Non-Poisson statistics of settling spheres (original) (raw)

Resolved simulations of sedimenting suspensions of spheres

Physical Review Fluids, 2019

Several results on sedimenting equal spheres obtained by resolved simulations with the Physalis method are presented. The volume fraction ranges from 8.7% to 34.9% and the particle Galilei number from 49.7 to 99.4. The results shown concern particle collisions, diffusivities, mean free path, particle pair distribution function and other features. It is found that many qualitative trends found in earlier studies continue to hold in the parameter range investigated here as well. The analysis of collisions reveals that particles interact prevalently via their flow fields rather than by direct contacts. A tendency toward particle clustering is demonstrated. The time evolution of the shape and size of particle tetrads is examined.

Fluctuations and stratification in sedimentation of dilute suspensions of spheres

Physics of Fluids, 2009

We have tested in experiments and simulations whether stratification can control velocity fluctuations in suspensions of sedimenting spheres. The initial value and early decay of the velocity fluctuations are not affected by stratification. On the other hand, in the descending front where the stratification is strong and well defined, the velocity fluctuations are inhibited according to a previously proposed scaling. In between, after the initial decay and before the arrival of the front, the local value of the stratification does not always play a role.

Sedimentation dynamics and equilibrium profiles in multicomponent mixtures of colloidal particles

Journal of Physics: Condensed Matter, 2014

In this paper we give a general theoretical framework that describes the sedimentation of multicomponent mixtures of particles with sizes ranging from molecules to macroscopic bodies. Both equilibrium sedimentation profiles and the dynamic process of settling, or its converse, creaming, are modeled. Equilibrium profiles are found to be in perfect agreement with experiments. Our model reconciles two apparently contradicting points of view about buoyancy, thereby resolving a long-lived paradox about the correct choice of the buoyant density. On the one hand, the buoyancy force follows necessarily from the suspension density, as it relates to the hydrostatic pressure gradient. On the other hand, sedimentation profiles of colloidal suspensions can be calculated directly using the fluid density as apparent buoyant density in colloidal systems in sedimentation-diffusion equilibrium (SDE) as a result of balancing gravitational and thermodynamic forces. Surprisingly, this balance also holds in multicomponent mixtures. This analysis resolves the ongoing debate of the correct choice of buoyant density (fluid or suspension): both approaches can be used in their own domain. We present calculations of equilibrium sedimentation profiles and dynamic sedimentation that show the consequences of these insights. In bidisperse mixtures of colloids, particles with a lower mass density than the homogeneous suspension will first cream and then settle, whereas particles with a suspension-matched mass density form transient, bimodal particle distributions during sedimentation, which disappear when equilibrium is reached. In all these cases, the center of the distribution of the particles with the lowest mass density of the two, regardless their actual mass, will be located in equilibrium above the so-called isopycnic point, a natural consequence of their hard-sphere interactions. We include these interactions using the Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) equation of state. Finally, we demonstrate that our model is not limited to hard spheres, by extending it to charged spherical particles, and to dumbbells, trimers and short chains of connected beads.

Size segregation and particle velocity fluctuations in settling concentrated suspensions

Rheologica Acta, 2009

We investigate the sedimentation of concentrated suspensions at low Reynolds numbers to study collective particle effects on local particle velocity fluctuations and size segregation effects. Experiments are carried out with polymethylmetacrylate (PMMA) spheres of two different mean diameters (190 and 25 μm) suspended in a hydrophobic index-matched fluid. Spatial repartitions of both small and large spheres and velocity fluctuations of particles are measured using fluorescently labelled PMMA spheres and a particle image velocimetry method. We also report measurements of the interstitial fluid pressure during settling. Experiments show that size segregation effects can occur during the sedimentation of concentrated suspensions of either quasi-monodisperse or bidisperse spheres. Size segregation is correlated to the organisation of the sedimentation velocity field into vortex-like structures of finite size. A loss of size segregation together with a significant decrease of the fluid pressure gradient in the bulk suspension is observed when the size of vortex-like structures gets on the order of the container size. However, the emergence of channels through the settling zone prevents a complete loss of size segregation in very concentrated suspensions.

Settling Statistics of Hard Sphere Particles

Physical Review Letters, 2001

Direct imaging of settling, non-Brownian, hard sphere, particles allows measurement of particle occupancy statistics as a function of time and sampling volume dimension. Initially random relative particle number fluctuations, ͗N 2 2 ͗N͘ 2 ͗͘͞N͘ 1, become suppressed, anisotropic, and ͗N͘ dependent. Fitting to a simple Gaussian pair correlation model suggests a minute long ranged correlation leads to strong if not complete suppression of number fluctuations. Calflisch and Luke predict a divergence in velocity fluctuations with increasing sample volume size based on random (Poisson) statistics. Our results suggest this is not a valid assumption for settling particles.

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.