Non-rotating Particles Research Articles

New one-parameter models of dynamical particles in spatially flat FLRW space-times

New one-parameter models of non-rotating dynamical particles are derived as isotropic solutions of Einstein’s equations with perfect fluid in space-times with FLRW asymptotic behaviour, thus generalizing the models recently proposed by Cotăescu (Eur. Phys. J. C 82:86, 2022). These particles are produced by central singularities of the fluid density but without changing the pressure of the asymptotic FLRW space-times. The principal features of these models are investigated using a brief graphical analysis to elucidate the role of the new free parameter. The conclusion is that this gives rise to families of models which behave as non-rotating black holes in the physical space domain bordered by the black hole and cosmological horizons.

A classical guide to entanglement

Two particles created from a single, nonrotating particle are rotating in opposite directions. Each has two matter-less strings attached to it. One string carries force impulse, and the other transmits clock times. If one reverses the rotation direction of the source particle, the target will almost immediately also reverse its rotation no matter how far the two particles are apart. I will investigate if the reason is the disparity in clock information from each particle.

Indentation and Scratching with a Rotating Adhesive Tool: A Molecular Dynamics Simulation Study

For the specific case of a spherical diamond nanoparticle with 10 nm radius rolling over a planar Fe surface, we employ molecular dynamics simulation to study the processes of indentation and scratching. The particle is rotating (rolling). We focus on the influence of the adhesion force between the nanoparticle and the surface on the damage mechanisms on the surface; the adhesion is modeled by a pair potential with arbitrarily prescribed value of the adhesion strength. With increasing adhesion, the following effects are observed. The load needed for indentation decreases and so does the effective material hardness; this effect is considerably more pronounced than for a non-rotating particle. During scratching, the tangential force, and hence the friction coefficient, increase. The torque needed to keep the particle rolling adds to the total work for scratching; however, for a particle rolling without slip on the surface the total work is minimum. In this sense, a rolling particle induces the most efficient scratching process. For both indentation and scratching, the length of the dislocation network generated in the substrate reduces. After leaving the surface, the particle is (partially) covered with substrate atoms and the scratch groove is roughened. We demonstrate that these effects are based on substrate atom transport under the rotating particle from the front towards the rear; this transport already occurs for a repulsive particle but is severely intensified by adhesion.

The effect of inter-particle hydrodynamic and magnetic interactions in a magnetorheological fluid

A magnetorheological fluid, which consists of magnetic particles suspended in a viscous fluid, flows freely with well-dispersed particles in the absence of a magnetic field, but particle aggregation results in flow cessation when a field is applied. The mechanism of dynamical arrest is examined by analysing interactions between magnetic particles in a magnetic field subject to a shear flow. An isolated spherical magnetic particle undergoes a transition between a rotating state at low magnetic field and a static orientation at high magnetic field. The effect of interactions for spherical dipolar and polarisable particles with static orientation is examined for an unbounded dilute viscous suspension. There are magnetic interactions due to the magnetic field disturbance at one particle caused by the dipole moment of another, hydrodynamic interactions due to the antisymmetric force moment of a non-rotating particle in a shear flow, and a modification of the magnetic field due to the particle magnetic moment density. When there is a concentration variation, the torque balance condition results in a disturbance to the orientation of the particle magnetic moment. The net force and the drift velocity due to these disturbances is calculated, and the collective motion generated is equivalent to an anisotropic diffusion process. When the magnetic field is in the flow plane, the diffusion coefficients in the two directions perpendicular to the field direction are negative, implying that concentration fluctuations are unstable in these directions. This instability could initiate field-induced dynamical arrest in a magnetorheological fluid.

