Rotational Motion Of Particles Research Articles

Kinematics and Dynamics of Transformation of Rotational Motion of Particles in a Disperse System into Macroscopic Motion

Kinematics and Dynamics of Transformation of Rotational Motion of Particles in a Disperse System into Macroscopic Motion

Micro-mechanical perspective on the role of particle shape in shearing of sands

This study presents a micro-mechanical perspective on the role of realistic particle shapes in shearing of sands through calibration with physical experiments and parametric studies using discrete element method (DEM) to reveal the different mechanics between irregular particles and spherical particles incorporating rolling resistance (μr). To achieve this goal, particle shapes of Toyoura sand were captured by micro-computed tomography and reconstructed using a clump generation algorithm in DEM. The use of clumps in DEM led to closer match with experimental results of triaxial tests at various porosities and confining pressures, which could not be achieved by sphere models with μr. With realistic particle shapes, initial rotations of clumps were allowed until they became interlocked, while the load resistance built up gradually. High coordination numbers were observed, with force chains relatively evenly distributed. In contrast, the use of μr in sphere models promoted the formation of voids that were sustained during the loading process, because rotational motions of particles were hampered by μr and they did not easily collapse into the voids. This was accompanied by polarised strong force network around the voids, leading to more dilative and brittle macroscopic behaviour than observed in physical experiments. These findings illustrate that particle shapes cannot be sufficiently replaced by the use of sphere models and μr due to intrinsic differences in their micro-mechanics.

Rotational dynamics of indirect optical bound particle assembly under a single tightly focused laser.

The optical binding of many particles has the potential to achieve the wide-area formation of a "crystal" of small materials. Unlike conventional optical binding, where the entire assembly of targeted particles is directly irradiated with light, if remote particles can be indirectly manipulated using a single trapped particle through optical binding, the degrees of freedom to create ordered structures can be enhanced. In this study, we theoretically investigate the dynamics of the assembly of gold nanoparticles that are manipulated using a single trapped particle by a focused laser. We demonstrate the rotational motion of particles through an indirect optical force and analyze it in terms of spin-orbit coupling and the angular momentum generation of light. The rotational direction of bound particles can be switched by the numerical aperture. These results pave the way for creating and manipulating ordered structures with a wide area and controlling local properties using scanning laser beams.

Model development of tangential hydrodynamic force on particles with pendular liquid bridge of power-law fluid

In this study, new models are proposed for hydrodynamic interaction forces acting on particles through a pendular liquid bridge. The liquid considered is a power-law fluid, and the tangential forces due to both translational and rotational motions of particles are independently modelled, which can be superposed as long as the Reynolds number is sufficiently small. The force models are derived by obtaining improved expressions for the pressure profile inside a liquid bridge which can be reduced to the solutions of the pressure equations based on the lubrication theory in the limiting cases. Direct Numerical Simulation (DNS) is also performed to provide reference data to compare. The forces obtained from the proposed model and DNS are in reasonable agreement compared to the model in the literature where significant overestimation can be seen especially when the power-law index is small. Furthermore, the models proposed are written in a closed-form and can be easily implemented in Discrete Element Method (DEM) for wet particle simulation in the future. • New models of tangential hydrodynamic forces on particles are developed. • The models consider a pendular liquid bridge of power-law fluid between particles. • Good agreement between the model developed and DNS are observed. • The models are written in a closed-form and can be easily implemented in DEM.

Dynamic Analysis and Simulation of an Optically Levitated Rotating Ellipsoid Rotor in Liquid Medium

Optical trap, a circularly polarized laser beam can levitate and control the rotation of microspheres in liquid medium with high stiffness. Trapping force performs as confinement while the trapped particle can be analog to a liquid floated gyroscope with three degree-of-freedom. In this work, we analyzed the feasibility of applying optically levitated rotor in the system. We presented the dynamic analysis and simulation of an ellipsoid micron particle. The precession motion and nutation motion of a rotating ellipsoid probe particle in optical tweezers were performed. We also analyzed the attitude changes of an optically levitated ellipsoid when there was variation of the external torque caused by deviation of the incident light that was provided. Furthermore, the trail path of the rotational axis vertex and the stabilization process of a particle of different ellipticities were simulated. We compared the movement tendencies of particles of different shapes and analyzed the selection criteria of ellipsoid rotor. These analytical formulae and simulation results are applicable to the analysis of the rotational motion of particles in optical tweezers, especially to the future research of the gyroscope effect.

