Nonequilibrium Velocity Research Articles

Analytical irreversible thermodynamics in conduction-radiative heat transfer of neutral gases through a lens of thermal radiation fields

An analytical investigation has been conducted on the steady-state conduction and a diluted gas exposed to a thermal radiation field experiences radiative heat transfer. Analytical solutions have been derived for the transport Boltzmann BGK partial differential equations system. The investigation delves into the irreversible thermodynamic behavior of the system through the utilization of the Liu-Lees model, which employs two-stream Maxwellian distribution functions. The moment approach is utilized to predict the behavior of macroscopic gas parameters like temperature, concentration, and Fourier heat flux. This process entails substituting these parameters into the two-stream Maxwellian distribution functions to analyze the system's non-equilibrium thermodynamic characteristics, which encompass gas particles and the heated plate. Through this analysis, kinetic coefficients, entropy, entropy flux, entropy production, and thermodynamic forces are determined. The investigation assesses the validation of Onsager's reciprocity relation, the Boltzmann H-theorem, the Le Chatelier principle, and the second law of thermodynamics within the system. Furthermore, the Gibbs formula is employed to estimate the ratios between various contributions to internal energy changes, which are determined by the total derivatives of extensive parameters. The non-equilibrium velocity distribution function was calculated for the first time, and its behavior was compared with that of the equilibrium one using 3D graphics. The behavior of the computed variables is predicted through graphical analysis and discussion of the results.

High-order relaxation methods for nonequilibrium two-phase flow equations

PurposeThe purpose of this paper is to investigate the two-phase flow problems involving gas–liquid mixture.Design/methodology/approachThe governed equations consist of a range of conservation laws modeling a classification of two-phase flow phenomena subjected to a velocity nonequilibrium for the gas–liquid mixture. Effects of the relative velocity are accounted for in the present model by a kinetic constitutive relation coupled to a collection of specific equations governing mass and volume fractions for the gas phase. Unlike many two-phase models, the considered system is fully hyperbolic and fully conservative. The suggested relaxation approach switches a nonlinear hyperbolic system into a semilinear model that includes a source relaxation term and characteristic linear properties. Notably, this model can be solved numerically without the use of Riemann solvers or linear iterations. For accurate time integration, a high-resolution spatial reconstruction and a Runge–Kutta scheme with decreasing total variation are used to discretize the relaxation system.FindingsThe method is used in addressing various nonequilibrium two-phase flow problems, accompanied by a comparative study of different reconstructions. The numerical results demonstrate the suggested relaxation method’s high-resolution capabilities, affirming its proficiency in delivering accurate simulations for flow regimes characterized by strong shocks.Originality/valueWhile relaxation methods exhibit notable performance and competitive features, as far as we are aware, there has been no endeavor to address nonequilibrium two-phase flow problems using these methods.

Subnanosecond Reconfiguration of Ferroelectric Domains in Bismuth Ferrite.

Domain switching is crucial for achieving desired functions in ferroic materials that are used in various applications. Fast control of domains at subnanosecond timescales remains a challenge despite its potential for high-speed operation in random-access memories, photonic, and nanoelectronic devices. In this work, ultrafast laser excitation is shown to transiently melt and reconfigure ferroelectric stripe domains in multiferroic bismuth ferrite on a timescale faster than 100ps. This dynamic behavior is visualized by picosecond- and nanometer-resolved X-ray diffraction measurements as well as time-resolved X-ray diffuse scattering. The disordering of stripe domains is attributed to the screening of depolarization fields by photogenerated carriers resulting in the formation of charged domain walls, as supported by phase field simulations. Furthermore, the recovery of disordered domains exhibits subdiffusive growth on nanosecond timescales, with a nonequilibrium domain velocity reaching up to 10 m/s. These findings present a new approach to image and manipulate ferroelectric domains on subnanosecond timescales, which can be further extended into other photoferroic systems to modulate their electronic, optical, and magnetic properties beyond GHz frequencies. This approach could pave the way for high-speed ferroelectric data storage, computing and photonic applications in a range of photoferroics, and, more broadly, defines new approaches for visualizing the non-equilibrium dynamics of heterogeneous and disordered materials. This article is protected by copyright. All rights reserved.