Effect of particle self-rotation on separation efficiency in mini-hydrocyclones

High-speed particle self-rotation near the wall of a hydrocyclone that causes the radial migration of the particles has been extensively investigated. However, the influence of this radial migration on the separation efficiency of the hydrocyclone remains unclear. Since this influence cannot be easily experimentally verified, we employed computational fluid dynamics to investigate the effect of particle rotation on the separation efficiency of a mini-hydrocyclone. A Reynolds stress model and discrete phase model were used to model the flow field and particle migration within the hydrocyclone. Considering the shear flow field and wall collision causing the rotation of particles, the movement trajectory, rotation velocity, and radial migration characteristics of particles entering from different inlet positions in a mini-hydrocyclone were studied. For the numerical simulation, the actual particle size distribution was considered. The results demonstrated that the particles rotated at a high velocity near the wall; the spiral-orbit radius of rotating particles was smaller than non-rotating particles; and high-speed rotating particles migrated from the wall to the central axis of the hydrocyclone. By including particle rotation into the hydrocyclone simulations, the simulated separation efficiency was consistent with experimental results. Further, the accuracy of the rotating particle simulation was 65% higher than the non-rotating particle simulation. Therefore, particle rotation is crucial for simulating the mini-hydrocyclone performance.

The Force Required to Detach a Rotating Particle from a Liquid-Fluid Interface.

The force required to detach a particle from a liquid–fluid interface is a direct measure of the capillary adhesion between the particle and the interface. Analytical expressions for the detachment force are available but are limited to nonrotating particles. In this work, we derive analytical expressions for the force required to detach a rotating spherical particle from a liquid–fluid interface. Our theory predicts that the rotation reduces the detachment force when there is a finite contact angle hysteresis between the particle and the liquid. For example, the force required to detach a particle with an advancing contact angle of 120° and a receding contact angle of 80° (e.g., polydimethylsiloxane particle at a water–air interface) is expected to be 25% lower when the particle rotates while it is detached.

Rotational speed measurements of small spherical particles driven by acoustic viscous torques utilizing an optical trap

Two orthogonal standing acoustic waves, generated by piezoelectric excitation, can form a two-dimensional pressure field in microfluidic devices. A phase difference of the excitation waves can be employed to rotate spherical µm-sized silica particles by a torque mediated through the viscous boundary δ around the particle. The measurement of the rotational rate is, so far, limited to high-speed cameras and their frame rate, and gets increasingly difficult when the sphere gets smaller. We report here a new method for measuring the rotational rate of µm sized spherical particles. We utilize an optical trap with high-speed position detection to overcome the frame rate limitation of wide field image recording. The power spectrum of an optically trapped, rotating particle reveals additional peaks corresponding to the rotational frequencies—compared to a non-rotating particle. We validate our method at low rotational rates against high-speed video observation. To demonstrate the potential of this method we addressed a recent controversy about the rotation of particles with a relatively large viscous boundary layer δ. We measured steady-state rotational rates up to 229 Hz (13.8 × 103 rpm) for a particle with a radius R ≈ δ. Recent numerical research suggests that in this regime the existing theoretical approach (valid for ) overpredicts the steady-state rotational rate by a factor of 10. With our new method we also confirm the numerical results experimentally.

Direct numerical simulation of rotating ellipsoidal particles using moving nonconforming Schwarz-spectral element method

We present application of a highly-scalable overlapping grid-based nonconforming Schwarz-spectral element method (Schwarz-SEM) to study the dynamics of rotating ellipsoidal particles. The current study is one of the first to explore the effect of rotation on ellipsoidal particles using direct numerical simulation. The rotating ellipsoidal particles show substantial difference in the dynamics of the flow, when compared against non-rotating particles. This difference is primarily due to periodic attachment and separation of the flow to the surface of the particle for the rotating cases, which results in a higher drag on the particle when compared to the corresponding non-rotating cases. The dynamics is also different from a rotating spherical particle, where a steady shear layer develops near the surface of the sphere. For the rotating ellipsoidal particles, we observe that there is a phase-difference between the position of observed maximum and minimum drag, and the position of expected maximum and minimum drag (i.e., maximum and minimum projected area). A similar phase-difference is also observed for the lift force acting on the rotating ellipsoidal particles. The results presented here demonstrate the importance of explicitly modeling the shape and rotation of particles for studying dynamics of non-spherical particles. Finally, this study also validates the use of non-conforming Schwarz-SEM for tackling problems in fully resolved particulate flow dynamics.