A Finite Element/Neural Network Framework for Modeling Suspensions of Non-spherical Particles

An accurate prediction of the translational and rotational motion of particles suspended in a fluid is only possible if a complete set of correlations for the force coefficients of fluid-particle interaction is known. The present study is thus devoted to the derivation and validation of a new framework to determine the drag, lift, rotational and pitching torque coefficients for different non-spherical particles in a fluid flow. The motivation for the study arises from medical applications, where particles may have an arbitrary and complex shape. Here, it is usually not possible to derive accurate analytical models for predicting the different hydrodynamic forces. The presented model is designed to be applicable to a broad range of shapes. Another important feature of the suspensions occurring in medical and biological applications is the high number of particles. The modelling approach we propose can be efficiently used for simulations of solid-liquid suspensions with numerous particles. Based on resolved numerical simulations of prototypical particles we generate data to train a neural network which allows us to quickly estimate the hydrodynamic forces experienced by a specific particle immersed in a fluid.

Propagation of Sound in Suspensions: Rotational Motions of Particles and Controlling Flows

Propagation of Sound in Suspensions: Rotational Motions of Particles and Controlling Flows

End wall effect on particle motion in a chute flow

The influence of the end wall of a chute on the rotation of internal characteristic particles is mainly on the z-axis. A measurement device based on inertial measurement technology does not require the assistance of external information; hence, it is especially suitable for measuring the angular and translational velocities of internal characteristic particles. To study the influence of the end wall of the chute on the motions of the internal characteristic particles, the z-axis rotational and translational velocities of the internal characteristic particles in the chute were measured, and it was found that the rotational velocity about the z-axis differs according to the initial position. The z-axis angular velocity of a characteristic particle at the centre fluctuates near 0, and the average value approaches 0. The z-axis angular velocity of a characteristic particle at the left end wall is typically negative. This phenomenon is due to the influence of the end wall on the rotational motions of particles with initial positions that are near the end wall. In addition, the average translational velocity of the characteristic particles is also affected by the end wall. The distributions of the average z-axis angular velocity and the average translational velocity are quantitatively analysed, and the correlation between the tilt angle of the chute and the end wall effect is studied.

The decay of isotropic turbulence carrying non-spherical finite-size particles

Direct particle–fluid simulations of heavy spheres and ellipsoids interacting with decaying isotropic turbulence are conducted. This is the rigorous extension of the spherical particle analysis in Schneiders et al. (J. Fluid Mech., vol. 819, 2017, pp. 188–227) to $O(10^{4})$ non-spherical particles. To the best of the authors’ knowledge, this represents the first particle-resolved study on turbulence modulation by non-spherical particles of near-Kolmogorov-scale size. The modulation of the turbulent flow is precisely captured by explicitly resolving the stresses acting on the fluid–particle interfaces. The decay rates of the fluid and particle kinetic energy are found to increase with the particle aspect ratio. This is due to the particle-induced dissipation rate and the direct transfer of kinetic energy, both of which can be substantially larger than for spherical particles depending on the particle orientation. The extra dissipation rate resulting from the translational and rotational particle motion is quantified to detail the impact of the particles on the fluid kinetic energy budget and the influence of the particle shape. It is demonstrated that the previously derived analytical model for the particle-induced dissipation rate of smaller particles is valid for the present cases albeit these involve significant finite-size effects. This generic expression allows us to assess the impact of individual inertial particles on the local energy balance independent of the particle shape and to quantify the share of the rotational particle motion in the kinetic energy budget. To enable the examination of this mechanistic model in particle-resolved simulations, a method is proposed to reconstruct the so-called undisturbed fluid velocity and fluid rotation rate close to a particle. The accuracy and robustness of the scheme are corroborated via a parameter study. The subsequent discussion emphasizes the necessity to account for the orientation-dependent drag and torque in Lagrangian point-particle models, including corrections for finite particle Reynolds numbers, to reproduce the local and global energy balance of the multiphase system.

