Sedimentation dynamics of spherical particles in confined geometries

Effects of boundary walls on the properties of settling spheres

Numerical Simulations are performed, using Eulerian two fluid model (TFM) to investigate the effects of solid volume fraction and no-slip side walls on the settling particles. It is found that average settling velocity decreases with increasing volume fraction for both gas-solid (GS) and liquid-solid (LS) systems, in good agreement with the Richardson-Zaki 1 − ϕ n ${\left(1-\phi \right)}^{n}$ law. It was also noted that average velocity is independent of the boundary condition for both gas-solid (GS) and liquid-solid (LS) systems. The root mean square value of the solid volume fraction shows the increasing trend with volume fraction, caused by the many particle interactions. Furthermore, no-slip sidewalls were found to damp the velocity fluctuations quantitively, while following the well-known ϕ 1 / 2 ${\phi }^{1/2}$ scaling with volume fraction. Side walls were found to act as kinetic trap for the particles, damping the fluctuation near the walls and plateauing in the mid plane. These simulations showed that the GS system shows the higher solid fraction fluctuations that the LS system at the same Reynolds number, mainly because of the higher collision frequency (higher Stokes number) among the particles.

Full Characterization of Colloidal Dynamics at Low Péclet Numbers

Although critical in applications, the dynamics of colloidal systems at low Péclet numbers is poorly understood. Here we introduce an optical technique that permits for the first time a complete characterization of this regime through a continuous and independent measurement of both the diffusive and the advective components of a system's dynamics. For the particular example of gravity-driven colloids, we demonstrate experimentally that the hydrodynamic size and the mass density of particulate suspensions can be measured simultaneously. The proven capabilities are of particular interest for studying the spatial and temporal properties of inhomogeneous colloidal systems where aggregation and structural evolution play major roles.

Large-scale parallel alignment of platelet-shaped particles through gravitational sedimentation

Parallel and concentric alignment of microscopic building blocks into several orders of magnitude larger structures is commonly observed in nature. However, if similarly aligned structures are artificially produced their thickness is generally limited to just about one or two orders of magnitude more than the dimensions of the smallest element. We show that sedimentation provides a promising approach to manufacture solid materials consisting of well-aligned platelet-shaped particles while being more than 30,000 times thicker than the individual particle. Such sediments contain up to 28 vol% of particles without any further treatment and can be densified to 67 vol% particle fraction by subsequent unidirectional pressing. The degree of orientation of the platelet-shaped particles within the sediments was tracked by high-energy X-ray diffraction measurements. The Hermans orientation parameter, a statistical measure of the quality of alignment, was determined to be 0.63 ± 0.03 already for as-sedimented samples while the standard deviation of the orientation distribution of particles, another measure of average misalignment, was found to be (21.5 ± 1.4)°. After pressing, these values further improved to (0.81 ± 0.01) and (14.6 ± 0.4)°, respectively. Such quality of alignment competes with, if not even exceeds, values reported in the literature.

Direct numerical simulations of sedimenting spherical particles at non-zero Reynolds number

We performed direct numerical simulations, using a smoothed profile method to investigate the inertial effects on the static and dynamic properties of a sedimenting suspension over a wide range of volume fractions from 0.01 to 0.4.

Speeding up of sedimentation under confinement

We show an increase of the sedimentation velocity as small particles are confined in circular capillaries. In general, confinement slows down sedimentation. But, we show that at low Reynolds numbers and in 1D confinement this is not the case. Particle sedimentation velocity is not homogeneous, which can lead to the formation of structures. These structures are enhanced and stabilized in the presence of walls and in the absence of other dissipative mechanisms. As a consequence, it is possible to achieve sedimentation velocities that even exceed the Stokes velocity. The segregation at critical capillary diameters has been directly observed using a large scale model. These simple experiments offer a new insight into the old problem of sedimentation under confinement.

Direct numerical simulations of anisotropic diffusion of spherical particles in sedimentation

We investigated the scaling of the hydrodynamic velocity fluctuations and self-diffusion in the sedimentation of monodispersed spherical particles via direct numerical simulations using the smoothed profile method over a moderate range of volume fractions (0.01≤φ≤0.12). Hydrodynamic velocity fluctuations are visible at large Peclet numbers (Pe), and they scale as (φL/a)(1/2) at low volume fractions (φ≤0.04). Their characteristics become independent of volume fraction at moderate volume fractions (0.06≤φ≤0.12). Both vertical and horizontal self-diffusion coefficients scale as (L/a)(3/2)φ(1/2) at low volume fractions. At moderate volume fractions, the vertical diffusion scales as (L/a)(3/2)φ(-1/2); in contrast, the horizontal diffusion is saturated with respect to volume fraction. The diffusion anisotropy increases with increasing Pe and saturates at high Pe values. The saturated value remains unchanged at low volume fractions, whereas further increase in the volume fraction decreases this anisotropy. The reduction of this anisotropy is attributed to the φ(-1/2) scaling of the vertical relaxation time at moderate volume fractions; however, the horizontal relaxation time is independent of the volume fraction at this regime.

