In this paper we present direct numerical simulations of monodisperse and polydisperse suspensions of non-Brownian particles sedimenting at low Reynolds number. We describe a scheme to generate ergodic ensembles of random particulate systems and a numerical procedure for computing interactions among spherical particles based on Ewald summation technique for hydrodynamic mobility tensors. From the generation process truly random both monodisperse and multimodal size distributions of particles were obtained for dilute and moderate densities based on a minimum energy criterion. Concerned with computations of the Ewald sums our numerical procedure drastically reduces the CPU simulation time providing results of the hindered settling function in good agreement with available experimental data and asymptotic results for ordered and random periodic arrays of particles. We show new computer simulations with no flux boundary perpendicular to gravity and periodic boundary conditions in horizontal direction. The simulations reproduce the experimental correlation-time and anisotropy of the velocity fluctuations, but have the magnitude of these fluctuations increasing proportional to the size of the system.
Issue Section:
Additional Technical Papers
1.
Davis
, R. H.
, and Acrivos
, A.
, 1985
, “Sedimentation of Noncolloidal Particles at Low Reynolds Number
,” Annu. Rev. Fluid Mech.
, 17
(91
), pp. 91
–118
.2.
Richardson
, J. F.
, and Zaki
, W. N.
, 1954
, “Sedimentation and Fluidization: I
,” Trans. Inst. Chem. Eng.
, 32
(35
), pp. 35
–52
.3.
Batchelor
, G. K.
, 1972
, “Sedimentation in a Dilute Dispersion of Spheres
,” J. Fluid Mech.
, 52
, pp. 245
–268
.4.
Batchelor
, G. K.
, 1982
, “Sedimentation in a Dilute Polydisperse System of Interacting Spheres. Part 1. General Theory
,” J. Fluid Mech.
, 119
, pp. 379
–408
.5.
Davis
, R. H.
, 1996
, “Hydrodynamic Diffusion of Suspended Particles: A Symposium
,” J. Fluid Mech.
, 310
, pp. 325
–335
.6.
Guazzelli
, E.
, 2001
, “Evolution of Particle-Velocity Correlations in Sedimentation
,” Phys. Fluids
, 13
(6
), pp. 1537
–1540
.7.
Caflisch
, R. E.
, and Luke
, J. H. C.
, 1985
, “Variance in the Sedimentation Speed of a Suspension
,” Phys. Fluids
, 28
(3
), pp. 759
–760
.8.
Hinch, E. J., 1988, Disorder and Mixing, Kluwer Academic, Dordrecht, pp. 153–161, Chap. 9.
9.
Koch
, D. L.
, and Shaqfeh
, E. S. G.
, 1991
, “Screening in Sedimenting Suspensions
,” J. Fluid Mech.
, 224
, pp. 275
–303
.10.
Koch
, D. L.
, 1992
, “Anomalous Diffusion of Momentum in a Dilute Gas-Solid Suspension
,” Phys. Fluids
, 4
(7
), pp. 1337
–1346
.11.
Cunha, F. R., 1995, “Hydrodynamic Dispersion in Suspensions,” Ph.D. Thesis, Department of Applied Mathematics and Theoretical Physics, Cambridge University, Cambridge, UK.
12.
Cunha
, F. R.
, 1997
, “On the Fluctuations in a Random Suspension of Sedimenting Particles
,” J. Braz. Soc. Mech. Sci.
, 19
(4
), pp. 474
–495
.13.
Brenner
, M. P.
, 1999
, “Screening Mechanisms in Sedimentation
,” Phys. Fluids
, 11
(4
), pp. 754
–772
.14.
Koch
, D. L.
, 1994
, “Hydrodynamic Diffusion in a Suspension of Sedimenting Point Particles With Periodic Boundary Conditions
,” Phys. Fluids
, 6
(9
), pp. 2894
–2900
.15.
Ladd
, A. J. C.
, 1993
, “Dynamical Simulation of Sedimenting Spheres
,” Phys. Fluids
, 5
(2
), pp. 299
–310
.16.
Ladd
, A. J. C.
, 1997
, “Sedimentation of Homogeneous Suspensions of Non-Brownian Spheres
,” Phys. Fluids
, 9
(3
), pp. 491
–499
.17.
Cunha
, F. R.
, Rosa
, O. S.
, and Sousa
, A. J.
, 2001
, “Do We Understand Hydrodynamic Dispersion in Sedimenting Suspensions?
” J. Braz. Soc. Mech. Sci.
, 23
(4
), pp. 379
–399
.18.
Nicolai
, H.
, and Guazzelli
, E.
, 1995
, “Effect of the Vessel Size on the Hydrodynamic Diffusion of Sedimenting Spheres
,” Phys. Fluids
, 7
(1
), pp. 3
–5
.19.
Se´gre
, P. N.
, Herbolzeimer
, E.
, and Chaikin
, P. M.
, 1997
, “Long-Range Correlations in Sedimentation
,” Phys. Rev. Lett.
, 79
(13
), pp. 2574
–2577
.20.
Kalthoff
, W.
, Schwarzer
, S.
, Ristow
, G.
et al., 1996
, “On the Application of a Novel Algorithm to Hydrodynamic Diffusion and Velocity Fluctuations in Sedimenting Systems
,” Int. J. Mod. Phys. C
, 7
(4
), pp. 543
–561
.21.
Davis
, R. H.