The Effects of Nonequilibrium Velocity Distributions on Alfvén Ion-cyclotron Waves in the Solar Wind

In this work, we investigate how the complex structure found in solar wind proton velocity distribution functions (VDFs), rather than the commonly assumed two-component bi-Maxwellian structure, affects the onset and evolution of parallel-propagating microinstabilities. We use the Arbitrary Linear Plasma Solver, a numerical dispersion solver, to find the real frequencies and growth/damping rates of the Alfvén modes calculated for proton VDFs extracted from Wind spacecraft observations of the solar wind. We compare this wave behavior to that obtained by applying the same procedure to core-and-beam bi-Maxwellian fits of the Wind proton VDFs. We find several significant differences in the plasma waves obtained for the extracted data and bi-Maxwellian fits, including a strong dependence of the growth/damping rate on the shape of the VDF. By applying the quasilinear diffusion operator to these VDFs, we pinpoint resonantly interacting regions in velocity space where differences in VDF structure significantly affect the wave growth and damping rates. This demonstration of the sensitive dependence of Alfvén mode behavior on VDF structure may explain why the Alfvén ion-cyclotron instability thresholds predicted by linear theory for bi-Maxwellian models of solar wind proton background VDFs do not entirely constrain spacecraft observations of solar wind proton VDFs, such as those made by the Wind spacecraft.

Instability of Langmuir-beam waves: Kappa-distributed electrons

In space plasmas, electron populations exhibit non-equilibrium velocity distributions with high-energy tails that are reproduced by the Kappa power-laws and contrast with the Maxwellian distributions often used in theoretical and numerical analyses. In this work, we investigate typical electron beam-plasma systems and show the influence of Kappa tails on the linear dispersion and stability spectra of Langmuir-beam waves. The most common scenarios invoke instabilities of Langmuir waves at the origin of radio emissions in solar flares and interplanetary shocks. However, the parametric domain of these instabilities is narrow (i.e., energetic beams but with very low density, nb/ne≲10−3), making their analytical and numerical characterization not straightforward, while the approximations used may lead to inconclusive results. Here, we provide exact numerical solutions of the Langmuir-beam mode, which distinguish from the classical ones (unaffected by the beam), and also from electron beam modes destabilized by more energetic and/or denser beams. Langmuir-beam solutions are only slightly modified by the Kappa distribution of the beam component, due to its very low density. However, if the main (core) population is Kappa distributed, the instability of the Langmuir-beam mode is strongly inhibited, if not suppressed. New analytical solutions are derived taking into account the more or less resonant involvement of the electron core and beam populations. As a result, the analytical solutions show an improved match with the exact solutions, making them applicable in advanced modeling of weak (weakly nonlinear) turbulence.

Quadrature-based moment methods for kinetic plasma simulations

Quadrature-based moment methods (QBMM) are applied to rarefied gas flow and plasma physics problems represented by the Boltzmann equation or the Vlasov-Poisson system of equations. QBMM are a computationally advantageous alternative to both direct Eulerian and Lagrangian particle solvers, able to provide a noise-free solution to the Boltzmann equation and capture non-equilibrium velocity distribution functions (VDF) without excessive computational cost. To provide a closure of the moment equations, the VDF is assumed to be represented by the sum of weighted kernel functions that are placed at given velocity abscissas. Three QBMM approaches, QMOM (Dirac delta kernels), HyQMOM (hyperbolic QMOM), and EQMOM (Gaussian kernels), are applied to canonical one-dimensional rarefied gas flow and plasma physics problems. A new algorithm for EQMOM that is able to treat pathological VDFs and provide control over large abscissas for more than two nodes is developed. QMOM and EQMOM are suitable for problems where the flow does not have shock-like features (for QMOM) or a discontinuity in the VDF (for EQMOM) and where the VDF is far from non-equilibrium and features strong phase-mixing. HyQMOM is generally applicable to all test problems and yields good representations of both the moments and the VDF. HyQMOM also provides significant wall-time improvement (factor of 10–100) compared to other direct Eulerian solvers.

