Suspensions Of Ellipsoids Research Articles

Characterization of lift force and torque in prolate ellipsoid suspensions

The paper derives correlations for lift force and fluid torques acting on stationary prolate ellipsoid suspensions of aspect ratio (AR) 2.5, 5, and 10 subjected to uniform flow. Particle Resolved Simulations (PRS) are conducted on a suspension of infinite extent in two directions for Reynolds number 10 ≤ Re ≤ 200 and solid fractions (φ) between 0.1 ≤ φ ≤ 0.3.The suspension-mean lift-to-drag ratio varies between 7% to 14% at Re=10 which increases to 14% ~ 22% at Re=200. The torque-induced tip rotational acceleration can reach 38% ~ 85% of drag-induced translational acceleration at Re = 200. Single particle lift force and torque correlations of (Fröhlich et al., 2020) are modified and adapted to predict current angular-mean lift and torque data. The resulting lift correlation captures the PRS data within an average deviation below 7%. Torque exhibits a somewhat more complex dependency at AR = 10 than the assumed sinθ ∙ cosθ variation but nevertheless the correlations predict angular-mean values with mean relative deviations of 16.6% at AR = 10.

Particle Scale Investigation of Influencing Factors on Heat Transfer in Nonspherical Particle–Fluid System

Abstract Heat transfer characteristics of random suspensions of 0.25 aspect ratio (AR) cylinders are investigated for Reynolds numbers (Re) between 10 and 300 and solid fraction (φ) ranging from 0.1 to 0.3 using particle resolved simulations. The effect of particle inclination with respect to flow and particle clustering on heat transfer is investigated. The Nusselt number decreases with an increase in inclination angle and the dependence becomes stronger as φ and Re increase. On the other hand, while prolate ellipsoid suspensions of AR 2.5 follow the same trend, the Nusselt number increases with inclination angle as AR increases to 5 and 10 and as φ increases. Local particle clustering nominally decreases the Nusselt number because of the dominance of thermal wakes. At low φ, this effect is felt only at low Re, but as φ increases, the effect spreads to higher Re. Similar but weaker trends are also found in suspensions of prolate ellipsoids of AR 2.5, 5, and 10. High AR, low Re prolate ellipsoids exhibit the greatest dependence of Nusselt number on local solid fraction. Implementation of two independent definitions of reference length, i.e., volume equivalent sphere diameter deq for ellipsoids and diameter dp of the cylindrical particle in the correlation of Tavassoli et al. (2015, “Direct Numerical Simulation of Fluid-Particle Heat Transfer in Fixed Random Arrays of Non-Spherical Particles,” Chem. Eng. Sci., 129, pp. 42–48) provides good estimates of the respective suspension mean Nusselt numbers.

Convective heat transfer in suspensions of prolate ellipsoids

Particle Resolved Simulations (PRS) using the Immersed Boundary Method (IBM) are performed for flow through suspensions of ellipsoids with aspect ratios of 2.5, 5, and 10 for solid volume fractions from 0.1 to 0.3 in the Reynolds number range from 10 to 200. The mean Nusselt number increases as Re1/2but shows only a weak dependence on the aspect ratio while increasing between 10-15% with an increase in solid fraction from 0.1 to 0.3. Two common practices of calculating Nusselt number in past literature are reconciled. It is shown that the suspension mean Nusselt number based on individual particles, by definition is always greater than or at the least equal to the Nusselt number based on the internal developing flow analogy. It is established that for Re≤50, the suspension heat transfer coefficient is very sensitive to the spatial distribution of particles or local-to-particle solid fractions. For the same mean solid fraction, suspensions dominated by particle clusters or high local solid fractions can exhibit Nusselt numbers which are lower than the minimum Nusselt number imposed by pure conduction on a single particle in isolation. This results from the dominant effect of thermal wakes at low Reynolds numbers. As the Reynolds number increases to 100 and beyond, the effect of particle clusters on heat transfer becomes less consequential. Unlike heat transfer, particle clustering has a less significant effect on mean fluid forces such as drag.

2D isotropic-nematic transition in colloidal suspensions of ellipsoids.

