Unusual thermal diffusion in polymer solutions

Thermal diffusion forced Rayleigh scattering results on thermal diffusion of poly(ethylene oxide) (PEO) in ethanol/water mixtures are presented. In water-rich solvent mixtures, PEO is found to migrate towards regions of lower temperature. This is typical for polymer solutions and corresponds to a positive Soret coefficient of PEO. In solvent mixtures with low water content, however, the polymer is found to migrate towards higher temperatures, corresponding to a negative Soret coefficient of PEO in ethanol-rich solutions. To our knowledge, this is the first observed sign change of the Soret coefficient of a polymer in solution. We also present a simple lattice model for the polymer solvent system and calculate Soret coefficients with statistical mechanics methods. The calculated values agree qualitatively with the experimental results.     

Thermodiffusion of charged micelles

We study diffusion of charged nanoparticles in a temperature gradient and derive the corresponding Ludwig-Soret transport coefficient. Charge effects are found to enhance thermodiffusion by up to 2 orders of magnitude. We show that the inverse Soret coefficient 1/S(T) is a linear function of the colloid density n; the proportionality factor, or second virial coefficient, varies algebraically with inverse salinity, n0(-alpha); the precise value of the exponent alpha depends on the ratio of particle size and Debye length. Our findings compare favorably with experimental observations and provide, without adjustable parameters, a good fit to the data on 3-nm sodium dodecylsulfate micelles.     

Precise determination of the Soret,thermodiffusion and isothermal diffusion coefficients of binary mixtures of dodecane,isobutylbenzene and 1,2,3,4-tetrahydronaphthalene (contribution of the University of Mons to the benchmark test)

Within the framework of an international benchmark test, the Soret coefficient S T , the thermodiffusion coefficient D T , and the isothermal mass diffusion coefficient D of the three binary systems formed with dodecane, isobutylbenzene and 1,2,3,4-tetrahydronaphthalene (with a mass fraction of 0.5 in each component at a temperature of 25C) have been measured. Convective coupling in thermogravitational columns has been used to determine D T based on the Furry-Jones-Onsager theory and the so-called open-ended capillary technique for D . The ratio of D T to D , obtained in these two independent experiments, provides the Soret coefficient. In one case, we were able to use laser Doppler velocimetry to measure the modifications of the velocity amplitude due to thermodiffusion, which is also a way to obtain the Soret coefficient. Our results for these three coefficients are in good agreement with those obtained by other benchmark tests.     

Thermophoresis in colloidal suspensions driven by Marangoni forces

In a hydrodynamic approach to thermophoretic transport in colloidal suspensions, the solute velocity u and the solvent flow v(r) are derived from Stokes' equation, with slip boundary conditions imposed by thermal Marangoni forces. The resulting fluid velocity field v(r) significantly differs from that induced by an externally driven particle. We find, in particular, that thermophoresis due to surface forces is insensitive to hydrodynamic interactions. As a consequence, the thermal diffusion coefficient D(T) of polymer solutions is independent of molecular weight and concentration.     

Thermal diffusion in ionic micellar solutions

Thermal diffusion studies of complex fluids may have a deep impact on determining the microscopic origins of the Soret effect, allowing in particular for a clear distinction between single-particle and collective effects. We show for instance that electrostatic interactions have a dramatic influence on the thermal diffusion of charged surfactant micelles. In the dilute regime, the Soret coefficient strongly decreases with increasing solution ionic strength and scales as the square of the Debye-Hückel screening length. Yet, collective effects yield a reversed scenario even at fairly low surfactant concentrations. We find that the single-particle behaviour can be explained using an interfacial tension-driven mechanism originally proposed by Ruckenstein. Interparticle interactions drastically change the Soret coefficient mainly owing to their effects on the solution's osmotic compressibility. The proposed mechanism can be extended to other kinds of solvent-particle interaction and may open up the way to a general picture of thermal diffusion in disperse systems.     

