Deposition Of Spherical Particles Research Articles

Combination of Variational and Empirical Methods to Determine the Porosity during the Deposition of Spherical Particles

Combination of Variational and Empirical Methods to Determine the Porosity during the Deposition of Spherical Particles

Production of ultrafine-grained spherical β-WC-W2C-Co microparticles by electro discharge erosion of WC-15Co alloy in glycerol and their solutions

The present work is devoted to the study of the production of ultrafine-grained (UFG) spherical microparticles by electro discharge erosion (EDE) of the WC-15Co cemented carbide in glycerol, distilled water, and their solutions. Energy costs, productivity, particle size distribution, and morphological and chemical compositions of the obtained powders were studied. It was found that energy cost is reduced by 2.2 times when glycerol was used instead of water. The use of water reduces carbon content from 5.2% to 1.4%. The use of glycerol and its aqueous solutions reduces carbon loss and increases its content in the obtained powders from 3.2% to 6.1%. During SE, cobalt, carbon, and tungsten evaporate from spherical particles and crystallize in the form of ultrafine particles, which subsequently remain in suspension after sedimentation of spherical particles. Mass fractions of sedimented spherical particle fractions ranged from 75% to 82%. Cobalt and carbon content in the spherical particles obtained in glycerol decrease from 15% to 10% and from 5.2% t to 3.1% respectively. The particles consist of rounded carbide grains (β-WC and W2C) with a diameter of up to 500 nm, the space between which is filled with cobalt. Microhardness of the particles increased from 12.1 GPa (initial alloy) to 15.6 (EDE in water)—23.7 GPa (EDE in glycerol).

Lift and drag force on a spherical particle in a viscoelastic shear flow

We present a comprehensive 3D numerical study of particles with imposed velocities relative to the local bulk flow (termed “slip velocities”) in a viscoelastic shear flow. We consider the force on a spherical particle sedimenting, a spherical bubble rising, and a spherical neutral squirmer swimming in an imposed viscoelastic shear flow. We demonstrate that any particle moving with a slip velocity in the flow or gradient direction of the shear flow experience a lateral lift force. We calculate and compare the magnitude and direction of the lift force in all situations. At small Deborah (De) and Weissenberg (Wi) numbers, our results show good agreement with an existing perturbation theory for rigid particles (Einarsson and Mehlig, 2017 [1]) and new perturbation theories for drops and for squirmers respectively. Our simulations extend these results to higher De and Wi regimes. Through our simulations, we uncover the physical mechanism of the lateral force on all particles. For rigid particles, we find the lift force arises from an imbalance in polymer stress on either side of the particle, which in turn is due to the imbalance of polymer stretch surrounding the particle. If this lift force is not balanced by an external force, a lateral drift velocity arises. We further consider the implication of this lateral drift for rigid particles hydrodynamically forced in a viscoelastic Poiseuille flow, where particles can migrate either toward the channel center plane or toward the wall, depending on whether the direction of the applied force is in the direction aligned or opposite to the direction of the Poiseuille flow, respectively. We study both the migration of a single particle as well as a suspension of particles in channel flow. Even with the addition of hydrodynamic interactions, we show that particles forced in the direction of the Poiseuille flow migrate towards the channel center.

Fully Resolved Numerical Simulation of Free Convection of Falling Spherical Particles in Sedimentation Transports Using Immersed Boundary Method

In this research, the direct numerical simulations are applied to study the sedimentation of spherical particles in an unsteady thermal condition in a viscous flow. The immersed boundary method is used to fully resolve the hydrodynamic interactions of solid–fluid phases, and a volume of fluid approach is employed to account the heat transfer both inside and outside the solid particles. The Boussinesq approximation is used to consider the density variation of the fluid. The behavior of particles is examined under different thermal conductivity ratios ($$k_{\mathrm{r}}$$) ranging between 0.1 to 10 and various Grashof numbers (Gr) up to 5000. The results indicate that for the Grashof and Galilean (Ga) numbers less than 5000 and 50, respectively, the threshold of $$k_{\mathrm{r}}$$ to solve the energy equation inside the particles is $$k_{\mathrm{r}}=0.1,$$ and for the thermal conductivity ratio higher than this value, the heating/cooling of the particles is fast enough to assume that the temperature over the solid particle changes uniformly. Furthermore, we investigate the well-known drafting–kissing–tumbling (DKT) phenomenon for a pair of spherical particles in an enclosed space at different $$k_{\mathrm{r}}$$ and Gr numbers. It is observed that the DKT motion of two particles with varied temperature is proceeded with any values of $$k_{\mathrm{r}}$$ and Grashof number; however, the natural convection delays this process.