Time correlation functions and kinetic coefficients in systems with molecular or chemical exchange

We develop a kinetic theory for systems with molecular or chemical exchange. In such systems, particles can successively reside in two different dynamical states with the inter-state transition. A prominent example of the molecular exchange (ME) is aqueous solutions of macromolecules (proteins, DNA) or metal ions, where a water molecule can move freely in a bulk of the solution or perform a constrained motion in a bound state. This may be the surface of the macromolecule or the ion's hydration shell. Another example, which refers to the chemical exchange (CE), is a molecule in a solution, that reversibly alternates its conformation — different conformations imply different rotational and translational motion. We consider the case of Poissonian exchange between states and general, non-Poissonian exchange and derive general relations for time correlation functions and kinetic coefficients. The application of the theory is illustrated by computation of time correlation functions and kinetic coefficients for translational and rotational motion of particles in systems with exchange.

Spatiotemporal analysis of strain localization in dense granular materials

Predicting localized failure in granular materials is a problem of great interest from both the scientific and technological perspectives. The initiation and growth of strain localization have been studied using laboratory experiments and particle-based numerical simulations, and their findings have been preliminarily implemented into continuum constitutive models. In this study, we revisit strain localization in granular materials using the spatiotemporal data analysis technique, which has been extensively employed in data mining science and social science for the sake of different applications. A dense packing of granular material subjected to biaxial compression was simulated using the combined finite and discrete element method. The large amount of particle-level kinematical data, including the translational and rotational particle motion, fluctuating velocity, granular temperature, and local strain, are collected for subsequent spatiotemporal data analysis. The spatiotemporal data analysis provides a new perspective on the strain localization in dense granular materials and a rich body of new insights are presented for the first time. The spatial autocorrelation analysis results in Moran’s I values close to 1, and positive Z scores and statistically significant p values, which indicate that a dense granular system features clustered patterns during shearing. This finding proves yet again that dense granular materials have an inherent short range order. Eventually, correspondence between localized modes with different particle kinematics and spatial distributions of local Moran statistics and quadrant location map are investigated. By assuming shearing of dense granular materials is a first-order Markov chain process, the convergence and time homogeneity of this process are analyzed. Both the maximum likelihood and Pearson test statistics clearly demonstrate that shearing of dense granular materials is a time-homogenous Markov chain process.

A two-way coupling scheme to model the effects of particle rotation on the rheological properties of a semidilute suspension

According to Einstein's viscosity formula, the effective viscosity of a suspension is related to the volume fraction ϕ of suspended particles. Higher-order terms, which include contributions from hydrodynamic interactions, become more important when the concentration of the suspension reaches around 25%. The coefficient β of the term quadratic in ϕ, however, has not been incontrovertibly validated. In order to investigate the effects on the macroscopic rheology of a suspension due to the rotational motions of the microscopic suspended particles—which are usually neglected in analytical and numerical studies—we have performed simulations of a pressure-driven flow using a two-way coupling method (defined in text). We used the regularized lattice Boltzmann equation for the fluid part of the calculation, and we employed Newton's second law of motion and the equation of angular motion for the translational and rotational motions of the rigid particles. As a result, we found that the particles rotate to achieve kinetic balance with the surrounding hydrodynamic forces, which results in a decrease in fluid resistance. It is therefore important to take into account the particles’ rotational motions and the accompanying changes in the flow field in order to evaluate the effective viscosity of a suspension. The spatial variation of the relative viscosity determined from the wall shear stress becomes more significant with increasing area fraction. We found that the value of the coefficient β may increase due to hydrodynamic resistance against the rotational motions of the particles.

Investigation on the photophoretic lift force acting upon particles under light irradiation

Considering the characteristics of photophoresis in the actual process, the viewpoint that particles in fluids will experience photophoretic lift force is proposed. The force is related to the particle motion with photophoresis but different from the traditional photophoretic force. Analysis shows that there are mainly two factors contributing to the lift force, one stems from the variation in the distribution of light intensity, the other originates from the rotational motion of particles in a direction which is perpendicular to the optical axis. The expression of the photophoretic lift force has been given in the study. The impacts of the force have been analyzed and validated by comparing with previous experimental results.