The Mott-Smith solution to the regular shock reflection problem

The classical Mott-Smith solution for one-dimensional normal shock wave structure is extended to the two-dimensional regular shock reflection problem. The solution for the non-equilibrium molecular velocity distribution function along the symmetry-plane streamline is obtained as a weighted sum of four Maxwellians. An analysis of applicability of the solution has been performed using the results of direct simulation Monte Carlo calculations for a range of incident shock wave intensities. Accuracy of the solution improves with increasing$Ma_n$, the Mach number normal to the shock front, so that the solution becomes rather accurate for strong shocks with$Ma_n>8$.

Effects of inter-pulse coupling on nanosecond pulsed high frequency discharge ignition in a flowing mixture

This work numerically investigates the effects of non-equilibrium nanosecond plasma discharge pulse repetition frequency, pulse number, and flow velocity on the critical ignition volume, minimum ignition energy, and chemistry in a plasma-assisted H2/air flow at 300 K and 1 atm using a multi-scale adaptive reduced chemistry solver for plasma assisted combustion (MARCS-PAC). The interactions between discharges/ignition kernels spanning decoupled, partially-coupled and fully-coupled regimes in a pulse train are studied. For a single pulse discharge, increased flow velocity increases the minimum ignition energy required due to the increase of convective heat loss and flame stretch. The results show that the minimum ignition kernel propagation speed at the critical ignition kernel volume increases with the flow velocity. The minimum critical ignition volume decreases with the increase of plasma discharge energy. For sequential two-pulse discharges, ignition fails at both decoupled and partially-coupled regimes even when the total discharge energy is above the minimum ignition energy, but succeeds only in the fully-coupled regime at a shorter inter-pulse time. Overlap of the OH radical pool between the sequential two-pulse discharges and the increase of the chemistry effect due to the increase of reduced electric field in the fully-coupled regime contribute to the ignition enhancement. In addition, for two-pulse discharges in the fully-coupled discharge regime, the mixture can be ignited at a total energy below the minimum ignition energy of a single pulse with the same flow conditions. Moreover, for a given total discharge energy with multiple pulsed discharges, the enhancement of the ignition kernel volume has a non-monotonic dependence on discharge frequency and pulse number. The effective ignition enhancement can be achieved with an optimal pulse repetition frequency and pulse number. This work provides a new understanding of the mechanism for repetitive plasma ignition and insights for the optimization of plasma ignition in a reactive flow.

Kinetic and thermodynamic examinations for the unsteady couette flow problem of a plasma using the BGK cylindrical model

We aim to investigate the kinetic and irreversible thermodynamic treatment of the Couette flow of gaseous plasma (GP) confined between two coaxial rotating circular rigid cylinders. The Bhatnagar-Gross-Krook (BGK) model of the Boltzmann kinetic equation (BKE) is solved by applying the perturbation method coupled with the moments' approach with a two-stream Maxwellian distribution function (MDF). Nonlinear partial differential equations are precisely solved. As an actual application, we are considering the laboratory Argon GP. An interesting comparison between the non-equilibrium electron velocity distribution function (EVDF) and the equilibrium EVDF is made carefully with 3-Dimensional graphics in various time values. We found that the system goes to an equilibrium state (ES) with time compatible with Le Chatelier's principles. Moreover, we determined with very high precision the value of the system equilibrium time, which is tequ.≅2.4. That great advantage cannot be reached by solving other macroscopic magnetohydrodynamic models. The relations between the various macroscopic variables of the GP are studied. The irreversible non-equilibrium thermodynamics (NT) properties of the system are presented. We present the extended Gibbs equation (EGE) for the internal energy variation (IEV) in cylindrical geometry for GP for the first time, to the best of our knowledge. We have shown that our model is compatible with the H-theorem of Boltzmann and the Onsager-Casimir relations. The various participations in IEV are introduced. The significance of this search is due to its vast implementations in various fields, such as in GP physics, electrical engineering, medicine, biological systems, and numerous commercial and industrial deployments.