Polymeric dispersants delay sedimentation in colloidal asphaltene suspensions

Asphaltenes, among the heaviest components of crude oil, can become unstable under a variety of conditions and precipitate and sediment out of solution. In this report, we present sedimentation measurements for a system of colloidal scale asphaltene particles suspended in heptane. Adding dispersants to the suspension can improve the stability of the system and can mediate the transition from a power-law collapse in the sedimentation front to a rising front. Additional dispersant beyond a crossover concentration can cause a significant delay in the dynamics. Dynamic light scattering measurements suggest that the stabilization provided by the dispersants may occur through a reduction of both the size and polydispersity of the asphaltene particles in suspension.

Full-scale solutions to particle-laden flows: Multidirect forcing and immersed boundary method

Towards getting the full-scale solutions to particle-laden flows, a multidirect forcing technique and immersed boundary method are proposed in the present work. The immersed solid boundary is represented by Lagrangian points and the no-slip condition is efficiently satisfied by exerting multidirect forcing. The hydrodynamic interactions between the stationary or moving solid boundary and the Newtonian fluid are able to be accurately described. This method is simple but efficient which is validated by simulating the flows around a stationary circular disc at different Reynolds numbers and the free sedimentation of a particle. The predicted results agree well with previous experimental and numerical data. When applying this method to study particle sedimentation near a vertical wall, the rotation shifting phenomenon is observed besides the anomalous rolling and the lateral migration.

Polymer scaling and dynamics in steady-state sedimentation at infinite Péclet number

We consider the static and dynamical behavior of a flexible polymer chain under steady-state sedimentation using analytic arguments and computer simulations. The model system comprises a single coarse-grained polymer chain of N segments, which resides in a Newtonian fluid as described by the Navier-Stokes equations. The chain is driven into nonequilibrium steady state by gravity acting on each segment. The equations of motion for the segments and the Navier-Stokes equations are solved simultaneously using an immersed boundary method, where thermal fluctuations are neglected. To characterize the chain conformation, we consider its radius of gyration RG(N). We find that the presence of gravity explicitly breaks the spatial symmetry leading to anisotropic scaling of the components of RG with N along the direction of gravity RG, parallel and perpendicular to it RG, perpendicular, respectively. We numerically estimate the corresponding anisotropic scaling exponents nu parallel approximately 0.79 and nu perpendicular approximately 0.45, which differ significantly from the equilibrium scaling exponent nue=0.588 in three dimensions. This indicates that on the average, the chain becomes elongated along the sedimentation direction for large enough N. We present a generalization of the Flory scaling argument, which is in good agreement with the numerical results. It also reveals an explicit dependence of the scaling exponents on the Reynolds number. To study the dynamics of the chain, we compute its effective diffusion coefficient D(N), which does not contain Brownian motion. For the range of values of N used here, we find that both the parallel and perpendicular components of D increase with the chain length N, in contrast to the case of thermal diffusion in equilibrium. This is caused by the fluid-driven fluctuations in the internal configuration of the polymer that are magnified as polymer size becomes larger.

Particle migration induced by confinement of colloidal suspensions along the gravitational direction

We confine charged spheres in cells with the smallest dimension along the direction of gravity ĝ. The particles are density mismatched with the surrounding medium and sediment along ĝ with typical Péclet numbers of Pe approximately 10(-3). After a certain time, we find that the number of particles N increases near both upper and lower plates until a characteristic time tau is reached; above this time N plateaus. We attribute the observed phenomenology to collective particle motions driven by gravity and mediated by hydrodynamic interactions; these could yield formation of swirls made of particles with correlated velocities that could eventually drive the particles towards the upper plate. The characteristic time for these migrations scales with plate-to-plate separation Lz as tau approximately Lz1.2, exactly as the characteristic decay time of velocity fluctuations in sedimentation processes [S. Y. Tee, Phys. Rev. Lett. 89, 054501 (2002)], despite that in these experiments the smallest cell dimension is perpendicular to ĝ and 7<Pe<50. In the absence of gravitational field, the observed particle migrations disappear, emphasizing the key role played by gravity in these experiments.