Simple Kinetic Theory Research Articles

First-Principles Diffusivity Ratios for Kinetic Isotope Fractionation of Water in Air.

Kinetic isotope fractionation between water vapor and liquid water or ice depends on the ratio of the diffusivities of the isotopic species in air, but there is disagreement as to the values of these ratios and limited information about their temperature dependence. We use state-of-the-art intermolecular potential-energy surfaces for the water-nitrogen and water-oxygen pairs, along with the kinetic theory of molecular gases, to calculate from first principles the diffusivities of water isotopologues in air. The method has sufficient precision to produce accurate diffusivity ratios. For the HDO/H2O ratio, we find that the often used hard-sphere kinetic theory is significantly in error, and confirm the 1978 experimental result of Merlivat. For the ratios involving 17O and 18O, the simple kinetic theory is relatively close to our more rigorous results. We provide diffusivity ratios from 190 K to 500 K, greatly expanding the range of temperatures for which these ratios are available.

Sodium ion self-diffusion in molten NaBr probed over different length scales.

The single-particle dynamics of sodium ions in molten sodium bromide has been investigated with quasielastic neutron scattering. A detailed and rather extensive data analysis procedure allowed determination of the pure sodium ion dynamics with increasing wave vector. Two different evaluation procedures agree perfectly on the resulting diffusion coefficient of sodium ions on long distances. A simple kinetic theory based on binary collisions of hard spheres is not able to reproduce the sodium diffusion coefficient. The derived reduced linewidth from modeling with a Lorentzian spectral function decreases with increasing wave vector towards the first structure factor maximum. That deviation from the hydrodynamic behavior signals the hindrance of the microscopic diffusion process due to the so-called cage effect when microscopic length scales are probed in a dense fluid. The observed quadratic wave-number-dependent decrease might be evidence for a coupling to density fluctuations as the source of the changes in the diffusion process. The results indicate that in the molten salt NaBr near the melting point the self-diffusion process might be governed by similar processes as already observed in dense metallic liquids.

Mie scattering of phonons by point defects in IV-VI semiconductors PbTe and GeTe

Point defects in solids such as vacancy and dopants often cause large thermal resistance. Because the lattice site occupied by a point defect has a much smaller size than phonon wavelengths, the scattering of thermal acoustic phonons by point defects in solids has been widely assumed to be the Rayleigh scattering type. In contrast to this conventional perception, using an ab initio Green's function approach, we show that the scattering by point defects in PbTe and GeTe exhibits Mie scattering characterized by a weaker frequency dependence of the scattering rates and highly asymmetric scattering phase functions. These unusual behaviors occur because the strain field induced by a point defect can extend for a long distance much larger than the lattice spacing. Because of the asymmetric scattering phase functions, the widely used relaxation time approximation fails with an error of ~20% at 300 K in predicting lattice thermal conductivity when the vacancy fraction is 1%. Our results show that the phonon scattering by point defects in IV-VI semiconductors cannot be described by the simple kinetic theory combined with Rayleigh scattering.

Flow in AA and pA as an interplay of fluid-like and non-fluid like excitations

To study the microscopic structure of quark–gluon plasma, data from hadronic collisions must be confronted with models that go beyond fluid dynamics. Here, we study a simple kinetic theory model that encompasses fluid dynamics but contains also particle-like excitations in a boost invariant setting with no symmetries in the transverse plane and with large initial momentum asymmetries. We determine the relative weight of fluid dynamical and particle like excitations as a function of system size and energy density by comparing kinetic transport to results from the 0th, 1st and 2nd order gradient expansion of viscous fluid dynamics. We then confront this kinetic theory with data on azimuthal flow coefficients over a wide centrality range in PbPb collisions at the LHC, in AuAu collisions at RHIC, and in pPb collisions at the LHC. Evidence is presented that non-hydrodynamic excitations make the dominant contribution to collective flow signals in pPb collisions at the LHC and contribute significantly to flow in peripheral nucleus–nucleus collisions, while fluid-like excitations dominate collectivity in central nucleus–nucleus collisions at collider energies.

