Initial Particle Orientation Research Articles

Particle orientation distribution in a rotating, dilute suspension of rod-shaped particles

We consider a theoretical model for the settling of rod-shaped particles of a dilute, initially homogeneous, suspension in rapid rotation. The particle Reynolds number and the particle Taylor number of the detailed flow around the particles are assumed small, representing a relevant limit for an industrial centrifugal separation process. By applying a statistical approach using the Fokker–Planck equation, and neglecting particle–particle interactions, we obtain an explicit, analytical solution for the time dependent, spatially uniform particle orientation distribution function. Not only does the volume fraction in the bulk of the suspension decrease with time due to the divergent centrifugal field, as similarly described in the literature for suspensions of spherical particles, the orientation of the rod particles also changes with time from an initially uniform distribution to one where the particles tend to align with a plane perpendicular to the axis of rotation. The corresponding particle trajectories, as also influenced by first-order effects from the Coriolis acceleration and gyroscopic effects, are obtained numerically for different initial particle orientation angles.

Predicting particle orientation: Is an accurate flow field more important than the actual orientation model?

Analytical orientation prediction models (OPMs) are widely applied to efficiently predict the orientation of particles in suspensions or pastes. One application of these prediction models are extrusion processes where the model is used to identify combination of process and paste parameters that yield anisotropic orientation within the extruded filament. The accuracy of these predictions mainly depends on two elements that are the correct choice of the orientation model itself and the rheology model. The rheology of a paste is commonly modeled with the help of the Herschel Bulkley (HB) rheology model. The optimal OPM is still topic of today’s research. Which of the two elements, however, has a stronger influence on the orientation has not been addressed, yet. We make use of a wide range of HB parameters reported in literature with a particular focus on data that is reported for varying paste compositions. Based on this data, we use the HB model to predict the velocity and shear rate profile within a pipe and perform orientation predictions with the help of the models by Jeffery and Folgar and Tucker (FT). These predictions are used to estimate the sensitivity of the final orientation on the HB parameters and on the OPM. For our study, we assume that the paste can be described by the standard Herschel Bulkley rheology model. We assume no-slip boundary conditions and no influence of the particle orientation on the rheology. Second, we assume that the initial particle orientation before entering the pipe is random. Our results suggest that capturing the rheology model correctly is generally more important than capturing the OPM correctly. This applies in particular when densely filled states are approached. We also provide universal relations for predicting the degree of particle alignment and the mean flow velocity as functions of process parameters and material properties. • A suitable rheology model is found to be more important than the actual orientation prediction model in terms of particle orientation. • Normalized diagrams enable quick estimations of the evolution of particle orientation based on process parameters and paste properties. • The derived methodology is applied to a large set of published rheology data.

Reorientation of Suspended Ceramic Particles in Robocasted Green Filaments during Drying.

This work considers the fabrication of ceramic parts with the help of an additive manufacturing process, robocasting, in which a paste with suspended particles is robotically extruded. Within the final part, the material properties depend on the orientation of the particles. A prediction of the particle orientation is challenging as the part usually undergoes multiple processing steps with varying contributions to the orientation. As the main contribution to the final particle orientation arises from the extrusion process, many corresponding prediction models have been suggested. Robocasting involves, however, further processing steps that are less studied as they have a smaller influence on the orientation. One of the processing steps is drying by natural convection, which follows directly after the extrusion process. A quantification of the reorientation that occurs during drying is mostly unknown and usually neglected in the models. Therefore, we studied the amount of reorientation of suspended particles in robocasted green filaments during drying in detail. For our study, we applied the discrete element method, as it meets various requirements: The exact particle geometry can be resolved precisely; particle–particle interactions can be described; the paste composition is reproduced exactly; the initial particle orientation can be set in accordance with the prediction from the analytical models for the extrusion part; macroscopic force laws exist to represent capillary forces due to the remaining fluid phase that remains during drying. From our study, we concluded that the magnitude of particle reorientation during drying is small compared to the orientation occurring during the extrusion process itself. Consequently, reorientation during drying might further be neglected within analytical orientation prediction models.