Liquid crystals are important condensed matter systems for technological applications, as well as for fundamental studies. An important unresolved issue is the nature of the phase transition in a two-dimensional (2D) liquid crystal system. In contrast to numerous computational studies reported in the last few decades, there have been no convincing experiments to verify these numerical results. Anisotropic colloids provide an excellent experimental model system to study phase transitions, such as crystallization and glass transition in condensed matter physics with single particle resolution. However, using colloids to probe the two-dimensional liquid crystal transition remains a challenge, since the condensed anisotropic colloids usually become stuck in the metastable glassy state rather than approaching their equilibrium liquid crystal phase. Here we report a method of using an external magnetic field to assist a colloidal system of super-paramagnetic anisotropic particles to overcome the local free energy barriers in the metastable states and approach the equilibrium phase. The experiments demonstrate a 2D isotropic-nematic phase transition with increasing packing density. The effects of the anisotropy of the colloidal particles on the 2D isotropic-nematic transition are explored. Our experimental results are compared with those from previous computational work, and quantitative agreements are reached.

Nature of the glass transition in 2D colloidal suspensions of short rods

The glass transition, a many-body system undergoes an apparent dynamic arrest with no appearance of long-range order, is one of the most challenging problems in condensed matter physics. Recently attention has been focused on the puzzling two-step transition observed in colloidal suspensions of ellipsoids. It was observed that micro nematic domains appearing with increasing packing density suggesting that such micro domains may be the structure origin of the two-step glass transition. Here we report an experimental study of monolayers of colloidal rods which exhibits a two-step glass transition with no appearance of pseudo-nematic domains. Instead, it was found that parallel and perpendicularly packed rods form local free energy minima in configurational space, separated by an activation barrier. This barrier increases significantly when rotational glass transition is approached, thereby the rotational motion is frozen while the translational one remains diffusive. We propose that the activation barrier for rotation is the key to the two-step glass transition in suspensions of rods. Such an activation barrier between well-defined local configurations holds the key to understanding the two-step glass transition in general.

Photo-Crosslinkable Colloids: From Fluid Structure and Dynamics of Spheres to Suspensions of Ellipsoids.

Recently-developed photo-crosslinkable PMMA (polymethylmethacrylate) colloidal spheres are a highly promising system for fundamental studies in colloidal physics and may have a wide range of future technological applications. We synthesize these colloids and characterize their size distribution. Their swelling in a density- and index- matching organic solvent system is demonstrated and we employ dynamic light scattering (DLS), as also the recently-developed confocal differential dynamic microscopy (ConDDM), to characterize the structure and the dynamics of a fluid bulk suspension of such colloids at different particle densities, detecting significant particle charging effects. We stretch these photo-crosslinkable spheres into ellipsoids. The fact that the ellipsoids are cross-linked allows them to be fluorescently stained, permitting a dense suspension of ellipsoids, a simple model of fluid matter, to be imaged by direct confocal microscopy.

Impact of Weak Particle Inertia on a Dilute Suspension of Ellipsoids

ABSTRACTIn this paper, we investigate asymptotical models for the motion of small rigid ellipsoids suspended in a Newtonian fluid. The microscale models account for particle inertia and form the basis for dilute suspension modeling. They were derived from the description of first principles for a coupled particle-fluid problem by asymptotical analysis in the size ratio in Vibe and Marheineke (2015), where the effect of inertia was incorporated via different scalings of the particle momentum balances. We classify three different inertial regimes and analyze numerically their impact on the particle motion. We observe reasonable physical translational and rotational behavior.

Two-Step Glass Transition Induced by Attractive Interactions in Quasi-Two-Dimensional Suspensions of Ellipsoidal Particles

We study experimentally the glass transition dynamics in quasi-two-dimensional suspensions of colloidal ellipsoids, aspect ratio α=2.1, with repulsive as well as attractive interactions. For the purely repulsive case, we find that the orientational and translational glass transitions occur at the same area fraction. Strikingly, for intermediate depletion attraction strengths, we find that the orientational glass transition precedes the translational one. By quantifying structure and dynamics, we show that quasi-long-range ordering is promoted at these attraction strengths, which subsequently results in a two-step glass transition. Most interestingly, within experimental certainty, we observe reentrant glass dynamics only in the translational degrees of freedom.

Self-diffusion in two-dimensional hard ellipsoid suspensions

We studied the self-diffusion of colloidal ellipsoids in a monolayer near a flat wall by video microscopy. The image processing algorithm can track the positions and orientations of ellipsoids with subpixel resolution. The translational and rotational diffusions were measured in both the laboratory frame and the body frame along the long and short axes. The long-time and short-time diffusion coefficients of translational and rotational motions were measured as functions of the particle concentration. We observed the nondiffusive crossover region in the intermediate time regime due to the caging of neighboring particles. Both the beginning and the ending times of the intermediate regime exhibit power-law dependence on concentration. The long-time and short-time diffusion anisotropies change nonmonotonically with concentration and reach minima in the semidilute regime because the motions along long axes are caged at lower concentrations than the motions along short axes. The time derivatives of mean-square displacements change linearly with the inverse of time in the intermediate time regimes at various particle densities. This indicates that their relaxation functions decay as 1/t which provides new challenges in theory. The effects of coupling between rotational and translational Brownian motions were demonstrated and the two time scales corresponding to anisotropic particle shape and anisotropic neighboring environment were measured.