Nonequilibrium quark production in the expanding QCD plasma

We present real-time lattice simulation results for nonequilibrium quark production from an over-occupied gluon plasma in longitudinally expanding geometry. The quark number density per unit transverse area and rapidity shows almost linear growth in time, and its growth rate appears to be consistent with a simple kinetic theory estimate involving only two-to-two scattering processes in small-angle approximation. We also find that quarks produced at early times satisfy a nonequilibrium scaling law.

Microlayer evaporation during steam bubble growth

This paper presents analysis of the evaporation of the microlayer beneath a steam bubble growing at a heated surface. The microlayer depletion rate, and the associated evaporative heat flux, have been assessed using optical measurements of its thickness, and infrared measurements of the temperature of the solid surface beneath the bubble. Depletion of the liquid film is modelled from a molecular point of view, and comparison with measurements is attempted. A model of evaporation based on a simple kinetic theory representation of the molecular fluxes impinging on and emitted from a liquid surface is studied. From this, strong support is obtained for the hypothesis that only a fraction of impinging vapour molecules are absorbed by a liquid surface. The measurements suggest a value for the ‘accommodation coefficient’, of approximately 0.03 and a corresponding ‘effective evaporative heat transfer coefficient’, that are reasonably consistent with estimates from other workers.

Effective two-dimensional model for granular matter with phase separation.

Granular systems confined in vertically vibrated shallow horizontal boxes (quasi-two-dimensional geometry) present a liquid-to-solid phase transition when the frequency of the periodic forcing is increased. An effective model, where grains move and collide in two-dimensions is presented, which reproduces the aforementioned phase transition. The key element is that besides the two-dimensional degrees of freedom, each grain has an additional variable ɛ that accounts for the kinetic energy stored in the vertical motion in the real quasi-two-dimensional motion. This energy grows monotonically during free flight, mimicking the energy gained by collisions with the vibrating walls and, at collisions, this energy is instantaneously transferred to the horizontal degrees of freedom. As a result, the average values of ɛ and the kinetic temperature are decreasing functions of the local density, giving rise to an effective pressure that can present van der Waals loops. A kinetic theory approach predicts the conditions that must satisfy the energy growth function to obtain the phase separation, which are verified with molecular dynamics simulations. Notably, the effective equation of state and the critical points computed considering the velocity-time-of-flight correlations differ only slightly from those obtained by simple kinetic theory calculations that neglect those correlations.

Nonequilibrium quark production in the expanding QCD plasma

We perform real-time lattice simulations of nonequilibrium quark production in the longitudinally expanding QCD plasma. Starting from a highly occupied gluonic state with vacuum quark sector, we extract the time evolution of quark and gluon number densities per unit transverse area and rapidity. The total quark number shows after an initial rapid increase an almost linear growth with time. Remarkably, this growth rate appears to be consistent with a simple kinetic theory estimate involving only two-to-two scattering processes in small-angle approximation. This extends previous findings about the role of two-to-two scatterings for purely gluonic dynamics in accordance with the early stages of the bottom-up thermalization scenario.

Transport coefficients in high-temperature ionized air flows with electronic excitation

Transport coefficients are studied in high-temperature ionized air mixtures using the modified Chapman–Enskog method. The 11-component mixture N2/N2+/N/N+/O2/O2+/O/O+/NO/NO+/e−, taking into account the rotational and vibrational degrees of freedom of molecules and electronic degrees of freedom of both atomic and molecular species, is considered. Using the PAINeT software package, developed by the authors of the paper, in wide temperature range calculations of the thermal conductivity, thermal diffusion, diffusion, and shear viscosity coefficients for an equilibrium ionized air mixture and non-equilibrium flow conditions for mixture compositions, characteristic of those in shock tube experiments and re-entry conditions, are performed. For the equilibrium air case, the computed transport coefficients are compared to those obtained using simplified kinetic theory algorithms. It is shown that neglecting electronic excitation leads to a significant underestimation of the thermal conductivity coefficient at temperatures higher than 25 000 K. For non-equilibrium test cases, it is shown that the thermal diffusion coefficients of neutral species and the self-diffusion coefficients of all species are strongly affected by the mixture composition, while the thermal conductivity coefficient is most strongly influenced by the degree of ionization of the flow. Neglecting electronic excitation causes noticeable underestimation of the thermal conductivity coefficient at temperatures higher than 20 000 K.