, and Hassen
, M. A.
, 1988
, “Spreading of the Interface at the Top of a Slightly Polydisperse Sedimenting Suspension
,” J. Fluid Mech.
, 196
, pp. 107
–134
.22.
Lee
, S.
, Jang
, J.
, Choi
, C.
, and Lee
, T.
, 1992
, “Combined Effect of Sedimentation Velocity Fluctuation and Self-Sharpening on Interface Broadening
,” Phys. Fluids
, 4
(12
), p. 2601
–2606
.23.
Ham
, J. M.
, and Homsy
, G. M.
, 1988
, “Hindered Settling and Hydrodynamic Dispersion in Quiescent Sedimenting Suspensions
,” Int. J. Multiphase Flow
, 14
(5
), pp. 533
–546
.24.
Xue
, J.-Z.
, Herboltzheimer
, E.
, Rutgers
, M. A.
, Russel
, W. B.
, and Chaikin
, P. M.
, 1992
, “Diffusion, Dispersion, and Settling of Hard Spheres
,” Phys. Rev. Lett.
, 69
(11
), pp. 1715
–1718
.25.
Nicolai
, H.
, Herzhaft
, B.
, Hinch
, E. J.
, Oger
, L.
, and Guazzelli
, E.
, 1995
, “Particle Velocity Fluctuations and Hydrodynamic Self-Diffusion of Sedimenting Non-Brownian Spheres
,” Phys. Fluids
, 7
(1
), pp. 12
–23
.26.
Cunha
, F. R.
, and Hinch
, E. J.
, 1996
, “Shear-Induced Dispersion in a Dilute Suspension of Rough Spheres
,” J. Fluid Mech.
, 309
, pp. 211
–223
.27.
Leighton
, D. T.
, and Acrivos
, A.
, 1987
, “The Shear-Induced Migration of Particles in Concentrated Suspensions
,” J. Fluid Mech.
, 181
, pp. 415
–439
.28.
Beenakker
, C. W. J.
, 1986
, “Ewald Sum of the Rotne-Prager Tensor
,” J. Chem. Phys.
, 85
(3
), pp. 1581
–1582
.29.
Nijboer
, B. R. A.
, and De Wette
, F. W.
, 1957
, “On the Calculation of Lattice Sums
,” Physica
, 23
, pp. 309
–321
.30.
Rotne
, J.
, and Prager
, S.
, 1969
, “Variational Treatment of Hydrodynamic Interaction in Polymers
,” J. Chem. Phys.
, 50
(11
), pp. 4831
–4837
.31.
Brady
, J. F.
, and Bossis
, G.
, 1988
, “Stokesian Dynamics
,” Annu. Rev. Fluid Mech.
, 20
, pp. 111
–157
.32.
Kim, S., and Karrila, S. J., 1991, Microhydrodynamics: Principles and Selected Applications, Butterworth-Heinemann.
33.
Blake
, J. R.
, 1971
, “A Note on the Image System for a Stokeslet in a No-Slip Boundary
,” Proc. Cambridge Philos. Soc.
, 70
, pp. 303
–310
.34.
Metropolis
, N.
, Rosenbluth
, A. W.
, Rosenbluth
, M. N.
, Teller
, A. H.
, and Teller
, E.
, 1953
, “Equation of State Calculations by Fast Computing Machines
,” J. Chem. Phys.
, 21
(6
), pp. 1087
–1092
.35.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., 1992, Numerical Recipes in Fortran 77, 1, Cambridge University Press, Cambridge, UK.
36.
Sierou
, A.
, and Brady
, J. F.
, 2001
, “Accelerated Stokesian Dynamics Simulations
” J. Fluid Mech.
, 448
, pp. 115
–146
.37.
Ladd
, A. J. C.
, 1994
, “Numerical Simulations of Particulate Suspensions via a Discretized Boltzmann Equation. Part 2. Numerical Results
,” J. Fluid Mech.
, 271
, pp. 311
–339
.38.
Mo
, G.
, and Sangani
, A. S.
, 1994
, “A Method for Computing Stokes Flow Interactions Among Spherical Objects and Its Application to Suspensions of Drops and Porous Particles
,” Phys. Fluids
, 6
(5
), pp. 1637
–1652
.39.
Saffman
, P. G.
, 1973
, “On the Settling Speed of Free and Fixed Suspensions
,” Stud. Appl. Math.
, 52
(2
), pp. 115
–127
.40.
Sangani
, A. S.
, and Acrivos
, A.
, 1982
, “Slow Flow Through a Periodic Array of Spheres
,” Int. J. Multiphase Flow
, 8
(4
), pp. 343
–360
.41.
Brady
, J. F.
, and Durlofsky
, L. J.
, 1988
, “The Sedimentation Rate of Disordered Suspensions
,” Phys. Fluids
, 31
(4
), pp. 717
–727
.42.
Davis
, R. H.
, and Gecol
, H.
, 1994
, “Hindered Settling Function with No Empirical Parameters for Polydisperse Suspensions
,” AIChE J.
, 40
(3
), pp. 570
–575
.43.
Batchelor
, G. K.
, and Wen
, C. S.
, 1982
, “Sedimentation in a Dilute Polydisperse System of Interacting Spheres. Part 2. Numerical Results
,” J. Fluid Mech.
, 124
, pp. 495
–528
.Copyright © 2002
by ASME
You do not currently have access to this content.