Local non-equilibrium phase density reconstruction with Grad and Chapman-Enskog methods

The study of the non-equilibrium velocity gas distribution function reconstruction was carried out due to extended gas dynamics methods. The bimodal Mott-Smith solution for a plane shock wave was used as a reference distribution function. The shock-wave solutions were considered in the range of Mach numbers from Ma = 2.0 to Ma = 8.0. The reconstruction of the original function was carried out using the Navier-Stokes-Fourier, 13-moment, regularized 13-moment and 26-moment approximating functions.

2D particle-in-cell simulations of the electron temperature anisotropy driven whistler instability in plasmas having kappa velocity distributions

This study presents the results of 2D particle-in-cell (PIC) simulations of the electron temperature anisotropy driven whistler instability for plasmas in which the electron species is modeled by a bi-kappa velocity distribution. These simulations utilize our previously developed method to generate the initial multi-dimensional kappa velocity distributions. The use of multi-dimensional kappa loadings in PIC simulations provides insights into the non-linear regime of wave evolution in plasmas having non-equilibrium velocity distributions. Three cases are considered, corresponding to κe=2,3, and ∞ (Maxwellian case). Owing to the use of a large value of electron anisotropy required for reasonable simulation run times, the Maxwellian electron run has the fastest growth rate, reaching saturation earliest. The κe=2 case exhibits the slowest growth rate. Spectral analysis of the fluctuating fields reveals considerable wave intensity at frequencies and wavenumbers that satisfy the linear whistler wave dispersion relation. In the runs with kappa distributions, the regions of most intense fluctuations comprise frequencies and wavenumbers that agree only qualitatively with linear whistler wave theory. The results suggest that after saturation, there is some degree of Landau damping of the oblique whistler modes, which returns energy to the electron species. The rate of damping of the oblique modes is highest in the Maxwellian case and lowest for κe=2. Evidence of significant superthermal acceleration of electrons in the direction parallel to the ambient magnetic field is also observed. Thus, the power-law index of the electron distribution is reduced by the anisotropic whistler turbulence produced.

A measurement system of the nonequilibrium velocity distributions of evaporating molecules from liquid-vapor interfaces pinned at a nanoporous surface

A measurement system of the nonequilibrium velocity distributions of evaporating molecules from liquid-vapor interfaces pinned at a nanoporous surface

Hydrodynamic and Thermodynamic Nonequilibrium Effects around Shock Waves: Based on a Discrete Boltzmann Method.

A shock wave that is characterized by sharp physical gradients always draws the medium out of equilibrium. In this work, both hydrodynamic and thermodynamic nonequilibrium effects around the shock wave are investigated using a discrete Boltzmann model. Via Chapman–Enskog analysis, the local equilibrium and nonequilibrium velocity distribution functions in one-, two-, and three-dimensional velocity space are recovered across the shock wave. Besides, the absolute and relative deviation degrees are defined in order to describe the departure of the fluid system from the equilibrium state. The local and global nonequilibrium effects, nonorganized energy, and nonorganized energy flux are also investigated. Moreover, the impacts of the relaxation frequency, Mach number, thermal conductivity, viscosity, and the specific heat ratio on the nonequilibrium behaviours around shock waves are studied. This work is helpful for a deeper understanding of the fine structures of shock wave and nonequilibrium statistical mechanics.