Photoinduced Bimolecular Electron Transfer in Ionic Liquids.

The present work seeks to better understand the role of solute diffusion and solvation dynamics on bimolecular electron transfer in ionic liquids (ILs). Steady-state and time-resolved measurements of the reductive fluorescence quenching of five fluorophores ("F") by six quenchers ("Q"; electron donors) are reported in acetonitrile and two ionic liquids, 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide and trihexyl(tetradecyl)phosphonium bis(trifluoromethylsulfonyl)amide. Data were collected on 66 different F-Q-solvent systems, which span a 2.0 eV range in driving force and viscosities that vary 1000-fold, enabling stringent tests of bimolecular electron transfer models. A Stern-Volmer analysis yielded much larger diffusion-limited rates than simple kinetic theory predictions in the ILs and the absence of a Marcus turnover. Use of an approximate solution to the spherical diffusion-reaction equation enabled testing of several models for the reaction rate distance dependence. The Smoluchowski and Collins-Kimball models, which assume reaction at a single distance, are able to fit the data collected in acetonitrile solutions reasonably well, but not the data in the IL solvents. An extended sink model, incorporating a finite reaction zone, was able to fit all data satisfactorily with only three adjustable parameters. Diffusion coefficients extracted from these fits were much larger for the neutral versus anionic quenchers and close to predicted values. Molecular dynamics simulations and density-functional methods were then used to explore solvation structures and electronic couplings. The electronic coupling between contact F-Q pairs was found to vary strongly with the relative location and orientation of the reactants. Information from these simulations was used to constrain a model based on classical Marcus theory, which provided physically reasonable fits with only two adjustable parameters, but required systematic reduction of the driving forces in order to suppress a rate turnover at large driving force. The latter requirement indicates that reaction rates in ionic liquids are limited by some factor not properly accounted for in bimolecular electron transfer models based on a spherical diffusion-reaction approach. Small-amplitude motions within contact F-Q pairs, which gate the electronic coupling, are suggested to be the limiting dynamics.

Exploiting kinetics and thermodynamics to grow phase-pure complex oxides by molecular-beam epitaxy under continuous codeposition

Epitaxial perovskite oxide thin films and heterostructures are a highly active materials research topic generating both fundamental and applied interest. This manuscript reports the roles of oxidation kinetics and film deposition rate on the growth of phase-pure complex oxides by molecular-beam epitaxy, one of the premier techniques for these materials, in a regime that is traditionally described as being governed by thermodynamics. It is found that oxidation kinetics on the film surface are surprisingly important for the growth of PbTiO${}_{3}$ and for formulating a simple kinetic theory to interpret experimental observations. The results are also enlightening to predict the conditions for improved growth of BiFeO${}_{3}$ and other complex oxides by MBE, of high interest to the broad community studying oxide films and heterostructures.

Non‐equilibrium dynamics of open systems and fluctuation‐dissipation theorems

The Non‐Equilibrium Fluctuation‐Dissipation Theorem (NE FDT) is formulated within the Non‐Equilibrium Green Function (NEGF) formalism. The relation of this theorem to a simplified kinetic theory of non‐equilibrium dynamics of electrons in open quantum systems is discussed. The possibility of such a simplified description is first discussed on non‐equilibrium dynamics of the molecular bridge model represented by calculations of transient magnetic currents between two ferromagnetic electrodes linked by tunneling junctions to a molecular size island of an Anderson local center type. This model can be treated by using the full set of equations for NEGF, which can be solved numerically. This provides a reference framework for testing the possibility of a simpler and physically more transparent solution based on a Non‐Markovian Generalized Master Equation (GME) as an approximation of the full set of NEGF equations. The advantages and limitations of the use of the Generalized Kadanoff‐Baym Ansatz (GKBA) for this simplified description is demonstrated. The basic question is the range of applicability of this approximation. It turns out that for our specific model the decisive feature is the spectral structure of the tunneling functions of both electrodes and their positioning with respect to the island level depending on the bias and the exchange splitting. Finally, the relation of this simplified description to non‐equilibrium generalization of FDT is shown independently on the chosen model. The connection between the NEGF reconstruction equations and the non‐equilibrium version of FDT is introduced and the possible approximations of this general scheme are discussed.