Dynamics of a Pair of Paramagnetic Janus Particles under a Uniform Magnetic Field and Simple Shear Flow

We numerically investigate the dynamics of a pair of circular Janus microparticles immersed in a Newtonian fluid under a simple shear flow and a uniform magnetic field by direct numerical simulation. Using the COMSOL software, we applied the finite element method, based on an arbitrary Lagrangian-Eulerian approach, and analyzed the dynamics of two anisotropic particles (i.e., one-half is paramagnetic, and the other is non-magnetic) due to the center-to-center distance, magnetic field strength, initial particle orientation, and configuration. This article considers two configurations: the LR-configuration (magnetic material is on the left side of the first particle and on the right side of the second particle) and the RL-configuration (magnetic material is on the right side of the first particle and on the left side of the second particle). For both configurations, a critical orientation determines if the particles either attract (below the critical) or repel (above the critical) under a uniform magnetic field. How well the particles form a chain depends on the comparison between the viscous and magnetic forces. For long particle distances, the viscous force separates the particles, and the magnetic force causes them to repel as the particle orientation increases above the configuration’s critical value. As the initial distance decreases, a chain formation is possible at a steady orientation, but is more feasible for the RL-configuration than the LR-configuration under the same circumstances.

Numerical Analysis of the Impact of Particle Friction on Bed Voidage in Fixed‐Beds

AbstractThe impact of the static friction coefficient, the initial particle orientation, and the particle height‐to‐diameter ratio on the bed voidage of random packings with a low tube‐to‐particle diameter ratio is investigated for spherical and cylindrical particles using the discrete element method. Based on the numerical results a correlation is proposed to predict the bed voidage as a function of the static friction coefficient and the tube‐to‐particle diameter ratio for spheres, equilateral and non‐equilateral cylinders. This correlation is extended for the use of hollow cylinders.

Transport of anisotropic particles under waves

Using a numerical model, we analyse the effects of shape on both the orientation and transport of anisotropic particles in wavy flows. The particles are idealized as prolate and oblate spheroids, and we consider the regime of small Stokes and particle Reynolds numbers. We find that the particles preferentially align into the shear plane with a mean orientation that is solely a function of their aspect ratio. This alignment, however, differs from the Jeffery orbits that occur in the residual shear flow (that is, the Stokes drift velocity field) in the absence of waves. Since the drag on an anisotropic particle depends on its alignment with the flow, this preferred orientation determines the effective drag on the particles, which in turn impacts their net downstream transport. We also find that the rate of alignment of the particles is not constant and depends strongly on their initial orientation; thus, variations in initial particle orientation result in dispersion of anisotropic-particle plumes. We show that this dispersion is a function of the particle’s eccentricity and the ratio of the settling and wave time scales. Due to this preferential alignment, we find that a plume of anisotropic particles in waves is on average transported farther but dispersed less than it would be if the particles were randomly oriented. Our results demonstrate that accurate prediction of the transport of anisotropic particles in wavy environments, such as microplastic particles in the ocean, requires the consideration of these preferential alignment effects.

Cross-stream migration of asymmetric particles driven by oscillating shear

We study the dynamics of asymmetric, deformable particles in oscillatory, linear shear flow. By simulating the motion of a dumbbell, a ring-polymer, and a capsule we show that cross-stream migration occurs for asymmetric elastic particles even in linear shear flow if the shear rate varies in time. The migration is generic as it does not depend on the particle dimension. Importantly, the migration velocity and migration direction are robust to variations of the initial particle orientation, making our proposed scheme suitable for sorting particles with asymmetric material properties.

Lattice Boltzmann simulations of settling behaviors of irregularly shaped particles.

We investigated the settling dynamics of irregularly shaped particles in a still fluid under a wide range of conditions with Reynolds numbers Re varying between 1 and 2000, sphericity ϕ and circularity c both greater than 0.5, and Corey shape factor (CSF) less than 1. To simulate the particle settling process, a modified lattice Boltzmann model combined with a turbulence module was adopted. This model was first validated using experimental data for particles of spherical and cubic shapes. For irregularly shaped particles, two different types of settling behaviors were observed prior to particles reaching a steady state: accelerating and accelerating-decelerating, which could be distinguished by a critical CSF value of approximately 0.7. The settling dynamics were analyzed with a focus on the projected areas and angular velocities of particles. It was found that a minor change in the starting projected area, an indicator of the initial particle orientation, would not strongly affect the settling velocity for low Re. Periodic oscillations developed for all simulated particles when Re>100. The amplitude of these oscillations increased with Re. However, the periods were not sensitive to Re. The critical Re that defined the transition between the steady and periodically oscillating behaviors depended on the inertia tensor. In particular, the maximum eigenvalue of the inertia tensor played a major role in signaling this transition in comparison to the intermediate and minimum eigenvalues.

Quantifying the evolution of soil fabric during shearing using directional parameters

Over the past 50 years, experimental studies have repeatedly demonstrated that the mechanical behaviour of sand is sensitive to the material fabric, that is, the arrangement of the grains. Up until now there have been relatively few attempts to describe this fabric quantitatively. Much of our understanding of the link between the particle movements and interactions and the macro-scale response of granular materials, including sand, comes from discrete-element modelling and experiments on ‘analogue' sands with simple, idealised shapes. This paper investigates methods of quantifying the directional fabric of a real sand and its evolution under loading. Statistical analyses of the distribution of fabric directional data in terms of particle, contact normal, branch vector and void orientations were carried out at different stages of shearing deformation. The data show that the initial particle orientation fabric that develops during the deposition of the material tends to persist during shearing, while in the post-peak regime the contact normals seem to be reoriented along the direction of the major principal stress. Different patterns were observed within the shear band, as both the particles and the contact normal vectors appeared to rotate along the shear plane.

