Non-Poisson statistics of settling spheres (original) (raw)
Spreading fronts in sedimentation of dilute suspension of spheres
Physics of Fluids, 2008
The thickness of the diffuse front between a sedimenting dilute suspension and the clear fluid above grows linearly in time due to polydispersity in the size of the particles and due to a hydrodynamic effect in which randomly heavy clusters fall out of the front leaving it depleted. Experiments and simplified point-particle numerical simulations agree that these two effects are not simply linearly additive.
Collective Effects in Settling of Spheroids under Steady-State Sedimentation
Physical Review Letters, 2003
We study the settling dynamics of non-Brownian prolate spheroids under steady-state sedimentation. We consider the case of moderate particle Reynolds numbers properly taking into account the hydrodynamic effects. For small volume fractions, we find an orientational transition of the spheroids, characterized by enhanced density fluctuations. Around the transition, the average settling velocity has a maximum which may even exceed the terminal velocity of a single spheroid, in accordance with experiments.
Simulation studies of microstructure of colloids in sedimentation
Molecular Simulation, 2014
Direct numerical simulations are performed to investigate the microstructure of sedimenting particles, using a smoothed profile method. We used pair distribution function to find out particle preference to orient themselves with respect to a test particle. We found that at low Peclet number (Pe), particles show an isotropic microstructure due to strong effects of thermal fluctuations and with increasing Pe at Pe * 30, particles prefer to orient themselves in the horizontal direction due to dominance of hydrodynamic interactions at low volume fraction. This preference decreases with increasing volume fraction and at high volume fraction (f * 0:15), microstructure becomes isotropic due to dominance of many-body interactions. The microstructure analysis at high Reynolds number (Re ¼ 1, 10) revealed the deficiency of the particles in the vicinity of a test particle. This deficiency decreases with the increase of volume fraction and at high volume fraction, we observed an isotropic microstructure due to many-body interactions. Moreover, we also observed that the range of volume fraction affected by this deficiency increases with increasing Re.
Colloidal sedimentation (and filtration)
Current Opinion in Colloid & Interface Science, 1997
Significant progress has been made in the understanding of various aspects of the processes of sedimentation and filtration of (mixtures of) colloidal spheres. These aspects include the hydrodynamic friction and the equation of state over a wide range of particle densities, the strongly hindered settling for charged spheres with long-range repulsions, and spontaneous layer formation. For nonspherical colloids, many issues, such as the sedimentation dynamics of interacting rods or platelets, are still unresolved.
Measurement of the average velocity of sedimentation in a dilute polydisperse suspension of spheres
Journal of Fluid Mechanics, 1990
An X-ray attenuation technique is used to obtain the local concentration of spherical particles in a polydisperse suspension as a function of vertical position and time. From these experimental data, the average velocity of sedimentation in the homogeneous part of the suspension is derived by considering the variation with time of the total volume of particles located above a given fixed horizontal plane. Measurements have been performed in suspensions of particles which differ from each other in size with a total volume concentration in particles between 0.13% and 2.5%, and also in suspensions of particles which differ from each other both in size and in density, the total volume concentration being 2%. For the first kind of suspension, the experimental hindered settling factor is plotted versus the concentration and a linear regression analysis provides the slope with its 90% confidence limits: Se = −5.3 ± 1.1. This experimental average coefficient of sedimentation is in good agre...
Dilute sedimenting suspensions of spheres at small inertia
Journal of Fluid Mechanics, 2021
The sedimentation dynamics of a dilute suspension of non-Brownian spheres is experimentally examined at small particle Reynolds numbers but at Reynolds numbers based on the container size extending up to the small-but-finite inertial regime. While the long-time velocity fluctuations are independent of the Reynolds number in the Stokes regime, they are seen to decrease with increasing Reynolds number above a critical container Reynolds number of approximately 0.1, and more precisely to vary as a power -0.1 of the Reynolds number. The microstructure of the suspension is also seen to evolve with increasing Reynolds number and to depart from random positioning as it becomes more sub-homogeneous and disordered.