Kinetic theory of discontinuous shear thickening

A simple kinetic theory to exhibit a discontinuous shear thickening (DST) is proposed. The model includes the collision integral and the friction from environment as well as a thermostat term characterized by $T_{\rm ex}$. The viscosity of this model is proportional to $\dot\gamma^2$ for large shear rate $\dot\gamma$, while it is Newtonian for low $\dot\gamma$. The emergence of the DST is enhanced for lower density and lower nonzero $T_{\rm ex}$.

Modification of kinetic theory of granular flow for frictional spheres, part II: Model validation

The hydrodynamics of a dense solid–gas fluidized bed is studied, using a two fluid model (TFM) based on our newly developed kinetic theory of granular flow (KTGF) for rotating rough particles. The TFM simulations are validated by comparing with PIV-DIA experimental data (Buist et al., 2014) and results obtained from discrete particle model (DPM) simulations of the bubbling fluidized bed. The TFM model predictions agree well with the experimental results for the time-averaged particle axial velocity and solids volume fraction. The predicted levels of the translational granular temperatures and solids circulation patterns compare reasonably well with the results obtained from the DPM simulations. The predicted rotational granular temperature in our TFM simulations shows an almost uniform distribution in the bed as a result of the assumptions that both the local mean rotational velocity and the gradient of the rotational granular temperature at the wall are zero, indicating directions for future improvement. A comparison between TFM simulations using the present KTGF model, and a more simple kinetic theory for rapid flow of slightly frictional, nearly elastic spheres derived by Jenkins and Zhang (2002), is carried out to investigate the influence of particle friction in the fluidized bed. The present KTGF model leads to better agreement with DPM simulations and experimental results for the axial particle velocity profiles and solids volume fraction distribution.

Spin Superfluidity in the ν=0 Quantum Hall State of Graphene.

Strong electron interactions can lead to a variety of broken-symmetry phases in monolayer graphene. In the quantum Hall regime, the interaction effect are enhanced by the formation of highly degenerate Landau levels, catalyzing the emergence of such phases. Recent magnetotransport studies show evidence that the ν=0 quantum Hall state of graphene is in an insulating canted antiferromagnetic phase with the Néel vector lying within the graphene plane. Here, we show that this Néel order can be detected via two-terminal spin transport. We find that a dynamic and inhomogeneous texture of the Néel vector can mediate nearly dissipationless (superfluid) transport of spin angular momentum polarized along the z axis, which could serve as a strong support for the antiferromagnetic scenario. The injection and detection of spin current in the ν=0 region can be achieved using the two spin-polarized edge channels of the |ν|=2 quantum Hall state. Measurements of the dependence of the spin current on the length of the ν=0 region would provide direct evidence for spin superfluidity.

Cellular softening mediates leukocyte demargination and trafficking, thereby increasing clinical blood counts

Leukocytes normally marginate toward the vascular wall in large vessels and within the microvasculature. Reversal of this process, leukocyte demargination, leads to substantial increases in the clinical white blood cell and granulocyte count and is a well-documented effect of glucocorticoid and catecholamine hormones, although the underlying mechanisms remain unclear. Here we show that alterations in granulocyte mechanical properties are the driving force behind glucocorticoid- and catecholamine-induced demargination. First, we found that the proportions of granulocytes from healthy human subjects that traversed and demarginated from microfluidic models of capillary beds and veins, respectively, increased after the subjects ingested glucocorticoids. Also, we show that glucocorticoid and catecholamine exposure reorganizes cellular cortical actin, significantly reducing granulocyte stiffness, as measured with atomic force microscopy. Furthermore, using simple kinetic theory computational modeling, we found that this reduction in stiffness alone is sufficient to cause granulocyte demargination. Taken together, our findings reveal a biomechanical answer to an old hematologic question regarding how glucocorticoids and catecholamines cause leukocyte demargination. In addition, in a broader sense, we have discovered a temporally and energetically efficient mechanism in which the innate immune system can simply alter leukocyte stiffness to fine tune margination/demargination and therefore leukocyte trafficking in general. These observations have broad clinically relevant implications for the inflammatory process overall as well as hematopoietic stem cell mobilization and homing.

