Do We Understand Hydrodynamic Dispersion in Sedimenting Suspensions?

Cunha, Francisco Ricardo; Rosa, Otávio Silva; Sousa, Aldo João de

doi:10.1590/s0100-73862001000400001

Cited by 4 publications

(1 citation statement)

References 24 publications

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“…The assumption is acceptable to simulate sedimentation of finegrained materials due to the small size and low deposition velocities of the particles. In addition, the action of the flow is analytically represented by the flow-particle interaction modelled by the drag force taking into account concentration of the neighboring particles, see [21], and by the squeezing of the intermediate flow when two particles are close, see [22,23]. These two models permit the calculation of forces other than the contact forces that are included into DEM, allowing a good representation of the long time deposition process at an affordable CPU cost.…”

Section: Introductionmentioning

confidence: 99%

Numerical sedimentation particle-size analysis using the Discrete Element Method

Bravo

Pérez-Aparicio

Gómez‐Hernández

2015

Advances in Water Resources

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Sedimentation processes are generally modelled using an equivalent continuum approach based on the coupling of the Navier-Stokes and the advection-dispersion equations; the sediment concentration within an elementary fluid volume is the variable of interest. Continuous advances in computational capabilities have brought up a new type of modelling that simulates the individual motion and contact interactions of grains: the Discrete Element Method (DEM). In this work, DEM interacts with the simulation of flow using the well known one-way-coupling method, a computationally affordable approach for the time-consuming numerical simulation of the ASTM-D422, buoyancy and pipette sedimentation tests. These tests are used in the laboratory to determine the particle-size distribution of fine-grained aggregates. Five samples with different particle-size distributions are modelled by about six million rigid spheres projected on two-dimensions, with diameters ranging from 2.5 × 10 −6 m to 70 × 10 −6 m, forming a water suspension in a sedimentation cylinder. DEM simulates the particle's movement considering laminar flow interactions of hydrostatic thrust, drag and lubrication forces. The simulation provides the temporal/spatial distributions of densities and concentrations of the suspension.The numerical simulation cannot replace the laboratory tests since it needs the final granulometry as initial data; but, as the results show, these simulations can identify the strong and weak points of each method and eventually recommend useful variations and draw conclusions on their validity, aspects very difficult to achieve in the laboratory.

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Section: Introductionmentioning

confidence: 99%

Numerical sedimentation particle-size analysis using the Discrete Element Method

Bravo

Pérez-Aparicio

Gómez‐Hernández

2015

Advances in Water Resources

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A five-parameter Markov model for simulating the paths of sedimenting particles

Bargieł

Tory

2007

Applied Mathematical Modelling

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Numerical simulations of magnetic suspensions with hydrodynamic and dipole-dipole magnetic interactions

Gontijo

Cunha

2017

Physics of Fluids

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This work describes a numerical model to compute the translational and rotational motion of N spherical magnetic particles settling in a quiescent viscous fluid under creeping flow condition. The motion of the particles may be produced by the action of gravitational forces, Brownian thermal fluctuations, magnetic dipole-dipole interactions, external magnetic field, and hydrodynamic interactions. In order to avoid particle overlap, we consider a repulsive force based on a variation of a screened-Coulomb potential mixed with Hertz contact forces. The inertia of the particles is neglected so that a mobility approach to describe the hydrodynamic interactions is used. The magnetic dipoles are fixed with respect to the particles themselves. Thus they can only interact magnetically between them and with an external applied magnetic field. Therefore the effect of magnetic field moment rotation relative to the particle as a consequence of a finite amount of particle anisotropy is neglected in this work. On the other hand, the inclusion of particle viscous hydrodynamic interactions and dipolar interactions is considered in our model. Both long-range hydrodynamic and magnetic interactions are accounted by a sophisticated technique of lattice sums. This work considers several possibilities of periodic and non-periodic particle interaction schemes. This paper intends to show the benefits and disadvantages of the different approaches, including a hybrid possibility of computing periodic and non-periodic particle interactions. The well-known mean sedimentation velocity and the equilibrium magnetization of the suspension are computed to validate the numerical scheme. The comparison is performed with the existent theoretical models valid for dilute suspensions and several empirical correlations available in the current literature. In the presence of dipole-dipole particle interactions, the simulations show a non-monotonic behavior of the mean sedimentation velocity as the particle volume fraction increased. This work is the first involving a magnetic suspension under the influence of both magnetic and hydrodynamic particle interactions. The mean sedimentation velocity and the suspension magnetization are examined under the steady-state condition over several realizations. Simulation results for the fluid magnetization are compared with a modified mean field theory, and a very good agreement for semi-dilute suspensions is observed. Additionally, the motion and shape transition of an initially spherical blob composed of magnetic spherical particles are investigated by computer simulations. We show the existence of velocity fluctuations due to the interplay of magnetically induced aggregates and their hydrodynamic dispersion. We find that the collective hydrodynamic interactions play a dispersive role opposite to the aggregative contribution of the magnetic dipole-dipole interactions.

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Do We Understand Hydrodynamic Dispersion in Sedimenting Suspensions?

Cited by 4 publications

References 24 publications

Numerical sedimentation particle-size analysis using the Discrete Element Method

Numerical sedimentation particle-size analysis using the Discrete Element Method

A five-parameter Markov model for simulating the paths of sedimenting particles

Numerical simulations of magnetic suspensions with hydrodynamic and dipole-dipole magnetic interactions

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