Structurally Coloured Coatings Prepared via the Electrophoretic Deposition of Spherical Particles

Structurally Coloured Coatings Prepared via the Electrophoretic Deposition of Spherical Particles

An integral equation approach for the solution of the Stokes flow with Hermite surfaces

An integral equation approach based on bi-cubic Hermite surfaces has been proposed to solve the three-dimensional complex Stokes flow problems. The numerical solutions are obtained by utilizing the boundary collocation method as well as the continuous distribution of Stokeslets, which are the fundamental solutions of the steady Stokes equations. The quadrilateral surface elements are represented with the bi-cubic Hermite functions that allow the continuous variation of the surface normal vectors between neighbouring elements. The unique normal vectors at the vertices are obtained using the MeanWeighted by Sine and Edge Length Reciprocal (MWSELR) approach. The singular integrations are evaluated using the Tanh−Sinh quadrature rule, meanwhile non-singular integrals are evaluated using the Gauss-Legendre quadrature rule. For the case of freely moving/falling rigid bodies, the integral equations are fully coupled with the equation of motion and the resulting algebraic equations are solved iteratively using the preconditioned Krylov subspace methods provided within the PETSc library. The accuracy of the numerical algorithm is initially verified for the three-dimensional unbounded Stokes flow around a sphere. Then the algorithm is applied to the more complex problems such as the sedimentation of spherical particles and helical swimmers. The numerical simulations show parallel scalability for a large number of processors.

Spherical particle sedimenting in weakly viscoelastic shear flow

We consider the dynamics of a small spherical particle driven through an unbounded viscoelastic shear flow by an external force. We give analytical solutions to both the mobility problem (velocity of forced particle) and the resistance problem (force on fixed particle), valid to second order in the dimensionless Deborah and Weissenberg numbers, which represent the elastic relaxation time of the fluid relative to the rate of translation and the imposed shear rate. We find a shear-induced lift at $O({\rm Wi})$, a modified drag at $O({\rm De}^2)$ and $O({\rm Wi}^2)$, and a second lift that is orthogonal to the first, at $O({\rm Wi}^2)$. The relative importance of these effects depends strongly on the orientation of the forcing relative to the shear. We discuss how these forces affect the terminal settling velocity in an inclined shear flow. We also describe a new basis set of symmetric Cartesian tensors, and demonstrate how they enable general tensorial perturbation calculations such as the present theory. In particular this scheme allows us to write down a solution to the inhomogenous Stokes equations, required by the perturbation expansion, by a sequence of algebraic manipulations well suited to computer implementation.

Comparative modeling of exposure to airborne nanoparticles released by consumer spray products

Consumer exposure to sprays containing nano-objects is a continuing concern as a potential health hazard. One potential hazard has been formulated in the overload hypothesis. It describes a volume fraction of the macrophages that is occupied by deposited nanoparticles that leads to reduced macrophage mobility. Subsequent chronic inflammation may then lead to severe health consequences including cancer. To calculate lung deposition of spherical particles, the Multiple-Path Particle Dosimetry (MPPD) model (ARA, Albuquerque, NM) provides different kinds of lung models and age settings. Using the MPPD v 2.11 software, we modeled several consumer-related exposure scenarios. Different body orientations and age groups were investigated. Moreover, a number of materials representing different densities were used, and the exposure calculated using MPPD is compared to the hazard derived from the overload hypothesis. Conditions leading to macrophage overload were found for exposures to high particle doses for prolonged times and repeated exposure. Such conditions are unlikely in the context of regular consumer exposure. The overload hypothesis assumes the particles to be inert and biopersistent, a condition that currently lacks a clear regulatory definition and is valid only for a few selected materials. Furthermore, because of material-specific effects and the possibility of surface adsorption of hazardous chemicals, nano-objects in propellant sprays remain of concern for consumer health.

