Lattice Boltzmann Simulation of Sedimentation of a Single Elastic Dumbbell in a Newtonian Fluid

Based on the lattice Boltzmann method (LBM), the sedimentations of a single elastic dumbbell in a Newtonian fluid under different initial positions and orientations, and also that of the elastic dumbbells with different free lengths of the spring under the same initial conditions have been simulated. All of the numerical results show that the final orientations of the elastic dumbbells are in the same horizontal direction, and the final positions of their centroids are all on the centerline of the tube no matter what the initial positions and orientations of the elastic dumbbell or the free lengths of the spring are. When the elastic dumbbell finally falls down vertically, the two circular cylinders of the elastic dumbbell rotate around their own symmetry-axis respectively, and their angular velocities are equal but opposite to each other. For the sedimentations of the elastic dumbbells with different free lengths of the spring, the shorter of the free length is, the faster the final angular velocity and vertical velocity of the circular cylinder will be.     

Lattice Boltzmann Simulation of Sedimentation of a Single Elastic Dumbbell in a Newtonian Fluid

Based on the lattice Boltzmann method (LBM), the sedimentations of a single elastic dumbbell in a Newtonian fluid under different initial positions and orientations, and also that of the elastic dumbbells with different free lengths of the spring under the same initial conditions have been simulated. All of the numerical results show that the final orientations of the elastic dumbbells are in the same horizontal direction, and the final positions of their centroids are all on the centerline of the tube no matter what the initial positions and orientations of the elastic dumbbell or the free lengths of the spring are. When the elastic dumbbell finally falls down vertically, the two circular cylinders of the elastic dumbbell rotate around their own symmetry-axis respectively, and their angular velocities are equal but opposite to each other. For the sedimentations of the elastic dumbbells with different free lengths of the spring, the shorter of the free length is, the faster the final angular velocity and vertical velocity of the circular cylinder will be.     

Lattice Boltzmann simulations of a dumbbell moving in a Poiseuille flow

In this paper, the lattice Boltzmann method is applied to simulate a dumbbell moving in a pressure-driven flow in a planar channel with the stress-integration method for the evaluation of hydrodynamic force acting on the cylinders. The simulation results show that the dumbbell also has the important feature of the Segr\'e--Silberberg effect like a particle in a Poiseuille flow. The dumbbell trajectories, orientations, the cylinders vertical velocities and angular velocities all reach their equilibrium values separately independent of their initial positions. It is also found that the dumbbell equilibrium positions depend on the flow Reynolds number, blockage ratio and elastic coefficient. This study is expected to be helpful to understand the dynamics of polymer solutions, polymer synthesis and reaction, etc.     

Stability and diffusion properties of self-interstitial atoms in tungsten:a first-principles investigation

Employing a first-principles method based on the density function theory,we systematically investigate the structures,stability and diffusion of self-interstitial atoms(SIAs) in tungsten(W).The <111> dumbbell is shown to be the most stable SIA defect configuration with the formation energy of ~9.43 eV.The on-site rotation modes can be described by a quite soft floating mechanism and a down-hill "drift" diffusion process from <110> dumbbell to <111> dumbbell and from <001> dumbbell to <110> dumbbell,respectively.Among different SIA configurations jumping to near neighboring site,the <111> dumbbell is more preferable to migrate directly to first-nearest-neighboring site with a much lower energy barrier of 0.004 eV.These results provide a useful reference for W as a candidate plasma facing material in fusion Tokamak.     

Dumbbell transport and deflection in a spatially periodic potential

We present theoretical results on the deterministic and stochastic motion of a dumbbell carried by a uniform flow through a three-dimensional spatially periodic potential. Depending on parameters like the flow velocity, there are two different kinds of movement: transport along a potential valley and a stair-like motion oblique to the potential trenches. The crossover between these two regimes, as well as the deflection angle, depend on the size of the dumbbell. Moreover, thermal fluctuations cause a resonance-like variation in the deflection angle as a function of the dumbbell extension.     

Integral equations for conventional correlation functions of simple dimerizing fluids

An integral equation theory is proposed for the atom-atom correlation functions of a simple reacting fluid, namely one in which a dimerization reaction is occurring. For a model fluid composed of hard sphere monomers and rigid dumbbell dimers the integral equations are solved exactly in the Percus-Yevick approximation, and an explicit expression for the equilibrium constant is derived. Comparison is made with the relevant Monte Carlo simulation data.     

Hydrodynamic impulse in a compressible fluid

A suitable expression for hydrodynamic impulse in a compressible fluid is deduced. The development of appropriate impulse formulation for compressible Euler equations confirms the propriety of the hydrodynamic impulse expression for a compressible fluid given here. Implications of the application of this formulation to a compressible vortex ring are pointed out. Extension of Benjamin's variational characterization of a moving axisymmetric vortex system to a compressible fluid is explored.     