A 14-moment maximum-entropy description of electrons in crossed electric and magnetic fields

A 14-moment maximum-entropy system of equations is applied to the description of non-equilibrium electrons in crossed electric and magnetic fields and in the presence of low collisionality, a characteristic of low-temperature plasma devices. The flexibility of this formulation is analyzed through comparison with analytical results for steady-state non-equilibrium velocity distribution functions and against particle-based solutions of the time-dependent kinetic equation. Electric and magnetic source terms are derived for the 14-moment equations, starting from kinetic theory. A simplified collision term based on the Bhatnagar–Gross–Krook operator is formulated to describe the collision of electrons with background neutrals, accounting for the large mass disparity and energy exchange. An approximated expression is proposed for the collision frequency, to include the effect of the electrons' drift velocity, showing good accuracy in the considered conditions. The capabilities of the proposed 14-moment closure to accurately capture the non-equilibrium behavior of electrons for space homogeneous problems under conditions representative of those found in Hall thrusters are demonstrated.

Study of regular reflection shock waves using a mesoscopic kinetic approach: Curvature pattern and effects of viscosity

The physical characteristics inside shock waves with nonequilibrium molecular motion are difficult to describe using conventional macroscopic methods. In this paper, nonequilibrium hydrodynamic and thermodynamic effects caused by the strong nonequilibrium molecular velocity distribution at a shock wave are studied using a mesoscopic kinetic approach. This approach is based on a lattice Boltzmann method and a kinetic nonequilibrium method. The former adopts a compressible double-distribution-function model with separated density and total energy distribution functions. The latter represents the nonequilibrium effects through nonequilibrium kinetic moments based on the nonequilibrium molecular velocity distribution. The nonequilibrium effects in the steady state and the process of the formation of a regular reflection shock wave are presented. Nonequilibrium effects inside the shock wave are further investigated. First, the curvature pattern during the formation of a regular reflection shock wave is addressed. The curvature characteristic leads to distinct features of nonequilibrium effects compared with the linear pattern. A vector-based approach for visualizing nonequilibrium effects is proposed to study the curvature pattern. Second, the influence of viscosity on nonequilibrium effects, which is related to the average collision time among molecules at the shock wave, is explored. The results obtained in this paper provide mesoscopic physical insight into the flow mechanisms occurring in shock waves.

Temperature relaxation in binary hard-sphere mixture system: Molecular dynamics and kinetic theory study.

Computational schemes to describe the temperature relaxation in the binary hard-sphere mixture system are given on the basis of molecular dynamics (MD) simulation and renormalized kinetic theory. Event-driven MD simulations are carried out for three model systems in which the initial temperatures and the ratios of diameter and mass of two components are different to study the temporal evolution of each component temperature in nanoscale molecular conditions mimicking those in living cells. On the other hand, the temperature changes of the two components are also described in terms of a mean-field kinetic theory with the correlation functions calculated in the Percus-Yevick approximation. The calculated results by both the computational approaches have shown fair agreement with each other, whereas slight deviations have been found in the temporal range of femto- to picoseconds when the initial temperatures of the two components are significantly different, such as 300 K vs 1000 K. This discrepancy can be ascribed to the fast intra-component temperature relaxation assumed in the kinetic theory, and its violation in the MD simulations can be evaluated in terms of the Kullback-Leibler divergence between the equilibrated Maxwell-Boltzmann distribution at each temperature and the actual non-equilibrium velocity distribution realized in the MD. Thus, the present analysis provides a quantitative basis for addressing the temperature inhomogeneities experimentally observed in nanoscale crowding conditions.