Investigation of granular batch sedimentation via DEM–CFD coupling

This paper presents three dimensional numerical investigations of batch sedimentation of spherical particles in water, by analyses performed by the discrete element method (DEM) coupled with computational fluid dynamics (CFD). By employing this model, the features of both mechanical and hydraulic behaviour of the fluid-solid mixture system are captured. Firstly, the DEM–CFD model is validated by the simulation of the sedimentation of a single spherical particle, for which an analytical solution is available. The numerical model can replicate accurately the settling behaviour of particles as long as the mesh size ratio (Dmesh/d) and model size ratio (W/Dmesh) are both larger than a given threshold. During granular batch sedimentation, segregation of particles is observed at different locations in the model. Coarse grains continuously accumulate at the bottom, leaving the finer grains deposited in the upper part of the granular assembly. During this process, the excess pore water pressure initially increases rapidly to a peak value, and then dissipates gradually to zero. Meanwhile, the compressibility of the sediments decreases slowly as a soil layer builds up at the bottom. Consolidation of the deposited layer is caused by the self-weight of grains, while the compressibility of the sample decreases progressively.

A numerical study of the dynamics of a particle settling at moderate Reynolds numbers in a linearly stratified fluid

AbstractIn this paper, the transient settling dynamics of a spherical particle sedimenting in a linearly stratified fluid is investigated by performing fully resolved direct numerical simulations. The settling behaviour is quantified for different values of Reynolds, Froude and Prandtl numbers. It is demonstrated that the transient settling dynamics is correlated to the induced Lagrangian drift of flow around the settling particle. A simplified model is provided to predict the maximum velocity of the settling particle in linearly stratified fluids. The peak velocity can be followed by the oscillation of the settling velocity and the particle can even reverse its direction of motion before reaching to its neutrally buoyant level. The frequency of oscillation of settling velocity scales with the Brunt–Väisälä frequency and the motion of the particle can lead to the formation of secondary and tertiary vortices following the primary vortex.

Axisymmetric sedimentation of spherical particles in a viscoelastic fluid: Sphere–wall and sphere–sphere interactions

Axisymmetric sphere–wall and two-sphere interactions were examined in a viscoelastic solution composed of polyisobutylene polymer in tetradecane. The Reynolds and Stokes numbers were small, so that inertia played at most a minor role, while the Deborah numbers De were in the range 0.4 < De < 3.5. When single spheres fell away from the solid top of the containing vessel, or toward the bottom, the range of the sphere–wall interaction was reduced in the viscoelastic fluid relative to a Newtonian fluid. The reduced range was more pronounced at higher settling speeds. In addition, the interaction in the viscoelastic fluid was reversible, in that the effect of the wall on a sphere moving away from it was the same as that on a sphere moving toward it. In the experiments with two equal spheres sedimenting along their line-of-centers, the spheres moved together until they touched. The rate at which they moved together was measured for sphere–sphere separations ranging from contact to many diameters, and for separations greater than 2 diameters was in fair agreement with analytic predictions. The average sedimentation rate of the two spheres increased as they moved together, by an amount that was in good agreement with the Newtonian solution at low Reynolds number.

Concentration instability of sedimenting spheres in a second-order fluid

The slow sedimentation of a dilute suspension of spherical particles in a second-order fluid is investigated using theory and numerical simulations. We first analyze the motion of a single isolated spherical particle sedimenting under gravity when placed in a linear flow field. In the limit of weak viscoelasticity (low Deborah number), the velocity of the particle is calculated, and the nonlinear coupling of the settling motion with the local flow field is shown to result in a lateral drift in a direction perpendicular to gravity. By the same effect, the mean flow driven by weak horizontal density fluctuations in a large-scale suspension of hydrodynamically interacting particles will also result in a horizontal drift, which has the effect of reinforcing the fluctuations as we demonstrate using a linear stability analysis. Based on this mechanism, an initially homogeneous suspension is expected to develop concentration fluctuations, a prediction supported by previous experiments on sedimentation in polymeric liquids. We further confirm this prediction using large-scale weakly nonlinear numerical simulations based on a point-particle model. Concentration fluctuations are indeed found to grow in the simulations, and are shown to result in an enhancement of the mean settling speed and velocity fluctuations compared to the Newtonian case.

