Particle Kinetic Theory Research Articles

Fast size estimation of single-levitated nanoparticles in a vacuum optomechanical system.

Optical trapping of single nanoparticles in vacuum has various applications in both precise measurements and fundamental physics. However, to date, the number and size of randomly loaded nanoparticles in an optical trap is difficult to determine unless in vacuum. In this Letter, an efficient method for nanoparticle size estimation in an optical tweezer system before the evacuation of air was proposed and demonstrated experimentally, using scattering light from levitated particles. The particle radii deduced from the scattering light power in our proposal and from the kinetic theory of particles in gas match well (with the differences of less than 10%). For sample particles with radii ranging within 50-100 nm, we also provide a preselection rule based on this method, where over half of the trapped particles are verified as single particles. Such a particle analysis method is applicable also for the size estimation of levitated diamond particles, gold particles, and other plasmonic particles and can be applied to discovering novel scattering effects.

Full non–LTE spectral line formation

Radiative transfer out of local thermodynamic equilibrium (NLTE) has been increasingly adressed, mostly numerically, for about six decades now. However, the standard NLTE problem most often refers to the only deviation of the distribution of photons from their equilibrium, that is to say a Planckian distribution. Hereafter we revisit after Oxenius (1986, Kinetic theory of particles and Photons – Theoretical Foundations of non–LTE Plasma Spectroscopy, Springer) the so-called full NLTE problem, which considers coupling and therefore solving self–consistently for deviations from equilibrium distributions of photons as well as for massive particles constituting the atmospheric plasma.

Comparison of Learning in Inductive and Deductive Approach to Increase Student’s Conceptual Understanding based on International Standard Curriculum

This study aimed to determine the pattern of a more effective learning approach between the inductive and deductive approach in improving students’ conceptual understanding referring to the international standard curriculum on the X graders for the material property particulate subject matter. Through the deductive approach, students already have a picture/concept in their minds. But by using an inductive approach, students use their logic to understand concepts and summarize it. The research method applied in this study is a descriptive-comparative method with a triangulation analysis technique. Instruments used in the study were a questionnaire for the students, observation sheets, and three-tier diagnostic test items for pretest and posttest. The average pretest scores for deductive and inductive classes were 54.70 and 48.25, respectively. The result of the observation sheet analysis showed the deductive approach surpassed 12 points more than the inductive approach in improving the student’s learning activity. The result of the questionnaire analysis showed that 38 of 68 students prefer the learning process using deductive to inductive approach, and thought that it was suitable with the students’ characteristics. While the average posttest scores for deductive and inductive classes were 68.16 and 55.47, respectively. The analysis result of the N-Gain test towards the pretest and posttest results regarding the three-tier diagnostic test items indicated achievement of student’s conceptual understanding using a deductive approach which was 14.2225% higher than the use of the inductive approach. The Triangulation Analysis stated that the deductive approach was more effective in improving students’ conceptual understanding of Chemistry and material topics as well as material classification. While the inductive approach was more effectively applied to the topic of Particle Kinetic theory.

Mini-Workshop: Lorentz Gas Dynamics: particle systems and scaling limits

This workshop had the aim to bring together leading experts from different fields, i.e. interacting particle systems, dynamical systems and kinetic theory, to consider questions related to the dynamics of the Lorentz gas and to promote the exchange of information concerning the techniques that have been developed in different contexts and communities.

Thermodynamics and relativistic kinetic theory for q-generalized Bose\u2013Einstein and Fermi\u2013Dirac systems

The thermodynamics and covariant kinetic theory are elaborately investigated in a non-extensive environment considering the non-extensive generalization of Bose–Einstein (BE) and Fermi–Dirac (FD) statistics. Starting with Tsallis’ entropy formula, the fundamental principles of thermostatistics are established for a grand canonical system having q-generalized BE/FD degrees of freedom. Many particle kinetic theory is set up in terms of the relativistic transport equation with q-generalized Uehling–Uhlenbeck collision term. The conservation laws are realized in terms of appropriate moments of the transport equation. The thermodynamic quantities are obtained in a weak non-extensive environment for a massive pion–nucleon and a massless quark–gluon system with non-zero baryon chemical potential. In order to get an estimate of the impact of non-extensivity on the system dynamics, the q-modified Debye mass and hence the q-modified effective coupling are estimated for a quark–gluon system.