Spinodal decomposition in a Lennard-Jones fluid

A microscopic theory for the early stages of spinodal decomposition in a one-component fluid is presented. We show that in the unstable region of the phase diagram the amplitude of density fluctuations with wave vectors less than some critical value q_c , where q_c is the position of the pole in the static density response function of the uniform fluid, increases exponentially with time. The corresponding amplification factor is related to the Ornstein-Zernike direct correlation function of the uniform fluid. We have calculated the amplification factor for a Lennard-Jones fluid at several densities and temperatures. We find that these amplification factors are qualitatively different from those obtained from the analogue of Cahn's linearized theory of spinodal decomposition. Our calculated value of q_c at reduced density 0·35 and temperature 0·8 is in fairly good agreement with the result of a recent molecular dynamics simulation of a Lennard-Jones fluid quenched to this state.     

Polydisperse fluid in contact with a semipermeable membrane

Using density functional theory developed by Rosefeld, a model polydisperse fluid has been studied in contact with a membrane permeable to some components of the fluid. Calculations were carried out for three kinds of polydisperse fluid, each characterized by a different distribution of particle sizes. The structure of fluid has been evaluated on both sides of the membrane, plus the distribution of the particles in bulk fluid and in the surface layers. The adsorption and osmotic pressure in the system have been calculated.     

Elasticity of a magnetic fluid in a strong magnetic field

Complex measurements of the following elastic-magnetic parameters of a magnetic fluid suspended by magnetic levitation within a horizontal tube in a strong magnetic field were performed: the oscillation frequency and decay coefficient; the static, ponderomotive, and dynamic elasticity coefficients; the fluid displacement under hydrostatic pressure; magnetization curve; and the magnetic field strength and gradient. Calculations based on a model of ponderomotive elasticity with correction for the resistance of a viscous fluid in motion and on the fluid column displacement for two magnetic fluid samples agree well with the experimental magnetization curve. The discussed technique holds promise for research into magnetophoresis and nanoparticle aggregation in magnetic colloids.     

Flow of a non-Newtonian fluid

The objective of the present study is to calculate flows of a non-Newtonian fluid in a plane channel. An exact solution that determines the distribution of the fluid velocity in the transverse cross section of the channel is obtained under certain conditions concerning the dependence of viscosity on the velocity gradient. It is shown that this distribution differs substantially from a parabolic profile of a Newtonian fluid. It is indicated that, in the flow of a non-Newtonian fluid, its special features never disappear-only the region of a non-Newtonian flow shrinks, becoming localized in the vicinity of the velocity maximum.     

微扩张管道内幂律流体非定常电渗流动

研究了电渗驱动下幂律流体在有限长微扩张管道内非稳态流动特性.基于Ostwald-de Wael幂律模型,采用高精度紧致差分离散二维Poisson-Nernst-Planck方程及修正的Cauchy动量方程,数值模拟了初始及稳态时刻微扩张管道内幂律流体电渗流流场分布情况,研究了管道截面改变对幂律流体无量纲剪切应变率及无量纲表观黏度的影响,以及无量纲表观黏度对拟塑性流体与胀流型流体流速分布的影响.数值模拟结果显示,当扩张角和无量纲电动宽度一定时,电场驱动下的幂律流体在近壁区域速度响应都很快;初始时刻,近壁处表观黏度的变化受到剪切应变率变化的影响,从而影响了三种幂律流体速度峰值的分布,出现拟塑性流体流速在扩张段上游及扩张段近壁处速度峰值均为幂律流体中最大、而在扩张段下游三种幂律流体速度峰值相近的现象;稳态时刻,幂律流体速度剖面呈现塞型分布,且满足连续性条件下,幂律流体流速随扩张管半径增大而减小,牛顿流体流动规律与宏观尺度下流动规律相同;初始时刻,在相同电动宽度、不同壁面电势作用下,幂律流体在扩张管近壁处剪切应变率分布的差异导致表观黏度分布的差异,并最终导致拟塑性流体与胀流型流体流速分布的差异.     

The existence and stability of “orbitally uniform” rotations of a vibrating dumbbell on an elliptic orbit

The problem of planar motions of a variable-length dumbbell-shaped body in the central field of the Newton attraction is considered. The rules of varying the dumbbell length, at which the dumbbell with respect to the true anomaly can rotate uniformly around the center of mass, are indicated for the equation of motion of the dumbbell written in a satellite approximation [1–8]. When fulfilling these rules, the necessary stability conditions of mentioned motions are investigated.     

Simulation of critical fluid Rayleigh linewidth behavior by a normal fluid system

The dynamic droplet model of a critical fluid provides a simple physical model of a critical fluid. We use this to model an emulsion which mimics the Rayleigh linewidth behavior of a critical fluid in the nonhydrodynamic regime.     