Magnetoviscosity of dilute suspensions of magnetic ellipsoids obtained through rotational Brownian dynamics simulations

The magnetic field dependent viscosity (magnetoviscosity) of dilute suspensions of magnetic tri-axial ellipsoidal particles suspended in a Newtonian fluid and under applied shear and magnetic fields was studied numerically. Brownian dynamics simulations were performed to compute the intrinsic magnetoviscosity of the suspension. Results are presented for the response of dilute suspensions of ellipsoidal particles to constant magnetic and shear flow fields. Suspensions of ellipsoidal particles show a significant effect of aspect ratio on the intrinsic magnetoviscosity of the suspension, and this effect is more pronounced as the aspect ratio becomes more extreme. The use of an effective rotational diffusion coefficient D r , eff collapses the normalized intrinsic magnetoviscosity of all suspensions to a master curve as a function of Péclet number with the Langevin parameter α = ( μ 0 μ H ) / ( k B T ) as parameter, up to a critical value of α for which the results for suspensions of spherical particles deviate from those of suspensions of ellipsoids. This discrepancy is attributed to the action of the shear-torque on the ellipsoidal particles, which tends to orient these particles in the direction of maximum deformation of the simple shear flow, and which does not act on spherical particles.

Rheology of semidilute suspensions of rigid polystyrene ellipsoids at high Peclet numbers

The rheology of semidilute suspensions of rigid polystyrene ellipsoids at rotational Peclet numbers greater than 103 was studied for two different aspect ratios. The ellipsoid suspensions exhibit shear thinning behavior for both aspect ratios, similar to previous experiments on suspensions of rigid fibers. Possible mechanisms for the rate dependent rheology are discussed and evaluated through a comparison with the rheology of suspensions of spheres with the same material properties as the ellipsoids. For the largest Peclet number, the relative viscosity scales linearly with dimensionless number density and is independent of the aspect ratio.

Simple monoclinic crystal phase in suspensions of hard ellipsoids

We present a computer simulation study on the crystalline phases of hard ellipsoids of revolution. For aspect ratios >or=3 the previously suggested stretched-fcc phase [Frenkel and Mulder, Mol. Phys. 55, 1171 (1985)] is replaced by a different crystalline phase. Its unit cell contains two ellipsoids with unequal orientations. The lattice is simple monoclinic. The angle of inclination of the lattice, beta, is a very soft degree of freedom, while the two right angles are stiff. For one particular value of beta, the close-packed version of this crystal is a specimen of the family of superdense packings recently reported [Donev, Phys. Rev. Lett. 92, 255506 (2004)]. These results are relevant for studies of nucleation and glassy dynamics of colloidal suspensions of ellipsoids.

Stress overshoots of organoclay nanocomposites in transient shear flow

Forward and reverse stress growth experiments have been conducted on polypropylene/organoclay nanocomposites containing the same clay loading but characterized by different microstructures. Stress overshoots have been observed for the initial start-up experiments and for the following reverse start-up experiments after a certain rest time. The amplitude of these overshoots increased with the applied shear rate and rest time, but the overshoots occurred at the same strain of about 1.7. The overshoots are related to the structure of the nanocomposites, in particular the magnitude of the overshoots increased with the degree of the clay exfoliation in the matrix. Two models, initially developed for colloidal suspensions and fiber suspensions, have been used to describe the observed phenomena. The overshoots are fairly well predicted by the first (structure network) model and explained by the competing effects of the structure breakdown under flow and reorganization during rest time. However, the model predicts that the shear stress following the overshoot decreases and reaches steady-state too rapidly. The second model developed for ellipsoid suspensions describes quite well the stress overshoots for the initial forward flow, but no effect of rest time is predicted. A modified version has been proposed by adding a molecular diffusivity contribution in the Folgar–Tucker equation. The effect of the particle disorientation is qualitatively predicted, but the kinetics is too slow compared to that deduced from experiments.

Shaping colloidal assemblies

An MeV ion beam penetrating an amorphous material causes rapid heating of a cylindrically shaped region around the ion track, which leads to anisotropic deformation: the irradiated material shrinks in the direction of the ion beam and expands perpendicular to it. This provides a unique way to tailor the shape of colloidal materials. Spherical silica particles are transformed into oblate ellipsoids, with anisotropy tuned by ion fluence. Ellipsoid suspensions can be used to test theories of colloidal phase transformations. Photonic crystals of ellipsoidal colloids can have enlarged optical band gaps. Deforming metal-silica or silica-metal core-shell particles leads to control over their surface plasmon resonance frequency. Two-dimensional colloidal crystals show complex deformation behavior, providing unique masks for nanolithography.