Colloidal aggregation with sedimentation: concentration effects
The European Physical Journal E - Soft Matter, 2004
The results of computer models for colloidal aggregation, that consider both Brownian motion and gravitational drift experienced by the colloidal particles and clusters, are extended to include concentrations spanning three orders of magnitude. In previous publications and for a high colloidal concentration, it was obtained that the aggregation crosses over from diffusion-limited colloidal aggregation (DLCA) to another regime with a higher cluster fractal dimension and a speeding up followed by a slowing down of the aggregation rate. In the present work we show, as the concentration is decreased, that we can still cross over to a similar regime during the course of the aggregation, as long as the height of the sample is increased accordingly. Among the differences between the mentioned new regimes for a high and a low colloidal concentration, the cluster fractal dimension is higher for the high concentration case and lowers its value as the concentration is decreased, presumably reaching for low enough concentrations a fixed value above the DLCA value. It is also obtained the fractal dimension of the sediments, arising from the settling clusters that reach the bottom and continue a 2D-like diffusive motion and aggregation, on the floor of the container. For these clusters we now see two and sometimes three regimes, depending on concentration and sedimentation strength, with their corresponding fractal dimensions. The first two coming from the crossover already mentioned, that took place in the bulk of the sample before the cluster deposition, while the third arises from the two-dimensional aggregation on the floor of the container. For these bottom clusters we also obtain their dynamical behavior and aggregation rate. PACS. 61.43.Hv Fractals; macroscopic aggregates (including diffusion-limited aggregates) -82.70.Dd Colloids -05.10.Ln Monte Carlo methods
Subtle order in settling suspensions
Pure and Applied Chemistry, 2001
A dilute suspension of uniform, non-Brownian spheres settles slowly in a viscous solvent. The initially well-mixed system showing Poisson or random occupancy statistics evolves to a system having reduced number fluctuations, but otherwise appearing random. The reduced number fluctuations are consistent with recent measurements of velocity fluctuations in settling suspensions. These experimental results test the assumptions leading to the theoretical predictions by Calflisch and Luke that the velocity fluctuations increase without limit with increasing sample dimension. The theoretical prediction assumes Poisson occupation statistics contrary to our observations.
Journal of Colloid and Interface Science, 1996
pendence of this sedimentation is expected to be the same The sedimentation velocity of uncharged, nonaggregated silica as for monodisperse spheres in a ''normal'' solvent. For the spheres under gravity is strongly reduced after addition of small hard spheres in Batchelor's theory this is indeed a plausible amounts of nonsedimenting small spheres. This reduction is scenario. In practice, however, even weak interparticle atlargely due to surface irregularities on a nanoscale of the large tractions may complicate interpretation (and acquisition) of spheres at which a limited number of small spheres adsorbs, leadsedimentation results. ing to an increase of the hydrodynamic friction per particle. This First, the small particles may induce a depletion attraction adsorption also screens effectively any weak Van der Waals atbetween the large spheres (7-9). This effect can be minitraction between the large spheres, which despite its weakness, mized by choosing sufficiently low particle concentrations. significantly influences the concentration dependence of settling in a pure solvent. The concentration dependence and magnitude Second, there may be a significant Van der Waals attraction of the large-sphere sedimentation velocity in a more concentrated between the large spheres, because this attraction increases dispersion of small spheres agree with the prediction by Batchelor with the particle radius. Therefore it can be suppressed by that the small particles mainly manifest themselves as an effective decreasing the sphere size, though a compromise must be viscosity increase. ᭧ 1996 Academic Press, Inc. made because the spheres should be large enough to settle under influence of gravity. But there are more attraction possibilities in a bidisperse 1. INTRODUCTION system. In studies on the rheology (10), scattering properties (11), and phase separation (8) of binary silica sphere systems, indications for an (unexplained) attraction between The concentration dependence of the sedimentation veloclarge and small spheres were reported. Remarkably, the inity has been studied extensively theoretically and experimenteractions in the separate monodisperse systems were clearly tally for monodisperse colloidal spheres (1-4). For polydisestablished to be purely repulsive. Our sedimentation experiperse spheres only the simplest case has been addressed, ments confirm the possibility of such an attraction between namely a bidisperse sphere mixture (5). Sedimentation relarge and small silica particles. Supplementary experiments sults on micrometer-sized particle mixtures (6) are available, with, among other things, dynamic light scattering show that but experimental information on colloidal sphere mixtures a small amount of small particles is adsorbed on the large is lacking. We designed an experiment in which large, unspheres. This does not contradict the fact that the separate charged colloidal silica spheres settle under influence of components do not stick. It is argued in Section 4.3. that gravity in a dispersion of nonsedimenting small ones. The surface roughness explains this peculiar phenomenon. moving boundary of the turbid system of large particles It turns out that a modest adsorption of small particles can be clearly detected against the background of the small on-and fairly weak Van der Waals forces between-the particles, which hardly scatter light. The silica particles are large spheres significantly change their settling velocity. sterically stabilized by a grafted alkane layer and form stable Nevertheless, for a sufficiently high concentration of free dispersions in cyclohexane. Sedimentation experiments were small particles, one expects to see, for example, Batchelor's performed on five silica dispersions and three mixtures of viscosity effect. them to assess whether any system-dependent features, like The paper is organized as follows. In Section 2 Batchelor's interparticle attractions, are present. equations for the sedimentation velocity in dilute mono-and For the silica systems under study, Batchelor's theory (5) bidisperse systems are briefly described. The synthesis and makes the following predictions. If the small particles are characterization of these particles and the experimental small enough they will mainly manifest themselves as a equipments can be found in Section 3. The sedimentation modest viscosity increase of the medium in which the large particles now sediment more slowly. The concentration de-results of the mono-and bidisperse sphere systems and the 427