纳米通道内气体剪切流动的分子动力学模拟

采用分子动力学模拟方法研究了表面力场对纳米通道内气体剪切流动的影响规律.结果显示通道内的气体流动分为两个区域:受壁面力场影响的近壁区域和不受壁面力场影响的主流区域.近壁区域内,气体流动特性和气体动力学理论预测差别很大,密度和速度急剧增大并出现峰值,正应力变化剧烈且各向异性,剪切应力在距壁面一个分子直径处出现突变.主流区域的气体流动特性与气体动力学理论预测相符合,该区域内的密度、正应力与剪切应力均为恒定值,速度分布亦符合应力-应变的线性响应关系.不同通道高度及密度下,近壁区域的归一化密度、速度及应力分布一致,表明近壁区域的气体流动特性仅由壁面力场所决定.随着壁面对气体分子势能作用的增强,气体分子在近壁区域的密度和速度随之增大,直至形成吸附层,导致速度滑移消失.通过剪切应力与切向动量适应系数(TMAC)的关系,得到不同壁面势能作用下的TMAC值,结果表明壁面对气体分子的势能作用越强,气体分子越容易在壁面发生漫反射.     

A kinetic theory of dense fluids

A new kinetic equation is developed which incorporates the desirable features of the Enskog, the Rice-Allnatt, and the Prigogine-Nicolis-Misguich kinetic theories of dense fluids. Advantages of the present theory over the latter three theories are (1) it yields the correct local equilibrium hydrodynamic equations, (2) unlike the Rice-Allnatt theory, it determines the singlet and doublet distribution functions from the same equation, and (3) unlike the Prigogine-Nicolis-Misguich theory, it predicts the kinetic and kinetic-potential transport coefficients. The kinetic equation is solved by the Chapman-Enskog method and the coefficients of shear viscosity, bulk viscosity, thermal conductivity, and self-diffusion are obtained. The predicted bulk viscosity and thermal conductivity coefficients are singular at the critical point, while the shear viscosity and self-diffusion coefficients are not.     

Boundary conditions for regularized 13-moment-equations for micro-channel-flows

Boundary conditions are the major obstacle in simulations based on advanced continuum models of rarefied and micro-flows of gases. In this paper, we present a theory how to combine the regularized 13-moment-equations derived from Boltzmann’s equation with boundary conditions obtained from Maxwell’s kinetic accommodation model. While for the linear case these kinetic boundary conditions suffice, we need additional conditions in the non-linear case. These are provided by the bulk solutions obtained after properly transforming the equations while keeping their asymptotic accuracy with respect to Boltzmann’s equation.After finding a suitable set of boundary conditions and equations, a numerical method for generic shear flow problems is formulated. Several test simulations demonstrate the stable and oscillation-free performance of the new approach.     

Kinetic equations for exactly solvable models of geminate reactions in the presence of scavengers

The kinetic equations for an exactly solvable scavenger problem were presented in the form of the equation of general kinetic theory. Presenting the memory function as the sum of Markovian and non-Markovian parts yielded a binary approximation corresponding to low scavenger concentrations. It was demonstrated that the bulk channel of the formation of product D can be separated into two subchannels: the reaction of a scavenger C with the reactant B that left a geminate pair AB for the bulk solution (bulk subchannel) and with the reactant B that retains a spatial correlation with the reactant A (geminate subchannel). Note that the geminate subchannel of the D-channel and the geminate subchannel of the formation of product P are of three-particle nature, and, therefore, their rates cannot be expressed through the relative mobilities of the reactants in pairs BC and AB. The obtained equations of general kinetic theory were transformed so as to impart them the regular form of the rate equations accepted in chemistry, with a bulk reaction rate constant and nonuniform terms (sources) associated with the initial spatial correlations between the reactants. Nevertheless, these equations differ substantially from those reported in the literature.     

Application of vortex sound theory to vortex-pairing noise: sensitivity to errors in flow data

Aeroacoustical analogies allow one to extract acoustical information from limited information about the flow. In the particular case of low Mach number compact flows, vortex sound theory has been quite successful. In the present paper, different formulations of the vortex sound theory are compared on the basis of their ability to provide realistic results for vortex-pairing sound when approximate flow models are used. In particular, these theories do not perform equally well when applied to a flow model in which the effective conservation of momentum and kinetic energy is not respected, as it should be in the absence of external forces and neglecting viscous dissipation and compressibility effects. A conservative form of the vortex sound theory is obtained by reiterating the assumptions of conservation of these flow invariants. This alternative form of the analogy allows one to obtain more robust results when applied to perturbed analytical flow models and experimental data.     