On the dynamics of Richtmyer–Meshkov bubbles in unstable three-dimensional interfacial coherent structures with time-dependent acceleration

Richtmyer–Meshkov instability (RMI) plays an important role in many areas of science and engineering, from supernovae and fusion to scramjets and nano-fabrication. Classical RMI is induced by a steady shock and impulsive acceleration, whereas in realistic environments, the acceleration is usually variable. We focus on RMI induced by acceleration with power-law time-dependence and apply group theory to study the dynamics of regular bubbles. For early time linear dynamics, we find the dependence of the growth rate on the initial conditions and show that it is independent of the acceleration parameters. For late-time nonlinear dynamics, we consider regular asymptotic solutions, find a continuous family of such solutions, including their curvature, velocity, Fourier amplitudes, and interfacial shear, and study their stability. For each solution, the interface dynamics is directly linked to the interfacial shear. The non-equilibrium velocity field has intense fluid motion near the interface and effectively no motion in the bulk. The quasi-invariance of the fastest stable solution suggests that the dynamics of nonlinear RM bubbles is characterized by two macroscopic length scales: the wavelength and the amplitude, in agreement with observations. The properties of a number of special solutions are outlined. These are the flat Atwood bubble, the curved Taylor bubble, the minimum shear bubble, the convergence limit bubble, and the critical bubble. We elaborate new theory benchmarks for future experiments and simulations.

Domain wall dynamics due to femtosecond laser-induced superdiffusive spin transport

Manipulation of magnetic domain walls via a helicity-independent laser pulse has recently been experimentally demonstrated and various physical mechanisms leading to domain wall dynamics have been discussed. Spin-dependent superdiffusive transport of hot electrons has been identified as one of the possible ways how to affect a magnetic domain wall. Here, we develop a model based on superdiffusive spin-dependent transport to study the laser-induced transport of hot electrons through a smooth magnetic domain wall. We show that the spin transfer between neighboring domains can enhance ultrafast demagnetization in the domain wall. More importantly, our calculations reveal that when the laser pulse is properly focused on to the vicinity of the domain wall, it can excite sufficiently strong spin currents to generate a spin-transfer torque that can rapidly move the magnetic domain wall by several nanometers in several hundreds of femtoseconds, leading to a huge nonequilibrium domain wall velocity.

Richtmyer–Meshkov dynamics with variable acceleration by group theory approach

Richtmyer–Meshkov instability (RMI) plays an important role in nature and technology, including supernovae, fusion, scramjets and nano-fabrication. Canonical RMI is induced by a steady shock and impulsive acceleration. In realistic environments the acceleration is often variable. We focus on the accelerations with power-law time-dependence, identify the values of the power-law exponent for which the dynamics is Richtmyer–Meshkov type, and apply group theory to solve the long-standing problem of RMI with variable acceleration. For early-time dynamics, we find that the RMI growth-rate depends on the initial conditions and not on the acceleration parameters. For late-time dynamics, we find a continuous family of regular asymptotic solutions, including their curvature, velocity, Fourier amplitudes, and interfacial shear function, and we study stability of these solutions. For each solution, the interface dynamics is set by the interfacial shear; the non-equilibrium velocity field has effectively no motion in the bulk and intense motion near the interface. The fastest stable solution in the family has the flattened front and the quasi-invariance property suggesting the multi-scale character of nonlinear dynamics in RMI. Our results agree with available observations and elaborate new benchmarks for future studies.

Propagating modes in a binary liquid mixture under thermal stress.

Nonequilibrium temperature and concentration fluctuations inside a binary liquid mixture under the action of a temperature gradient relax back to equilibrium either due to conduction and diffusion at large wave numbers, or due to the quenching determined by gravity at small wave numbers. We investigate the dynamics of nonequilibrium fluctuations in a binary liquid mixture of polystyrene and toluene heated from above under stationary conditions in a thermodiffusion experiment. We show that the strong gravitational stabilization at small wave numbers determines the appearance of propagating modes of nonequilibrium fluctuations as detected through the structure function of shadowgraph images. The propagating modes are the combined effect of temperature and velocity nonequilibrium fluctuations induced by the buoyancy force. The experimental results are in good agreement with a fluctuating hydrodynamics theroretical model including the coupling of fluctuations of velocity, temperature and concentration.