Electrokinetic motion of a deformable particle: Dielectrophoretic effect

Electrokinetics-induced motion and deformation of a hyperelastic particle confined in a slit microchannel has been numerically investigated for the first time with a full consideration of the fluid-particle-electric field interactions and the dielectrophoretic (DEP) effect. When the initial orientation of a cylindrical particle with respect to the applied electric field, θ(p0), is 90°, the particle tends to curl up as a "C" shape when moving from left to right. The electrokinetics-induced particle deformation is due to the joint effects of the shear force arising from the non-uniform Smoluchowski slip velocity on the particle surface and the asymmetric DEP force with respect to the center of the deformed particle arising from the spatially non-uniform electric field surrounding the particle. The electrokinetics-induced particle deformation is opposite to that of a particle moving in the same direction subjected to a pressure-driven flow. When the initial particle orientation is 0<θ(p0) <90°, a net torque arising from the DEP effect progressively rotates and aligns the particle with its longest axis parallel to the applied electric field, thus decreasing the non-uniformity of the electric field and accordingly the particle deformation. The numerical predictions are in qualitative agreement with our previous experimental observation. The results show that the DEP effect is significant and must be taken into account in the modeling of electrokinetic motion of a deformable particle in microfluidics.

DC dielectrophoretic particle–particle interactions and their relative motions

When particles in an electrolyte subjected to an external electric field get close to each other, the presence of particles could alter the local electric field and consequently induce mutual dielectrophoretic (DEP) forces on each other. In this paper, a transient, two-dimensional (2D) multiphysics model taking into account the particle–fluid–electric field interactions under a thin electrical double layer (EDL) assumption is performed to investigate the effects of the imposed electric field, the initial particle’s orientation and distance on the DEP particle–particle interaction between a pair of micro-sized particles and their relative motions. Prior to the study of the DEP particle–particle interaction, the magnitude comparison between the DEP particle–particle interaction and the Brownian motion is analyzed. When the DEP particle–particle interaction dominates the random Brownian motion, it is expected to observe the particle chaining along the direction of the imposed electric field, independent of the initial particle orientation. The numerical predictions are in qualitative agreement with the experimental observations available from the literature. During the attraction motion of particles, their velocities tend to dramatically decrease due to the rapid increase in the repulsive hydrodynamic pressure force when the particle distance decreases to a certain value. One exclusive exception of the particle chaining occurs when the initial connecting line of the particles is perpendicular to the imposed electric field, which is extremely unstable owing to the inevitable Brownian motion.

Fabric evolution in a numerical direct shear test

This paper presents a three-dimensional discrete element study on the mechanical behaviour and fabric changes of elongated particle assemblages in a direct shear test. Assemblages with elongated particles are prepared under different preparation methods: random placing and deposition. Particles are generated inside a direct shear box with arbitrary orientations in the random placing method. In the deposition approach, two directions of deposition are used: perpendicular and parallel to the shear direction. Assemblages formed by different methods give significantly different initial particle orientations. Different dilatancy responses and shear strengths are resulted upon shearing. Change in fabric along the shear plane is noticeable and the magnitude of such rotation depends highly on the initial particle orientation.

2-D shape preferred orientations of rigid particles in transtensional viscous flow

Ghosh and Ramberg [Tectonophysics 34 (1976) 1–70] studied the two-dimensional (2-D) rotational behaviour of individual rigid particles embedded in a viscous medium subject to simple shear and transpression ( S r>0), at low/medium shear strains. We now extend this theoretical study to transtension ( S r<0) by deriving a new analytical solution, to non-interacting populations of rigid particles and to high shear strains. We used different initial orientations of particles in the same graph to simulate populations of particles in an originally isotropic rock. Our results show that: (1) shape preferred orientations (SPOs) developed in viscous simple shear flow are transient and cyclical, except for particles with aspect ratio=∞ (or material lines), which tend to the shear direction; (2) stable SPOs can develop in transpression; they dip towards the shear sense but, when defining an S/C structure with the shear foliation, this composite fabric is always antithetic and, thus, indicates the wrong sense of shear; (3) stable SPOs can also develop in transtension; they dip opposite to the shear sense but, when defining an S/C structure with the shear foliation, this composite fabric is always synthetic and, thus, indicates the correct sense of shear; (4) SPOs produced in transpression or transtension can be used as vorticity gauges only when they represent stable orientations, which must be demonstrated a priori.