On the variable order dynamics of the nonlinear wake caused by a sedimenting particle

In this work we develop a variable order (VO) differential equation of motion for a spherical particle sedimenting in a quiescent viscous liquid. In particular, we examine the various force terms in the equation of motion and propose a new form for the history drag acting on the particle. We show that the variable order formulation allows for an effective way to express the dynamic transition of the dominant forces over the entire time of the motion of the particle from rest to terminal velocity. The use of VO operators also allows us to examine the evolving dynamics of the wake during sedimentation. Using numerical data from a finite element simulation of a sedimenting particle, we first solve for the order of the derivative that returns the correct decay of the history force. We then propose a relatively simple expression for the history force that is a function of the Reynolds number and particle-to-fluid density ratio. The new history drag expression correlates very well ( R 2 > 0.99 ) with the numerical data for terminal Reynolds numbers ranging from 2.5 to 20, and for particle-to-fluid density ratios of interest in practice ( 1 < β < 10 ).

Eulerian-Eulerian CFD Model for the Sedimentation of Spherical Particles in Suspension with High Particle Concentrations

A computational study of the process of sedimentation of spherical particles in suspensions with high particle concentrations has been performed with the two-fluid Eulerian approach. The solid stress induction in the dispersed phase was modelled through modification of the suspension viscosity. Convectional flow patterns were found and studied during the simulations. The presence of these patterns, which are also observed experimentally, makes the sedimentation process dependent on the rheological behaviour of the suspension. The results of the simulation were validated with experimental results. The present paper shows that Eulerian-Eulerian simulations can account for some of the detailed processes taking place in a settling suspension of particles.

Migration and sedimentation of spherical particles in a yield stress fluid flowing in a horizontal cylindrical pipe

AbstractThis study looks at the dynamics of a particle suspended in a viscoplastic fluid, flowing in a horizontal circular cylindrical pipe. Inertia effects are negligible in comparison with viscous effects and plastic effects. The suspensions are highly stabilized and at rest the spheres cannot settle under gravity alone. The results of Merkak et al. (AIChE J. 2008;54:1129–1138) are extended, taking into consideration both particles of the same density or denser than the fluid and pipe‐to‐particle diameter ratios of 8 or 56. New migration phenomena in the sheared zone are thus evidenced when buoyancy forces are nil. In the case of particles denser than the fluid, it is shown how the spheres settle by bypassing the plug‐flow zone. A map showing the stability of flowing suspensions could, thus, be drawn. © 2009 American Institute of Chemical Engineers AIChE J, 2009

Evaluation of Respirator Filters for Asbestos Fibers

Fiber aerosols are known to have different aerodynamic behaviors than spherical particles and usually carry higher electrostatic charges. We investigated the effects of flow rate and charge status of filter cartridges on the penetration of spherical and fiber aerosols. Four types of test respirator filters were selected: two for passive respirators, one for a powered respirator, and one disposable respirator. Surface charges on respirator filters were determined using a noncontact field electrostatic field meter. Penetration tests were performed for filter cartridges before and after charge neutralization. The surface charge measurements on the respirator filters showed that some filters, including those used in disposable face masks, are charged to enhance the collection efficiency. Only high-efficiency particulate air filters performed consistently for both spherical test aerosols and the three types of asbestos fibers. The surface charge potential of filter cartridges and flow rate did not appear to affect the performance of these filters. In contrast to the high-efficiency filters, the aerosol penetration performance of low-efficiency filters and face masks deteriorated when the charge potential on the filter was removed. Our data also showed that the surface charges decreased in a high-temperature, high-humidity environment and disappeared after 1 week. Deposition of spherical particles and fibers in the charged disposable facemask filter was enhanced. For charged-neutralized, low-efficiency filter cartridges, asbestos fibers may penetrate more than spherical particles with a mean particle size of 0.3 μ m diameter.