Micro-interface temperature field of catalytic particle under self-rotation regulation

The micro-interface formed inside and on the surface of the catalytic particle is the place where the catalytic reaction proceeds. The micro-interface temperature is one of the important factors determining the reaction efficiency. Numerical simulation was used to investigate the fluid-solid coupled heat transfer law of micro-interface under the regulation of spherical particles’ self-rotation. The results show it takes up to 4.78 s that the average surface temperature of non-rotating particle with a diameter of 3 mm decreases from 300 ℃ to 150 ℃, which is the lowest temperature required for high-efficiency selective catalytic reduction reaction of NOx with NH3, while self-rotation can reduce the cooling rate of particles. When the direction of particle self-rotation is perpendicular to gas velocity, as the self-rotation speed increases, the high-temperature area of the particle surface diffuses more fully to the latitude direction. Significant effect can be made as the self-rotation speed reaches 5 rad/s, the uniformity of the surface temperature can be increased by 27.1 % ~ 37.7 % compared with non-rotating particle, and the uniformity can be increased by a maximum of 49.5 % at a self-rotation speed of 500 rad/s.

Numerical simulation of micro-particle rotation by the acoustic viscous torque.

We present the first numerical simulation setup for the calculation of the acoustic viscous torque on arbitrarily shaped micro-particles inside general acoustic fields. Under typical experimental conditions, the particle deformation plays a minor role. Therefore, the particle is modeled as a rigid body which is free to perform any time-harmonic and time-averaged translation and rotation. Applying a perturbation approach, the viscoacoustic field around the particle is resolved to obtain the time-averaged driving forces for a subsequent acoustic streaming simulation. For some acoustic fields, the near-boundary streaming around the fluid-suspended particle induces surface forces on the nonrotating particle that integrate into a non-zero acoustic viscous torque. In the equilibrium state, this torque is compensated by an equal and opposite drag torque due to the particle rotation. The rotation-induced flow field is superimposed on the acoustic streaming field to obtain the total fluid motion around the rotating particle. In this work, we only consider cases within the Rayleigh limit even though the presented numerical model is not strictly limited to this regime. After a validation by analytical solutions, the numerical model is applied to challenging experimental cases. For an arbitrary particle density, we consider particle sizes that can be comparable to the viscous boundary layer thickness. This important regime has not been studied before because it lies beyond the validity limits of the available analytical solutions. The detailed numerical analysis in this work predicts nonintuitive phenomena, including an inversion of the rotation direction. Our numerical model opens the door to explore a wide range of experimentally relevant cases, including non-spherical particle rotation. As a step toward application fields such as micro-robotics, the rotation of a prolate ellipsoid is studied.

Controlling inertial focussing using rotational motion.

In inertial microfluidics lift forces cause a particle to migrate across streamlines to specific positions in the cross section of a microchannel. We control the rotational motion of a particle and demonstrate that this allows to manipulate the lift-force profile and thereby the particle's equilibrium positions. We perform two-dimensional simulation studies using the method of multi-particle collision dynamics. Particles with unconstrained rotational motion occupy stable equilibrium positions in both halfs of the channel while the center is unstable. When an external torque is applied to the particle, two equilibrium positions annihilate by passing a saddle-node bifurcation and only one stable fixpoint remains so that all particles move to one side of the channel. In contrast, non-rotating particles accumulate in the center and are pushed into one half of the channel when the angular velocity is fixed to a non-zero value.

Interactions between Protein Coated Particles and Polymer Surfaces Studied with the Rotating Particles Probe

Nonspecific interactions between proteins and polymer surfaces have to be minimized in order to control the performance of biosensors based on immunoassays with particle labels. In this paper we investigate these nonspecific interactions by analyzing the response of protein coated magnetic particles to a rotating magnetic field while the particles are in nanometer vicinity to a polymer surface. We use the fraction of nonrotating (bound) particles as a probe for the interaction between the particles and the surface. As a model system, we study the interaction of myoglobin coated particles with oxidized polystyrene surfaces. We measure the interaction as a function of the ionic strength of the solution, varying the oxidation time of the polystyrene and the pH of the solution. To describe the data we propose a model in which particles bind to the polymer by crossing an energy barrier. The height of this barrier depends on the ionic strength of the solution and two interaction parameters. The fraction of nonrotating particles as a function of ionic strength shows a characteristic shape that can be explained with a normal distribution of energy barrier heights. This method to determine interaction parameters paves the way for further studies to quantify the roles of protein coated particles and polymers in their mutual nonspecific interactions in different matrixes.