Diffusion of two-dimensional particles on an air table

Rapid granular flow is diffusive in character. This diffusive nature is important in the generation of constitutive properties such as effective shear and bulk viscosities, effective conductivity of particle fluctuation energy, and self-diffusion coefficients. Experiments were performed in a large air-table apparatus that can sustain up to a few thousand small, light disks just above a horizontal porous plane. Experiments on 2D diffusion processes were performed using this apparatus. Measurements of self-diffusion coefficients and granular temperature in systems having different areal concentrations are in good agreement with predictions based on the kinetic theory and on numerical simulations.     

Flow birefringence in gases at room temperature: New absolute values

Absolute flow birefringence data are required for a final consistency test of the kinetic theory of angular momentum polarizations. In order to obtain reliable values the possible sources of error in the experimental set-up used to measure flow birefringence in gases have been investigated. Special attention has been given to the calibration procedure and to the flow characteristics of the cylindrical Couette flow cell. New absolute data for various simple gases at 293 K are presented. The results will be used in a subsequent paper to get information on the scalar factor of the angular momentum polarization in viscous flow.     

提升管内稠密气粒两相流动大涡模拟

本文采用双流体模型,引入颗粒动力学理论,对提升管内的稠密气粒两相流动进行了大涡模拟。采用改进的分步投影法对滤波后的方程进行显式求解,小尺度量采用Smagorinsky亚格子模式模拟。模拟结果给出的颗粒相速度分布、浓度分布与实验值基本吻合,气固两相存在速度滑移。模拟结果合理预报出了提升管内的环-核流动结构。     

Shear Alfvén wave perpendicular propagation from the kinetic to the inertial regime

We report on observations of shear Alfvén waves radiated from a source of small transverse size, and the subsequent radial confinement of wave magnetic field energy within a cylindrical plasma. The radius of confinement lies between the kinetic regime of the bulk plasma and the inertial regime at the plasma edge; this radius is found to be a function of wave frequency. Numerical calculations using kinetic theory predict a zero in the perpendicular group velocity at a radius which varies in accord with the observations. An analytic expression for the perpendicular group velocity (valid for small perpendicular wave numbers) is given in the vicinity of the zero crossing.     

Kinetic Theory of Polydisperse Granular Mixtures: Influence of the Partial Temperatures on Transport Properties—A Review

It is well-recognized that granular media under rapid flow conditions can be modeled as a gas of hard spheres with inelastic collisions. At moderate densities, a fundamental basis for the determination of the granular hydrodynamics is provided by the Enskog kinetic equation conveniently adapted to account for inelastic collisions. A surprising result (compared to its molecular gas counterpart) for granular mixtures is the failure of the energy equipartition, even in homogeneous states. This means that the partial temperatures Ti (measuring the mean kinetic energy of each species) are different to the (total) granular temperature T. The goal of this paper is to provide an overview on the effect of different partial temperatures on the transport properties of the mixture. Our analysis addresses first the impact of energy nonequipartition on transport which is only due to the inelastic character of collisions. This effect (which is absent for elastic collisions) is shown to be significant in important problems in granular mixtures such as thermal diffusion segregation. Then, an independent source of energy nonequipartition due to the existence of a divergence of the flow velocity is studied. This effect (which was already analyzed in several pioneering works on dense hard-sphere molecular mixtures) affects to the bulk viscosity coefficient. Analytical (approximate) results are compared against Monte Carlo and molecular dynamics simulations, showing the reliability of kinetic theory for describing granular flows.     

Highly resolved fluid flows: "liquid plasmas" at the kinetic level

Fluid flow around an obstacle was observed at the kinetic (individual particle) level using "complex (dusty) plasmas" in their liquid state. These "liquid plasmas" have bulk properties similar to water (e.g., viscosity), and a comparison in terms of similarity parameters suggests that they can provide a unique tool to model classical fluids. This allows us to study "nanofluidics" at the most elementary-the particle-level, including the transition from fluid behavior to purely kinetic transport. In this (first) experimental investigation we describe the kinetic flow topology, discuss our observations in terms of fluid theories, and follow this up with numerical simulations.     

Analytical treatment of high-energy nucleus-nucleus collisions

We review an analytical study of high-energy nucleus-nucleus collisions based on Boltzmann's kinetic theory of gases. In the first part of the paper, we do not take effects of the nuclear mean field into account. This turns out to be appropriate for particle inclusive production, as the good agreement of the theory with a large variety of inclusive experimental data demonstrates. As soon as physical observables extracted from measurements on an event per event basis are considered, the nuclear potential plays a decisive rôle. To account for this fact, we extend the theory by including the nuclear mean field in the Boltzmann equation. The results obtained are in qualitative agreement with experimental exclusive observables such as the sideward kinetic energy flow angle and the average transverse momentum, despite the absence of strong compression of nuclear matter in the theory presented.     