Shear banding, discontinuous shear thickening, and rheological phase transitions in athermally sheared frictionless disks.

We report on numerical simulations of simple models of athermal, bidisperse, soft-core, massive disks in two dimensions, as a function of packing fraction ϕ, inelasticity of collisions as measured by a parameter Q, and applied uniform shear strain rate γ[over ̇]. Our particles have contact interactions consisting of normally directed elastic repulsion and viscous dissipation, as well as tangentially directed viscous dissipation, but no interparticle Coulombic friction. Mapping the phase diagram in the (ϕ,Q) plane for small γ[over ̇], we find a sharp first-order rheological phase transition from a region with Bagnoldian rheology to a region with Newtonian rheology, and show that the system is always Newtonian at jamming. We consider the rotational motion of particles and demonstrate the crucial importance that the coupling between rotational and translational degrees of freedom has on the phase structure at small Q (strongly inelastic collisions). At small Q, we show that, upon increasing γ[over ̇], the sharp Bagnoldian-to-Newtonian transition becomes a coexistence region of finite width in the (ϕ,γ[over ̇]) plane, with coexisting Bagnoldian and Newtonian shear bands. Crossing this coexistence region by increasing γ[over ̇] at fixed ϕ, we find that discontinuous shear thickening can result if γ[over ̇] is varied too rapidly for the system to relax to the shear-banded steady state corresponding to the instantaneous value of γ[over ̇].

すべりなし効果を考慮した液架橋力モデルの提案

DEM simulation of wet granulation has been performed by applying population balance in most cases found in the literature. From the point of view of industry, DEM simulation based on force balance in required for discussing the effects of the amount of binder, spray characteristics, and so on. This paper proposes new idea of capillary force model, considering non-slip boundary condition between particles and particle/wall, called “Non-slip capillary force model.” In this model, capillary forces work between interacting points, which are generated on the surface of particle when capillary is created between particles, and the interacting points are fixed on the surface of particles, meaning that the position of the interacting point changes according to rotational motions of particles. This force model is applied to the two systems: 1) collision of an aggregate against wall, and 2) wet granular system. The following results are achieved through the research: a) aggregates are generated with non-slip capillary force model and the aggregate shows properties of rigid body, b) the aggregate can be broken, when the collision force is over the capillary force. From these results, it can be expected that “Non-slip capillary force model” is inevitable for DEM simulation for wet granulation process.

Stability analysis of the Gyroscopic Power Take-Off wave energy point absorber

The Gyroscopic Power Take-Off (GyroPTO) wave energy point absorber consists of a float rigidly connected to a lever. The operational principle is somewhat similar to that of the so-called gyroscopic hand wrist exercisers, where the rotation of the float is brought forward by the rotational particle motion of the waves. At first, the equations of motion of the system are derived based on analytical rigid body dynamics. Next, assuming monochromatic waves simplified equations are derived, valid under synchronisation of the ring of the gyro to the angular frequency of the excitation. Especially, it is demonstrated that the dynamics of the ring can be described as an autonomous nonlinear single-degree-of-freedom system, affected by three different types of point attractors. One where the ring vibrations are attracted to a static equilibrium point indicating unstable synchronisation and two types of attractors where the ring is synchronised to the wave angular frequency, either rotating in one or the opposite direction. Finally, the stability conditions and the basins of attraction to the point attractors defining the synchronised motion are determined.

A description of rotations for DEM models of particle systems

In this work, we show how a vector parameterization of rotations can be adopted to describe the rotational motion of particles within the framework of the discrete element method (DEM). It is based on the use of a special rotation vector, called Rodrigues rotation vector, and accounts for finite rotations in a fully exact manner. The use of fictitious entities such as quaternions or complicated structures such as Euler angles is thereby circumvented. As an additional advantage, stick-slip friction models with inter-particle rolling motion are made possible in a consistent and elegant way. A few examples are provided to illustrate the applicability of the scheme. We believe that simple vector descriptions of rotations are very useful for DEM models of particle systems.

Coarsening dynamics of binary liquids with active rotation.