Dipole interaction of the Quincke rotating particles

We study the behavior of particles having a finite electric permittivity and conductivity in a weakly conducting fluid under the action of the external electric field. We consider the case when the strength of the external electric field is above the threshold, and particles rotate due to the Quincke effect. We determine the magnitude of the dipole interaction of the Quincke rotating particles and the shift of frequency of the Quincke rotation caused by the dipole interaction between the particles. It is demonstrated that depending on the mutual orientation of the vectors of angular velocities of particles, vector-directed along the straight line between the centers of the particles and the external electric field strength vector, particles can attract or repel each other. In contrast to the case of nonrotating particles when the magnitude of the dipole interaction increases with the increase of the strength of the external electric field, the magnitude of the dipole interaction of the Quincke rotating particles either does not change or decreases with the increase of the strength of the external electric field depending on the strength of the external electric field and electrodynamic parameters of the particles.

Ideal Rate of Collision of Cylinders in Simple Shear Flow

The collision of particles influences the behavior of suspensions through the formation of aggregates for adhesive particles or through the contributions of solid-body contacts to the stress for nonadhesive particles. The simplest estimate of the collision rate, termed the ideal collision rate, is obtained when particles translate and rotate with the flow but have no hydrodynamic or colloidal interactions. Smoluchowski calculated the ideal collision frequency of spherical particles in 1917. So far, little work has been done to understand rate of collision for nonspherical particles. In this work, we calculate the ideal collision rate for cylindrical particles over a broad range of particle aspect ratios r defined as the ratio of length to diameter. Monte Carlo simulations are performed with initial relative positions and orientations that model the rate of approach of noninteracting particles following Jeffery orbits with several choices of the orbit distribution. The role of rotational motion of particles on collision frequency is elucidated by comparing the ideal collision rate calculations with similar calculations for nonrotating particles. It is shown that the ratio of the collision rate of cylinders to that of spheres that circumscribe the cylinders is proportional to 1/rr(e) for r ≫ 1 and r(e) for r ≪ 1. Here, r(e) is the effective aspect ratio defined as the aspect ratio of a spheroid having the same period of rotation as the cylinder. The effective aspect ratio of the cylindrical particles was determined using finite element calculations of the torque on nonrotating cylinders with their axes parallel to the velocity and velocity gradient directions. In addition to deriving the total collision rate, we categorize collisions as side-side, edge-side, and face-edge based on the initial point of contact. Most collisions are found to be side-edge for r ≫ 1 and face-edge for r ≪ 1, suggesting that nonlinear aggregates will develop if particles stick at the point of first contact.

Exact solution of the EM radiation-reaction problem for classical finite-size and Lorentzian charged particles

An exact solution is given to the classical electromagnetic (EM) radiation-reaction (RR) problem, originally posed by Lorentz. This refers to the dynamics of classical non-rotating and quasi-rigid finite size particles subject to an external prescribed EM field. A variational formulation of the problem is presented. It is shown that a covariant representation for the EM potential of the self-field generated by the extended charge can be uniquely determined, consistent with the principles of classical electrodynamics and relativity. By construction, the retarded self 4-potential does not possess any divergence, contrary to the case of point charges. As a fundamental consequence, based on Hamilton variational principle, an exact representation is obtained for the relativistic equation describing the dynamics of a finite-size charged particle (RR equation), which is shown to be realized by a second-order delay-type ODE. Such equation is proved to apply also to the treatment of Lorentzian particles, i.e., point-masses with finite-size charge distributions, and to recover the usual LAD equation in a suitable asymptotic approximation. Remarkably, the RR equation admits both standard Lagrangian and conservative forms, expressed respectively in terms of a non-local effective Lagrangian and a stress-energy tensor. Finally, consistent with the Newton principle of determinacy, it is proved that the corresponding initial-value problem admits a local existence and uniqueness theorem, namely it defines a classical dynamical system.