Texture enhancement by inoculation during casting of ferritic stainless steel strip

Melt/substrate contacting experiments, designed to approximate conditions encountered during strip casting, were carried out to produce as-cast ferritic stainless steel strip. The results show that inoculation of the melt to produce TiN particles, together with casting onto a smooth substrate, results in the optimum conditions for nucleation and subsequent growth of an exceedingly high volume fraction of ferrite grains with 〈001〉 oriented within a few degrees of the normal direction (ND) of the strip surface. It is argued that, during casting, TiN particles either nucleate or deposit onto the substrate with 〈001〉 parallel to the ND, and since these particles exhibit crystallographic features similar to δ-ferrite, subsequent epitaxial growth inherits the initial particle orientation. Such oriented nucleation of ferrite from a smooth substrate results in the optimum heat-transfer conditions for further growth of dendrites with 〈001〉 perpendicular to the substrate, thus producing the intense through-thickness 〈001〉//ND fiber texture in the as-cast strip. The potential for producing grain-oriented silicon iron by direct strip casting is outlined.

Collection of prolate spheroidal aerosol particles by charged spherical collectors

The effects of electrostatic forces and torques on the dynamics of prolate spheroidal particles are examined in relation to collision with a 30 μm radius collector droplet. When the non-spherical particles are uncharged the influence of the electrostatic torque can lead to either increases or decreases in collision efficiencies. Initial particle orientation is shown to be important for low collector charges but insignificant for high collector charges, when the electrostatic torque aligns the particle parallel to the electric field. For the charged particle case, where the Coulombic force is dominant, the collision efficiencies for particles having large aspect ratios are significantly lower than those for spherical particles. Depending on the particle and collector charge levels, both front and back capture modes are found. Image forces are shown to be insignificant for highly charged particles.

Collection of uncharged prolate spheroidal aerosol particles by spherical collectors—I: 2D motion

The dynamics of prolate spheroidal particles are examined in relation to collisions with a 30 μm radius collector droplet. The rotations of the particles along their trajectories are determined for different particle aspect ratios. The initial particle orientation and position with respect to the collector and the particle rotational inertia are found to have strong influences on the collision efficiencies. Large differences in efficiency can occur for particles if the aerodynamic size is defined at different particle orientations. Capture of prolate spheroidal particles on the downstream side of the collector can occur in the absence of attractive forces in contrast to the case of spherical particles.

Anisotropic swelling in black cotton soil

The influence of initial moisture content and the nature of granular material on the anisotropic swell behaviour in black cotton soil has been examined. It was observed that the amount and rate of swelling are guided by the initial particle orientation. For samples compacted with moisture below the optimum value, the variation in swelling trends in vertical and horizontal directions is a result of the particle arrangement, the pressure exerted by the air in the voids and also the subsequent expulsion of the same. In samples compacted with moisture content above the optimum, the initial dispersed state of the particles guides the anisotropy. The swelling in such samples is considerable in directions transverse to the particle orientation. At optimum moisture levels, because of the minimal differences in the particle arrangement for samples in vertical and horizontal directions, the swelling is similar in both cases and as such no anisotropic behaviour was noticed. Increasing presence of granular component in the soil reduces the rate of swelling, protracts the time for completion of swelling and also reduces the anisotropic behaviour. Reduction in the grain size of the granular material facilitates quick swelling. The variations in such samples for vertical and horizontal directions are explained on the basis of packing in the system and the constraints imposed by sand grains on osmotic swelling. Since similar variables exist in field conditions, the present study enables an understanding of their role in the anisotropic swell behaviour of black cotton soils.

Classical Mechanics of Rotational–Translational and Other Energy Transfer. I. A Hamilton–Jacobi (Action-Angle) Treatment

The classical-mechanical equations of motion describing collisional energy transfer are converted to a form involving constants of the elastic collision, using a Hamilton–Jacobi formalism. These constants frequently vary only slowly during an inelastic collision. An approximate version of the transformed equations, related to a variation of constants procedure, is next introduced. The collision of an atom with a rigid linear diatomic molecule is considered in some detail. Several desirable features of the approximation are that the change in rotational angular momentum is obtained directly, all initial orientations of particles and angular momenta occur outside the integrals, an approximate error estimate can be made, results can be calculated relatively quickly, and further insight is obtained into the energy-transfer process. Because of the close relationship of Hamilton–Jacobi and Schrödinger formalisms, a comparison of exact and approximate classical results is also expected to provide estimates of range of validity of some commonly used approximations in the quantum case.