Simulation of 3D gas–solid fluidized bed reactor hydrodynamics

ABSTRACTIn this article, an attempt is made to develop a 3D gas–solid fluidized bed reactor (FBR). Basically, it deals with simulation of a FBR in computational fluid dynamics (CFD) using the software, Ansys Fluent v14. The simulation of gas–solid flow is carried out using Eulerian multifluid model which is integrated with the solid particle kinetic theory. The coefficients of exchange momentum are estimated using the Syamlal & O'Brien, Gidaspow, Wen-Yu, and Huilin–Gidaspow drag functions. The results of the simulation have been validated with the experimental data available in literature and had proven that the model is capable to predict the hydrodynamics of FBR. The variation in kinetic energy of the solid phase is calculated by varying the restitution coefficient (RC) from 0.90 to 0.99. The predictions of pressure drop compare excellently with the experimental data. Finally, the effect of particle diameter on the expanded bed height has been studied for FBR.

A Two-Way Coupled Model of Particle-Laden Turbulence

A model for turbulent suspensions involving two-way coupling between a liquid carrier phase and a solid dispersed phase is presented. Closure relations are obtained from particle kinetic theory, with both drag and virtual mass effects taken into account. It is shown that the feedback on the flow due to the particles mainly depends on the particle concentration, the characteristic Stokes numbers, and the density ratio between the particle and liquid phases. Over a broad parameter range, we find that drag coupling gives turbulence damping and an increased streaming velocity. Added mass coupling has the opposite effect. Some of the model predictions are compared with data given in the literature, and with PIV experimental data. It is found that the model is generally consistent with experiments; in particular, when it comes to the observed turbulence damping and drag reduction effects. The model can be used as a stand-alone tool to calculate turbulent stresses, mean velocities and concentration profiles of both phases. Alternatively, it can serve as basis for a reduced parametric model of particle feedback effects on; for example, the eddy viscosity, and thus the pressure drop and superficial speed.

Simulation of shock-powder interaction using kinetic theory of granular flow

Numerical simulation of the shock-powder interaction in a shock tube is carried out using the Eulerian-Eulerian approach, and special emphasis is placed on the particle phase behavior responding to the shock wave. The kinetic theory of granular flow is incorporated into the mathematical model of the compressible gas-particle flow. Since the particle phase pressure is provided by the kinetic theory, characteristics analysis demonstrates that the set of particle phase governing equations is a well-posed system, and the Roe scheme is then used in the numerical simulation process. The predicted results show that the particle phase is compressed by the shock wave, and the accumulation of particles increases the pressure of the particle phase. While, the reflected and transmitted shock waves are generated after the shock-powder interaction, the expansion waves in the particle powder show a decrease trend in the gas phase pressure. In addition, the passage of the shock wave gives rise to a sharp increase of the velocity slip between the gas phase and the particle phase. Performance of the particle kinetic theory in the present model is examined by the experimental data, which provides the numerical basis for implementing the particle kinetic theory in compressible multiphase flow problems.

On the modeling of crowd dynamics: An overview and research perspectives

This paper presents an overview of the mathematical approaches to modeling crowd dynamics by taking into account the complexity of living systems. The contents refer to the classical representation scales (microscopic, kinetic, and macroscopic) and to the mathematical frameworks that can be used for the modeling approach. The analysis focuses on the kinetic scale and, specifically, on developments of the mathematical kinetic theory of particles with heterogeneous behaviors. The existing literature is critically analyzed looking ahead to research perspectives and, more precisely, to a unified modeling strategy in view also of swarm dynamics modeling.