Tornadoes in a microchannel

In non-dilute colloidal suspensions, gradients in particle volume fraction result in gradients in electrical conductivity and permittivity. An externally applied electric field couples with gradients in electrical conductivity and permittivity and, under some conditions, can result in electric body forces that drive the flow unstable forming vortices. The experiments are conducted in square 200 micron PDMS microfluidic channels. Colloidal suspensions consisted of 0.01 volume fraction of 2 or 3 micron diameter polystyrene particles in 0.1 mM Phosphate buffer and 409 mM sucrose to match particle-solution density. AC electric fields at 20 Hz and strength of 430 to 600 V/cm were used. We present a fluid dynamics video that shows the evolution of the particle aggregation and formation of vortical flow. Upon application of the field particles aggregate forming particle chains and three dimensional structures. These particles form rotating bands where the axis of rotation varies with time and can collide with other rotating bands forming increasingly larger bands. Some groups become vortices with a stable axis of rotation. Other phenomena showed include counter rotating vortices, colliding vortices, and non-rotating particle bands with internal waves.

Micromechanical definition of an entropy for quasi-static deformation of granular materials

A micromechanical theory is formulated for quasi-static deformation of granular materials, which is based on information theory. A reasoning is presented that leads to the definition of an information entropy that is appropriate for quasi-static deformation of granular materials. This definition is based on the hypothesis that relative displacements at contacts with similar orientations are independent realisations of a random variable. This hypothesis is made plausible based on the results of Discrete Element simulations. The developed theory is then used to predict the elastic behaviour of granular materials in terms of micromechanical quantities. The case considered is that of two-dimensional assemblies consisting of non-rotating particles with an elastic contact constitutive relation. Applications of this case are the initial elastic (small-strain) deformation of granular materials. Theoretical results for the elastic moduli, relative displacements, energy distribution and probability density functions are compared with results obtained from the Discrete Element simulations for isotropic assemblies with various average numbers of contacts per particle and various ratios of tangential to normal contact stiffness. This comparison shows that the developed information theory is valid for loose systems, while a theory based on the uniform-strain assumption is appropriate for dense systems.

Micromechanical bounds for the effective elastic moduli of granular materials

This study deals with bounds for the effective elastic moduli of granular materials in terms of micromechanical parameters. The case considered is that of two-dimensional isotropic assemblies of non-rotating particles with bonded contacts and a linear elastic contact constitutive relation. Based on variational principles, rigorous upper and lower bounds are obtained for the elastic moduli. To this end, compatible and equilibrated fields are constructed from local characteristics, based on approximate equilibrium and compatibility, respectively. Results of discrete element simulations are used to compare the obtained bounds with the actual moduli. This comparison shows that the actual moduli are narrowly bracketed by these bounds. The corresponding fields of relative displacement and force at the contacts are analysed, showing fairly close agreement with those obtained from the discrete element simulations.

Statistics of the elastic behaviour of granular materials

The elastic behaviour of isotropic assemblies of granular materials consisting of two-dimensional, bonded and non-rotating particles is studied from the micromechanical viewpoint. Discrete element simulations have been performed of assemblies of 50,000 particles with various coordination numbers (average number of contacts per particle) and various ratios of tangential to normal stiffness. Statistics, such as mean, standard deviation and probability distribution function, have been computed for geometrical quantities and contact displacements under compressive and shearing loading. A linear relation is observed between the average number of contacts of a particle and its circumference. Average displacements do not conform to (generalised) uniform strain as is often assumed. The probability density functions for normal and tangential displacements are nearly Gaussian. None of the considered energies satisfy an equipartition of energy between normal and tangential modes.

Optical measurement of microscopic torques

Abstract In recent years there has been an explosive development of interest in the measurement of forces at the microscopic level, such as within living cells, as well as the properties of fluids and suspensions on this scale, using optically trapped particles as probes. The next step would be to measure torques and associated rotational motion. This would allow measurement on very small scales since no translational motion is needed. It could also provide an absolute measurement of the forces holding a stationary non-rotating particle in place. The laser-induced torque acting on an optically trapped microscopic birefringent particle can be used for these measurements. Here we present a new method for simple, robust, accurate, simultaneous measurement of the rotation speed of a laser trapped birefringent particle, and the optical torque acting on it, by measuring the change in angular momentum of the light from passing through the particle. This method does not depend on the size or shape of the particle or the laser beam geometry, nor does it depend on the properties of the surrounding medium. This could allow accurate measurement of viscosity on a microscopic scale.