Unsteady solution of viscous fluid flow in an infinite cylinder with a variable body force

In this Brief Communication, the unsteady viscous flow with a variable body force in an infinite cylinder is solved exactly. The solution describes the transient velocity profiles and pressure gradients, which can be used in the application of sedimentation of spherical particles in viscous fluid. The current solution is compared with the previously solved problem between two infinite parallel plates. It is found that, for a similar body force, the central-line velocity of the cylinder will be greater than that of the two-infinite-plate case. But the slip velocity at the wall of cylinder will be smaller than that of the flow between two infinite plates. The transient pressure gradients are also different, resulting in a smaller value for the cylindrical case with a similar body force.

Dynamic simulations of the inhomogeneous sedimentation of rigid fibres

We have simulated the dynamics of suspensions of fibres sedimenting in the limit of zero Reynolds number. In these simulations, the dominant inter-particle force arises from hydrodynamic interactions between the rigid, non-Brownian fibres. The simulation algorithm uses slender-body theory to model the linear and rotational velocities of each fibre. To include far-field interactions between the fibres, the line distribution of force on each fibre is approximated by making a Legendre polynomial expansion of the disturbance velocity on the fibre, where only the first two terms of the expansion are retained in the calculation. Thus, the resulting linear force distribution can be specified completely by a centre-of-mass force, a couple, and a stresslet. Short-range interactions between particles are included using a lubrication approximation, and an infinite suspension is simulated by using periodic boundary conditions. Our numerical results confirm that the sedimentation of these non-spherical, orientable particles differs qualitatively from the sedimentation of spherical particles. The simulations demonstrate that an initially homogeneous, settling suspension develops clusters, or streamers, which are particle rich surrounded by clarified fluid. The instability which causes the heterogeneous structure arises solely from hydrodynamic interactions which couple the particle orientation and the sedimentation rate in particle clusters. Depending upon the concentration and aspect ratio, the formation of clusters of particles can enhance the sedimentation rate of the suspension to a value in excess of the maximum settling speed of an isolated particle. The suspension of fibres tends to orient with gravity during the sedimentation process. The average velocities and orientations, as well as their distributions, compare favourably with previous experimental measurements.

Diffusion and Flow in Porous Domains Constructed Using Process-Based and Stochastic Techniques

Two model mesoporous materials, namely Vycor glass and alumina membrane made by compaction of spherical monosize alumina particles, are reconstructed and the transport properties (Knudsen diffusivity, molecular diffusivity and permeability) of the resulting 3-dimensional binary domains are investigated through computer simulations. For the alumina membrane, two reconstruction alternatives are used, a ballistic deposition of spherical particles (process-based approach) and a stochastic procedure based on the porosity and the two-point correlation function of the porous matrix. For Vycor glass, only the stochastic reconstruction technique is employed. The obtained 3-D samples are structurally characterized in terms of their two-point correlation and chord length distribution functions. This type of information along with the comparisons between computed and reported transport coefficients indicate that the random sphere pack obtained from the ballistic-deposition procedure represents quite well the porous structure of the alumina membrane while the stochastically reconstructed domain fails to do so. In contrast, for the Vycor glass it is shown that the stochastic reconstruction technique is sufficient for a faithful representation of the porous matrix. It is furthermore argued that in the case of Vycor the stochastic reconstruction technique constitutes a kind of process-based approach.

Transport and Deposition of Spherical Particles and Fibers in an Improved Virtual Impactor

ABSTRACT Flow velocity in an improved virtual impactor was calculated for a Reynolds number of 4000 using a finite-element method. The governing equations of motion for spherical particles and fibers were used along with flow field information to calculate transport and losses in the impactor. The calculated separation efficiency and loss fraction for spherical particles agreed with experimental results reported in the literature. For fibers, separation efficiency curves were obtained in terms of fiber Stokes number and aspect ratio. The calculated collection efficiency curve moved to higher Stokes numbers with increasing fiber aspect ratio. All fiber sizes showed significant losses at the tip of the collecting probe of the impactor. As a result, the separation efficiency never reached 100%. The computational approach illustrated here can be used for predicting separation characteristics, which will lead to improved and cost-effective design of the impactor.