Diffusion within a near-critical nanopore fluid

Results are presented for grand canonical Monte Carlo (GCMC) and both equilibrium and non-equilibrium molecular dynamics simulations (EMD and NEMD) conducted over a range of densities and temperatures that span the two-phase coexistence and supercritical regions for a pure fluid adsorbed within a model crystalline nanopore. The GCMC simulations provided the low temperature coexistence points for the open pore fluid and were used to locate the capillary critical temperature for the system. The equilibrium configurational states obtained from these simulations were then used as input data for the EMD simulations in which the self-diffusion coefficients were computed using the Einstein equation. NEMD colour diffusion simulations were also conducted to validate the use of a system averaged Einstein analysis for this inhomogeneous fluid. In all cases excellent agreement was observed between the equilibrium (linear response theory) predictions for the diffusivities and non-equilibrium colour diffusivities. The simulation results are also compared with a recently published quasi-hydrodynamic theory of Pozhar and Gubbins (Pozhar, L. A., and Gubbins, K. E., 1993, J. Chem. Phys., 99, 8970; 1997, Phys. Rev. E, 56, 5367.). The model fluid and the nature of the fluid wall interactions employed conform to the decomposition of the particle–particle interaction potential explicitly used by Pozhar and Gubbins. The local self-diffusivity was calculated from the local fluid–fluid and fluid wall hard core collision frequencies. While this theory provides reasonable results at moderate pore fluid densities, poor agreement is observed in the low density limit.     

Critical behavior of a heavy particle in a granular fluid

A second order phase transition is observed for the homogeneous cooling state of a heavy impurity particle in a granular fluid. The order parameter straight phi is the ratio of impurity mean square velocity to that of the fluid, with a conjugate field h proportional to the mass ratio. A parameter beta, measuring the fluid cooling rate relative to the impurity-fluid collision rate, is the analog of the inverse temperature. For beta<1 the fluid is "normal" with straight phi = 0 at h = 0, as in the case of elastic collisions. For beta>1 an "ordered" state with straight phi not equal0 occurs at h = 0, representing an extreme breakdown of equipartition. Critical slowing and qualitative changes in the velocity distribution function near the transition are noted.     

Point-force excited vibrations of a thin,infinite panel separating a fluid layer from a fluid half-space

A coupled system consisting of a thin, infinite panel separating a fluid layer and a fluid half-space is considered. The response of the panel when driven by a point harmonic force is evaluated by using Hankel transform analysis in conjunction with complex variable integration techniques. The emphasis is placed on frequencies well below the panel critical frequency, on dense fluid loading, and on the condition of shallow layer depth. The analysis yields the free propagation wave numbers of the coupled system: below the critical frequency, all but one are complex. From the solutions of the response integrals, the panel flexural velocity, the acoustic pressures, the power transmitted into the structure and into the fluid layer, and the radiated acoustic power, are obtained.     

Caging dynamics in a granular fluid

We report an experimental investigation of the caging motion in a uniformly heated granular fluid for a wide range of filling fractions, varphi. At low varphi the classic diffusive behavior of a fluid is observed. However, as varphi is increased, temporary cages develop and particles become increasingly trapped by their neighbors. We statistically analyze particle trajectories and observe a number of robust features typically associated with dense molecular liquids and colloids. Even though our monodisperse and quasi-2D system is known to not exhibit a glass transition, we still observe many of the precursors usually associated with glassy dynamics. We speculate that this is due to a process of structural arrest provided, in our case, by the presence of crystallization.     

Acoustic streaming in a rotating fluid

Acoustic streaming theory is derived that is applicable to a fluid that is slow moving in a reference frame that rotates with a constant angular velocity omega. A simplified streaming equation is obtained for the special case in which the acoustic angular frequency omega is large relative to omega, and the change in fluid density due to rotation alone is negligible. For this special case it is shown that the "driving force" for the acoustic streaming is independent of omega. Thus, if no acoustic streaming is present in a fluid system that is stationary, then no steady-state acoustic streaming is predicted for a similar system that rotates with constant angular velocity. For a system in which acoustic streaming is present, the flow behavior depends on the relative magnitudes of the Coriolis forces and the viscous forces. If the Ekman number is large (that is, the viscous force dominates) then the predicted flow is identical to that which would exist in a stationary system. If, on the other hand, the Ekman number is small then the Coriolis force dominates and the component of flow in the direction of the axis of rotation can be much smaller in the rotating system than in a similar system at rest.     

Rotational friction coefficient of a permeable cylinder in a viscous fluid

An exact expression is derived for the rotational friction coefficient of a cylinder of infinite length and constant permeability immersed in an incompressible viscous fluid. An asymptotic expression for the translational friction coefficient of a permeable cylinder moving in a sheet of viscous fluid embedded on both sides in a fluid of much lower viscosity is also given.