Res. Des.
75
, S82
–S100
(1997
).62.
J.
Chawner
, “Quality and control-two reasons why structured grids aren't going away
,” Pointwise (2013
). http://www. pointwise. com/theconnector/March-2013/Structured-Grids-in-Pointwise. shtml (last accessed March 8, 2015).© 2025 Author(s). Published under an exclusive license by AIP Publishing.
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