Brownian dynamics simulations for suspension of ellipsoids in liquid crystalline phase under simple shear flows

Brownian dynamics simulations of shear flows are carried out for various suspensions of ellipsoids interacting via the Gay-Berne potential. In this simulation all the systems of the suspension are in a liquid crystalline phase at rest. In a shear flow they exhibit various motions of the director depending on the shear rate: the continuous rotation, the intermittent rotation, the wagging-like oscillation, and the aligning. The director is almost always out of the vorticity plane when it rotates, that is the kayaking. The number density of the system and the inter-particle potential intensity significantly affect the shear rate dependence of orientation. In particular, the continuous rotation of director is maintained to higher shear rates for the system with a stronger potential. Furthermore, the rheological properties are examined. The shear-thinning in viscosity is observed, but the negative first normal difference is not obtained.

Dielectric behaviour of gap junction connected cells: a microscopic approach

The dielectric behaviour of interconnected cells is simulated by taking into account the ‘real’ shape. In previous work, we derived the polarizability of non-spherical, shelled, particles by solving the related integral equation using a spectral decomposition. The permittivity and impedance modulus spectra of gap junction connected cells are compared with those provided by a suspension of ellipsoids (prolate spheroids) having the same shape as the individual cells connected through gap junction, and the same volume fraction.This approach aims to provide a microscopic hint on the effect of the closing of gap junctions reported on the dielectric behaviour of ischaemic tissues, as well as to offer a rough approximation of a tissue by considering high concentrations of oriented gap junction connected cells.

Simple Shear Flows of Suspensions of Brownian Ellipsoids Interacting Via the Gay-Berne Potential

Brownian dynamics simulations of shear flows were carried out for the suspensions of ellipsoids interacting via the Gay-Berne potential. When the number density of ellipsoid was increased through a compression process of the primitive cell, the phase transition from an isotropic phase to a nematic one occurred. In the simple shear flow for the suspension which exhibits the LC phase at equilibrium, the orientation behavior was examined. The kayaking motion and the intermittent rotation of director were observed at low shear rates. In their director motions, the director is out of the vorticity plane. At high shear rates, however, the flow-aligning was found.

Measurements of the effective dielectric permittivity of suspensions

A technique to measure the effective dielectric permittivity of suspensions is described. In these measurements, test powders are suspended in petroleum jelly at any desired voidage. The technique is illustrated using spherical glass beads of various sizes, a catalyst powder with and without water contamination, metal spheres, and metal flakes. For each suspension, a model is selected to fit the data. In the context of metal flakes, a model is derived for the effective dielectric permittivity of a suspension of ellipsoids in an electric field of random orientation. For complex powders, the technique is shown to represent a necessary step towards quantitative measurements of voidage using capacitance diagnostics.

Singularity solutions for ellipsoids in low-Reynolds-number flows: With applications to the calculation of hydrodynamic interactions in suspensions of ellipsoids

The disturbance velocity fields due to translational and rotational motions of an ellipsoid in a uniform stream. constant vorticity and constant rate-of-strain. required in fundamental studies of behavior of suspensions. have been obtained by the singularity method. These solutions extend earlier solutions for prolate spheroids. Although equivalent solutions problems were obtained by Oberbeck. Edwardes and Jeffery by separation of variables in ellipsoidal coordinates. the singularity solutions are far more simple in form. Other significant results obtained by the singularity method include the exposition of the unified structure shared by the three boundary value problems and the construction of new forms of the Faxen laws for ellipsoids through application of the reciprocal theorem. The disturbance solutions and Faxen laws. the basis for Smoluchowski's method-of-reflections technique. are used to calculate hydrodynamic interactions between two or more arbitrarily oriented ellipsoids. In particular. mobility problems are solved directly to order R −5 . where R is the centroid-to-centroid separation between the ellipsoids.

Fraunhofer diffraction pattern of an oriented monodisperse system of prolate ellipsoids

Human erythrocytes subjected to sufficiently intense shear stress in suspension will deform to shapes approaching those of prolate ellipsoids and align themselves with the direction of flow. Laser diffractometry has been used to follow such shear-induced shape change and orientation. In this paper a theoretical diffraction pattern due to an aligned, monodisperse suspension of ellipsoids is derived.