Numerical Simulation of Fluid Dynamics in a Two-Dimension Gas-Solid Bubbling Fluidized Bed

The process of bubbles from formation to eruption was simulated by using the two-fluid model combined with the particle kinetic theory to investigate the flow characterization of gas-solid in a bubbling fluidized bed. The velocity distributions of solid-phase in different axial height were also studied. The results show that the numerical simulation method can success simulates the flow characterization of gas-solid bubbling fluidized bed. The flow characterization in bubbling fluidized bed is circulating flow structure, while the central region is upward flow and the wall region is downward flow. The simulation results agree with the experiment results.

Steady flow of smooth, inelastic particles on a bumpy inclined plane: Hard and soft particle simulations

We study smooth, slightly inelastic particles flowing under gravity on a bumpy inclined plane using event-driven and discrete-element simulations. Shallow layers (ten particle diameters) are used to enable simulation using the event-driven method within reasonable computational times. Steady flows are obtained in a narrow range of angles (13 degrees-14.5 degrees); lower angles result in stopping of the flow and higher angles in continuous acceleration. The flow is relatively dense with the solid volume fraction, nu approximately 0.5 , and significant layering of particles is observed. We derive expressions for the stress, heat flux, and dissipation for the hard and soft particle models from first principles. The computed mean velocity, temperature, stress, dissipation, and heat flux profiles of hard particles are compared to soft particle results for different values of stiffness constant (k). The value of stiffness constant for which results for hard and soft particles are identical is found to be k>or=2x10(6) mg/d, where m is the mass of a particle, g is the acceleration due to gravity, and d is the particle diameter. We compare the simulation results to constitutive relations obtained from the kinetic theory of Jenkins and Richman [J. T. Jenkins and M. W. Richman, Arch. Ration. Mech. Anal. 87, 355 (1985)] for pressure, dissipation, viscosity, and thermal conductivity. We find that all the quantities are very well predicted by kinetic theory for volume fractions nu<0.5. At higher densities, obtained for thicker layers (H=15d and H=20d), the kinetic theory does not give accurate prediction. Deviations of the kinetic theory predictions from simulation results are relatively small for dissipation and heat flux and most significant deviations are observed for shear viscosity and pressure. The results indicate the range of applicability of soft particle simulations and kinetic theory for dense flows.

Double-bracket dissipation in kinetic theory for particles with anisotropic interactions

We derive equations of motion for the dynamics of anisotropic particles directly from the dissipative Vlasov kinetic equations, with the dissipation given by the double-bracket approach (double-bracket Vlasov, or DBV). The moments of the DBV equation lead to a non-local form of Darcy’s law for the mass density. Next, kinetic equations for particles with anisotropic interaction are considered and also cast into the DBV form. The moment dynamics for these double-bracket kinetic equations is expressed as Lie–Darcy continuum equations for densities of mass and orientation. We also show how to obtain a Smoluchowski model from a cold plasma-like moment closure of DBV. Thus, the double-bracket kinetic framework serves as a unifying method for deriving different types of dynamics, from density-orientation to Smoluchowski equations. Extensions for more general physical systems are also discussed.

A droplet transport model for channel and pipe flow based on particle kinetic theory and a stress– ω turbulence model

A model for droplet transport in turbulent gas–liquid flow in horizontal channels or pipes is developed. We invoke the kinetic theory of Reeks and co-workers for inertial particles, and the Reynolds stress– ω model of Wilcox for the gas turbulence. We introduce a suitable turbulence boundary condition at the gas–liquid interface. The full kinetic model is compared to experimental data using high density SF 6 gas and Exxsol oil, and the model gives a good prediction of the droplet distribution. A simplified “first order model” that adopts a diameter-averaged eddy diffusivity from the full turbulence model, and that ignores the variation of the turbulence over the cross section, gives reasonable order of magnitude estimates of the droplet concentration profiles. There is, however, a clear tendency to overestimate the droplet concentration near the interface (and hence the axial droplet transport rate). Furthermore, the classical single phase pipe flow diffusivity ( 0.075 Ru ∗ ) underestimates the averaged eddy diffusivity by a factor of about two (giving too small concentration and transport rate). The strength of the full kinetic model is that it correctly predicts a droplet diffusivity that accounts for the droplet inertia. This is important for the larger droplets close to the interface which contribute the most to the axial droplet transport rate. Hence, a simple eddy diffusivity will not correctly predict the droplet transport rate, since the droplet inertia is then ignored. The droplet concentration in the upper half of the flow volume is dominated by the smaller droplets, and these are in contrast subject to the scalar eddy diffusivity. An elevated concentration close to the upper wall may be accounted for by a double-vortex secondary flow perpendicular to the axial mean flow.