Active matter comprised of many self-driven units can exhibit emergent collective behaviors such as pattern formation and phase separation in both biological (e.g., mussel beds) and synthetic (e.g., colloidal swimmers) systems. While these behaviors are increasingly well understood for ensembles of linearly self-propelled "particles", less is known about the collective behaviors of active rotating particles where energy input at the particle level gives rise to rotational particle motion. A recent simulation study revealed that active rotation can induce phase separation in mixtures of counter-rotating particles in 2D. In contrast to that of linearly self-propelled particles, the phase separation of counter-rotating fluids is accompanied by steady convective flows that originate at the fluid-fluid interface. Here, we investigate the influence of these flows on the coarsening dynamics of actively rotating binary liquids using a phenomenological, hydrodynamic model that combines a Cahn-Hilliard equation for the fluid composition with a Navier-Stokes equation for the fluid velocity. The effect of active rotation is introduced though an additional force within the Navier-Stokes equations that arises due to gradients in the concentrations of clockwise and counter-clockwise rotating particles. Depending on the strength of active rotation and that of frictional interactions with the stationary surroundings, we observe and explain new dynamical behaviors such as "active coarsening" via self-generated flows as well as the emergence of self-propelled "vortex doublets". We confirm that many of the qualitative behaviors identified by the continuum model can also be found in discrete, particle-based simulations of actively rotating liquids. Our results highlight further opportunities for achieving complex dissipative structures in active materials subject to distributed actuation.

A Numerical Study on Agglomeration in High Temperature Fluidized beds

Soft-sphere discrete element method (DEM) and Navier-Stokes equations were coupled with equations of energy for gas and solids to investigate the process of agglomeration in fluidized bed of polyethylene particles at high temperature. The Newton’s second law of motion was adapted for translational and rotational motion of particles and agglomerates. The cohesive force for polyethylene particles was calculated based on a time dependent model for solid bridging by the viscous flow mechanism. The motion of agglomerates was described by means of the multi-sphere method. By taking into account the cohesiveness of particles at high temperatures and considering real dynamic agglomerates, the fluidization behavior of a bed of polyethylene particles was successfully simulated in terms of increasing the size of agglomerates. Effect of the inlet gas temperature on mass and size of agglomerates was investigated. A mechanistic study in terms of contact time, cohesive force and repulsive force, which are the key parameters in the formation of agglomerates, were also carried out.

A second-order accurate immersed boundary-lattice Boltzmann method for particle-laden flows

A new immersed boundary-lattice Boltzmann method (IB-LBM) is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles. The immersed boundary method (IBM) recently developed by Breugem (2012) [19] is adopted in the present method, development including the retraction technique, the multi-direct forcing method and the direct account of the inertia of the fluid contained within the particles. The present IB-LBM is, however, formulated with further improvement with the implementation of the high-order Runge–Kutta schemes in the coupled fluid–particle interaction. The major challenge to implement high-order Runge–Kutta schemes in the LBM is that the flow information such as density and velocity cannot be directly obtained at a fractional time step from the LBM since the LBM only provides the flow information at an integer time step. This challenge can be, however, overcome as given in the present IB-LBM by extrapolating the flow field around particles from the known flow field at the previous integer time step. The newly calculated fluid–particle interactions from the previous fractional time steps of the current integer time step are also accounted for in the extrapolation. The IB-LBM with high-order Runge–Kutta schemes developed in this study is validated by several benchmark applications. It is demonstrated, for the first time, that the IB-LBM has the capacity to resolve the translational and rotational motion of particles with the second-order accuracy. The optimal retraction distances for spheres and tubes that help the method achieve the second-order accuracy are found to be around 0.30 and −0.47 times of the lattice spacing, respectively. Simulations of the Stokes flow through a simple cubic lattice of rotational spheres indicate that the lift force produced by the Magnus effect can be very significant in view of the magnitude of the drag force when the practical rotating speed of the spheres is encountered. This finding may lead to more comprehensive studies of the effect of the particle rotation on fluid–solid drag laws. It is also demonstrated that, when the third-order or the fourth-order Runge–Kutta scheme is used, the numerical stability of the present IB-LBM is better than that of all methods in the literature, including the previous IB-LBMs and also the methods with the combination of the IBM and the traditional incompressible Navier–Stokes solver.