CFD study of mixing and segregation in CFB risers: Extension of EMMS drag model to binary gas–solid flow

The Energy Minimization Multi-Scale (EMMS) drag model, using Sauter mean particle diameter to represent real particle size distribution, has proven to be effective in improving the accuracy of continuum modeling of gas–solid flow. Nevertheless, mixing and segregation characteristics in circulating fluidized bed (CFB) risers are very important in many situations, which necessitates the explicit consideration of the effects of particle size distribution on the bed hydrodynamics. To this end, an attempt is made to extend the EMMS drag model to binary gas–solid system, where four input parameters that can be obtained from computational fluid dynamics (CFD) simulation, including two slip velocities between gas and each particle phase and two particle concentrations of each phase, are used to solve the proposed EMMS drag model. Heterogeneous indexes, which are used to modify the drag correlation obtained from homogeneous fluidization, are then predicted and fed into multifluid model (MFM) to predict the dynamical behavior of mixing and segregation of binary gas–solid flow in a CFB riser. The effects of different drag force models, kinetic theories and particle–particle drag force models are also systematically evaluated. It was shown that (i) MFM with the proposed EMMS drag model and the kinetic theory developed by Chao et al. (Chemical Engineering Science 2011, 66: 3605–3616) is able to correctly predict the mixing and segregation pattern in the studied riser, while MFM with homogenous drag forces and the simplified kinetic theory available in commercial software FLUENT completely fails; and (ii) with or without particle–particle drag force has a substantial influence upon the particle behavior.

Memory effects in the relaxation of a confined granular gas.

The accuracy of a model to describe the horizontal dynamics of a confined quasi-two-dimensional system of inelastic hard spheres is discussed by comparing its predictions for the relaxation of the temperature in a homogenous system with molecular dynamics simulation results for the original system. A reasonably good agreement is found. Next the model is used to investigate the peculiarities of the nonlinear evolution of the temperature when the parameter controlling the energy injection is instantaneously changed while the system was relaxing. This can be considered as a nonequilibrium generalization of the Kovacs effect. It is shown that, in the low-density limit, the effect can be accurately described by using a simple kinetic theory based on the first Sonine approximation for the one-particle distribution function. Some possible experimental implications are indicated.

Active microrheology of driven granular particles.

When pulling a particle in a driven granular fluid with constant force Fex, the probe particle approaches a steady-state average velocity v. This velocity and the corresponding friction coefficient of the probe ζ=Fex/v are obtained within a schematic model of mode-coupling theory and compared to results from event-driven simulations. For small and moderate drag forces, the model describes the simulation results successfully for both the linear as well as the nonlinear region: The linear response regime (constant friction) for small drag forces is followed by shear thinning (decreasing friction) for moderate forces. For large forces, the model demonstrates a subsequent increasing friction in qualitative agreement with the data. The square-root increase of the friction with force found in [Fiege et al., Granul. Matter 14, 247 (2012)] is explained by a simple kinetic theory.

Phonon mean free path of graphite along thec-axis

Phonon transport in the c-axis direction of graphite thin films has been studied using non-equilibrium molecular dynamics (MD) simulation. The simulation results show that the c-axis thermal conductivities for films of thickness ranging from 20 to 500 atomic layers are significantly lower than the bulk value. Based on the MD data, a method is developed to construct the c-axis thermal conductivity as an accumulation function of phonon mean free path (MFP), from which we show that phonons with MFPs from 2 to 2000 nm contribute ∼80% of the graphite c-axis thermal conductivity at room temperature, and phonons with MFPs larger than 100 nm contribute over 40% to the c-axis thermal conductivity. These findings indicate that the commonly believed value of just a few nanometers from the simple kinetic theory drastically underestimates the c-axis phonon MFP of graphite.