Thermal Conductivity Equations Based on Brownian Motion in Suspensions of Nanoparticles (Nanofluids)

Thermal conductivity equations for the suspension of nanoparticles (nanofluids) have been derived from the kinetic theory of particles under relaxation time approximations. These equations, which take into account the microconvection caused by the particle Brownian motion, can be used to evaluate the contribution of particle Brownian motion to thermal transport in nanofluids. The relaxation time of the particle Brownian motion is found to be significantly affected by the long-time tail in Brownian motion, which indicates a surprising persistence of particle velocity. The long-time tail in Brownian motion could play a significant role in the enhanced thermal conductivity in nanofluids, as suggested by the comparison between the theoretical results and the experimental data for the Al2O3-in-water nanofluids.

A second-order moment turbulence model for power law fluid with particles

The USM - θ model of power law fluid for dense two-phase turbulent flow was developed, which combines the unified second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. This model was used to simulate the turbulent flow of power law fluid single-phase in pipe. It is shown that the USM - θ model has better prediction result than the κ f - ɛ- f - k p - ɛ p - θ model. The USM - θ model was then used to simulate the dense two-phase turbulent up flow of power law fluid with particles. With the increase of the flow exponent, the velocities of power law fluid and particles increase near the pipe centre. Comparison between the two-phase flow of power law fluid-particle and of liquid-particle indicates that the axial fluctuation velocity of fluid phase and particle phase in liquid-particle two-phase flow is smaller than that in the power law fluid two-phase flow, but the two-phase velocities of power law fluid-particle and liquid-particle are close to each other.

Second-order moment model for dense two-phase turbulent flow of Bingham fluid with particles

The USM-ϑ model of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-ϑ model in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-ϑ model has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-ϑ model was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.

Long-time discrete particle effects versus kinetic theory in the self-consistent single-wave model

The influence of the finite number N of particles coupled to a monochromatic wave in a collisionless plasma is investigated. For growth as well as damping of the wave, discrete particle numerical simulations show an N-dependent long time behavior resulting from the dynamics of individual particles. This behavior differs from the one due to the numerical errors incurred by Vlasov approaches. Trapping oscillations are crucial to long time dynamics, as the wave oscillations are controlled by the particle distribution inhomogeneities and the pulsating separatrix crossings drive the relaxation towards thermal equilibrium.

Trapping oscillations, discrete particle effects and kinetic theory of collisionless plasma

Effects induced by the finite number N of particles on the evolution of a monochromatic electrostatic perturbation in a collisionless plasma are investigated. For growth as well as damping of a single wave, discrete particle numerical simulations show a N-dependent long-time behavior which differs from the numerical errors incurred by Vlasovian approaches and follows from the pulsating separatrix crossing dynamics of individual particles.

Kinetic Theory for Particles in Dilute and Dense Solid-Liquid Flows

This paper presents a kinetic theory for modeling the vertical profile of particle concentration in dilute and dense solid-liquid flow conditions. The kinetic theory properly describes the mechanism of suspended sediment transport over a wider range of conditions and gives more detailed microscopic information than previous theories. Experimental data have been measured using laser Doppler anemometry. The results are in agreement with measurements by Wang and Qian in 1989, Michalik in 1973, and Segré and Silberberg in 1962. The present work makes a special contribution in predicting the particle concentration distribution in a dense liquid-particle flow with reasonable accuracy.

Kinetic theory of particles and photons

Kinetic theory of particles and photons