Sedimentation is container-size dependent

Abstract In very dilute, bounded dispersions of identical spheres, the initial distributions of particle and fluid velocities in small containers differ enormously from those in very large ones. In the latter, local interactions are dwarfed by the massive collective influence of distant spheres. Large regions move downward or upward virtually en masse. Since particles and fluid in these clusters move with almost the same velocity, the mean of the initial distribution is scarcely affected by the much larger container size, but individual velocities can exceed the mean by one or more orders of magnitude. Experimental evidence of cluster settling, including the effect of container size, is ancient and abundant.

[1]  B. Koglin.  Experimentelle Untersuchungen zur Sedimentation von Teilchenkomplexen in Suspensionen , 1972 .

[2]  P. Mazur,et al.  Many-sphere hydrodynamic interactions and mobilities in a suspension , 1982 .

[4]  R. C. Kerr.  Erosion of a stable density gradient by sedimentation-driven convection , 1991, Nature.

[5]  D. K. Pickard,et al.  On the divergence problem in calculating particle velocities in dilute dispersions of identical spheres , 1986 .

[6]  F. Hamdullahpur,et al.  Motion of hydrodynamic aggregates , 1989 .

[7]  M. T. Kamel,et al.  Sedimentation of clusters of identical spheres I. Comparison of methods for computing velocities , 1989 .

[8]  S. Mirza,et al.  Sedimentation of suspensions of particles of two or more sizes , 1979 .

[9]  Chjan C. Lim,et al.  Periodic solutions for three sedimenting spheres , 1988 .

[10]  Naoya Yoshioka,et al.  The behavior of a swarm of particles moving in a viscous fluid , 1978 .

[11]  D. K. Pickard,et al.  Extensions and refinements of a Markov model for sedimentation , 1982 .

[12]  P. Saffman,et al.  On the Settling Speed of Free and Fixed Suspensions , 1973 .

[13]  D. K. Pickard,et al.  A Markov model for sedimentation , 1977 .

[14]  Anthony J. C. Ladd,et al.  Hydrodynamic transport coefficients of random dispersions of hard spheres , 1990 .

[15]  R. G. Cox,et al.  The stokes translation of a particle of arbitrary shape along the axis of a circular cylinder , 1966 .

[16]  Bandaru V. Ramarao,et al.  On instabilities arising during sedimentation of two-component mixtures of solids , 1984, Journal of Fluid Mechanics.

[17]  Russel E. Caflisch,et al.  Variance in the sedimentation speed of a suspension , 1985 .

[18]  G. Batchelor,et al.  Structure formation in bidisperse sedimentation , 1986, Journal of Fluid Mechanics.

[19]  Robert H. Davis,et al.  Spreading of the interface at the top of a slightly polydisperse sedimenting suspension , 1988, Journal of Fluid Mechanics.

[20]  D. Ornstein,et al.  Statistical properties of chaotic systems , 1991 .

[21]  P. Mazur,et al.  Many-sphere hydrodynamic interactions: IV. Wall-effects inside a spherical container , 1985 .

[22]  Amos Tversky,et al.  On the reciprocity of proximity relations , 1980 .

[23]  P. T. Shannon,et al.  Batch and Continuous Thickening. Basic Theory. Solids Flux for Rigid Spheres , 1963 .

[24]  A three-parameter markov model for sedimentation II. Simulation of transit times and comparison with experimental results , 1987 .

[25]  B. Koglin.  Statistische Verteilung der Sedimentationsgeschwindigkeit in niedrig konzentrierten Suspensionen , 1971 .

[26]  P. T. Shannon,et al.  Batch and Continuous Thickening. Prediction of Batch Settling Behavior from Initial Rate Data with Results for Rigid Spheres , 1964 .

[27]  M. T. Kamel,et al.  On the divergence problem in calculating particle velocities in dilute dispersions of identical spheres III. Sedimentation in a spherical container , 1988 .

[28]  P. Mazur,et al.  On the Smoluchowski paradox in a sedimenting suspension , 1985 .

[29]  Louis J. Durlofsky,et al.  Dynamic simulation of hydrodynamically interacting particles , 1987, Journal of Fluid Mechanics.

[30]  G. Batchelor.  Sedimentation in a dilute dispersion of spheres , 1972, Journal of Fluid Mechanics.

[31]  R. C. Kerr,et al.  Convection and particle entrainment driven by differential sedimentation , 1991, Journal of Fluid Mechanics.

[32]  Andreas Acrivos,et al.  Enhanced sedimentation in settling tanks with inclined walls , 1979, Journal of Fluid Mechanics.

[33]  David J. Jeffrey,et al.  Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow , 1984, Journal of Fluid Mechanics.

[34]  D. R. Oliver.  The sedimentation of suspensions of closely-sized spherical particles , 1961 .

[35]  Robert H. Davis,et al.  Hindered settling of semidilute monodisperse and polydisperse suspensions , 1988 .

[36]  Sheldon Weinbaum,et al.  A numerical-solution technique for three-dimensional Stokes flows, with application to the motion of strongly interacting spheres in a plane , 1978, Journal of Fluid Mechanics.

[37]  L. M. Hocking.  The behaviour of clusters of spheres falling in a viscous fluid Part 2. Slow motion theory , 1964, Journal of Fluid Mechanics.

[38]  Eric S. G. Shaqfeh,et al.  Screening in sedimenting suspensions , 1991, Journal of Fluid Mechanics.

[39]  G. J. Kynch.  A theory of sedimentation , 1952 .

[40]  Joseph Ford,et al.  How random is a coin toss , 1983 .

[41]  D. K. Pickard,et al.  Experimental implications of a Markov model for sedimentation , 1979 .

[42]  George M. Homsy,et al.  HINDERED SETTLING AND HYDRODYNAMIC DISPERSION IN QUIESCENT SEDIMENTING SUSPENSIONS , 1988 .

[43]  The accelerated motion of rigid bodies in non-steady stokes flow , 1990 .

[44]  D. K. Pickard.  Isolated nearest neighbors , 1982 .

[45]  G. Batchelor,et al.  Sedimentation in a dilute polydisperse system of interacting spheres. Part 1. General theory , 1982, Journal of Fluid Mechanics.

[46]  P. Mazur,et al.  Many-sphere hydrodynamic interactions: III. The influence of a plane wall , 1984 .

[47]  B. J. Mason,et al.  The behaviour of clusters of spheres falling in a viscous fluid Part 1. Experiment , 1964, Journal of Fluid Mechanics.

[48]  D. K. Pickard,et al.  A three‐parameter markov model for sedimentation , 1977 .

[49]  Martin Golubitsky,et al.  Time-reversibility and particle sedimentation , 1991 .

[50]  R. Johne.  Einfluß der Konzentration einer monodispersen Suspension auf die Sinkgeschwindigkeit ihrer Teilchen , 1966 .

[51]  M. T. Kamel,et al.  On the divergence problem in calculating particle velocities in dilute dispersions of identical spheres II. Effect of a plane wall , 1988 .