Detectable states,cycle fluxes,and motility scaling of molecular motor kinesin: An integrative kinetic graph theory analysis

The process by which a kinesin motor couples its ATPase activity with concerted mechanical hand-over-hand steps is a foremost topic of molecular motor physics. Two major routes toward elucidating kinesin mechanisms are the motility performance characterization of velocity and run length, and single-molecular state detection experiments. However, these two sets of experimental approaches are largely uncoupled to date. Here, we introduce an integrative motility state analysis based on a theorized kinetic graph theory for kinesin, which, on one hand, is validated by a wealth of accumulated motility data, and, on the other hand, allows for rigorous quantification of state occurrences and chemomechanical cycling probabilities. An interesting linear scaling for kinesin motility performance across species is discussed as well. An integrative kinetic graph theory analysis provides a powerful tool to bridge motility and state characterization experiments, so as to forge a unified effort for the elucidation of the working mechanisms of molecular motors.     

流化床内超细颗粒的流动

基于气体分子运动论和颗粒动理学,建立超细颗粒气固两相湍流流动模型,模型考虑了气相与颗粒聚团之间以及颗粒聚团之间的动量和能量的传递和耗散。建立超细颗粒固相粘性系数、超细颗粒压力等物性参数计算模型。超细颗粒的聚团改变了单颗粒碰撞动力学以及颗粒相压力、粘性系数等输运特性。模型模拟计算颗粒聚团直径分布与Zhaolin等[1]实测值相吻合。     

Hydrodynamics beyond Navier-Stokes: exact solution to the lattice Boltzmann hierarchy

The exact solution to the hierarchy of nonlinear lattice Boltzmann (LB) kinetic equations in the stationary planar Couette flow is found at nonvanishing Knudsen numbers. A new method of solving LB kinetic equations which combines the method of moments with boundary conditions for populations enables us to derive closed-form solutions for all higher-order moments. A convergence of results suggests that the LB hierarchy with larger velocity sets is the novel way to approximate kinetic theory.     

Kinetic theory for sheared granular flows

Rapid granular flows are far-from-equilibrium-driven dissipative systems where the interaction between the particles dissipates energy, and so a continuous supply of energy is required to agitate the particles and facilitate the rearrangement required for the flow. This is in contrast to flows of molecular fluids, which are usually close to equilibrium, where the molecules are agitated by thermal fluctuations. Sheared granular flows form a class of flows where the energy required for agitating the particles in the flowing state is provided by the mean shear. These flows have been studied using the methods of kinetic theory of gases, where the particles are treated in a manner similar to molecules in a molecular gas, and the interactions between particles are treated as instantaneous energy-dissipating binary collisions. The validity of the assumptions underlying kinetic theory, and their applicability to the idealistic case of dilute sheared granular flows are first discussed. The successes and challenges for applying kinetic theory for realistic dense sheared granular flows are then summarised.     

Modelling early stages of sequential versus hierarchical self-assembly in supramolecular architectures

We present a comparative analysis of sequential versus hierarchical mechanisms of self-assembly in supramolecular architectures. The analysis is multifaceted, drawing on and inter-relating insights from a kinetic mean-field analysis and one based on the theory of finite Markov processes, complemented by Monte Carlo calculations. We give explicit results for two reaction pathways that are likely to dominate in early stages of self-assembly, and draw attention to experimental studies to which our results pertain: crystallization of zeolites from the bulk phase and aggregation of surface-supported supramolecular structures. Among the several conclusions that can be drawn from the theory and the simulations is a crossover from one mechanism to another, depending on the values of system parameters.     

Nonlinear kinetic Sunyaev-Zeldovich effect

We derive fully nonlinear expressions for temperature fluctuations from the kinetic Sunyaev-Zeldovich (SZ) effect, the scattering of cosmic microwave background photons off hot electrons in bulk motion. Our result reproduces the Ostriker-Vishniac effect to second order in perturbation theory but contains nonlinear corrections to the electron velocities and densities that were neglected previously. We use the recently developed halo model for nonlinear gravitational clustering to compute the nonlinear kinetic SZ power spectrum, which dominates the primary anisotropy on small angular scales.     

Poiseuille flow of a micropolar fluid

We use non-equilibrium molecular dynamics simulations to study the flow of a micropolar fluid and to test an extended Navier-Stokes theory (ENS) for such fluids. The angular streaming velocity (which is of course missing in the classical Navier-Stokes theory) and the translational streaming velocity are found to be in good agreement with the predictions of ENS theory. Besides, owing to molecular rotation, the translational streaming velocity profile is shown to deviate from the classical parabolic profile. Finally, temperature profiles calculated using three different expressions (a kinetic translational, a kinetic rotational and a recently derived configurational expression) are found to be in excellent agreement, demonstrating that the equipartition principle still holds in this non-equilibrium system. No deviation from the classical quartic temperature profile is observed.