Collective motion of polar active particles on a sphere

Collective motion of active particles with polar alignment is investigated on a sphere. We discussed the factors that affect particle swarm motion and define an order parameter that can show the degree of particle swarm motion. In the model, we added a polar alignment strength, along with Gaussian curvature, affecting particles swarm motion. We find that when the force exceeds a certain limit, the order parameter will decrease with the increase of the force. Combined with our definition of order parameter and observation of the model, the reason is that particles begin to move side by side under the influence of polar forces. In addition, the effects of velocity, rotational diffusion coefficient, and packing fraction on particle swarm motion are discussed. It is found that the rotational diffusion coefficient and the packing fraction have a great influence on the clustering motion of particles, while the velocity has little influence on the clustering motion of particles.     

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用密度调制的方法研究了等离子体中粒子输运问题。采用了注入脉冲式补充送气和超声分子束两种不同的密度调制方法。在HL-2A装置常规欧姆放电的情况下,运用有限差分法和Nagashima矩阵技术,求解了粒子平衡方程。计算出了粒子的输运系数(对流速度v和扩散系数D)。研究了粒子输运系数与等离子体线平均密度之间的关系。实验结果表明,在欧姆放电的情况下,等离子体芯部的粒子对流速度方向始终是向内的,并且密度低时,粒子输运系数(粒子扩散系数D和对流速度v)较大;密度高时,粒子输运系数较小。     

Microscopic interpretation of a pure chemical contribution to the Soret effect

In a recent Letter by K?hler [Phys. Rev. Lett. 87, 055901 (2001)], it has been shown that the Soret effect or thermal diffusion can be split into three different contributions: mass, moment of inertia, and a so-called chemical effect, but only the chemical effect gives rise to a composition dependent contribution. As it is experimentally difficult to deal with the chemical contribution without changing the two others, it has not been studied accurately yet. Our Letter presents both equilibrium and nonequilibrium Molecular Dynamics in simple Lennard-Jones mixtures. By thoroughly changing the strength of direct and cross interaction energies between particles, we show that the composition dependence and the change of sign of the Soret coefficient is driven only by the nature of interactions between unlike particles and propose a microscopic interpretation of the Soret effect.     

Onsager Reciprocity in Premelting Solids

The diffusive motion of foreign particles dispersed in a premelting solid is analyzed within the framework of irreversible thermodynamics. We determine the mass diffusion coefficient, thermal diffusion coefficient and Soret coefficient of the particles in the dilute limit, and find good agreement with experimental data. In contrast to liquid suspensions, the unique nature of premelting solids allows us to derive an expression for the Dufour coefficient and independently verify the Onsager reciprocal relation coupling diffusion to the flow of heat.     

Derivation of diffusion coefficient of a Brownian particle in tilted periodic potential from the coordinate moments

In this research, diffusion of an overdamped Brownian particle in the tilted periodic potential is investigated. Using the one-dimensional hopping model, the formulations of the mean velocity VN and effective diffusion coefficient DN of the Brownian particle have been obtained [B. Derrida, J. Stat. Phys. 31 (1983) 433]. Based on the relation between the effective diffusion coefficient and the moments of the mean first passage time, the formulation of effective diffusion coefficient Deff of the Brownian particle also has been obtained [P. Reimann, et al., Phys. Rev. E 65 (2002) 031104]. In this research, we'll give another analytical expression of the effective diffusion coefficient Deff from the moments of the particle's coordinate.     

Cosmic ray anisotropy in fractional differential models of anomalous diffusion

The problem of galactic cosmic ray anisotropy is considered in two versions of the fractional differential model for anomalous diffusion. The simplest problem of cosmic ray propagation from a point instantaneous source in an unbounded medium is used as an example to show that the transition from the standard diffusion model to the Lagutin-Uchaikin fractional differential model (with characteristic exponent α = 3/5 and a finite velocity of free particle motion), which gives rise to a knee in the energy spectrum at 10⁶ GeV, increases the anisotropy coefficient only by 20%, while the anisotropy coefficient in the Lagutin-Tyumentsev model (with exponents α = 0.3 and β = 0.8, a long stay of particles in traps, and an infinite velocity of their jumps) is close to one. This is because the parameters of the Lagutin-Tyumentsev model have been chosen improperly.     

HL-1M装置弹丸和分子束加料的粒子输运研究

研究了IL-1M装置上弹丸和分子束加料的粒子输运。在研究粒子输运时拟合了粒子源分布,利用调制送气模型研究了分子束送气时的粒子输运。由弹丸注入后较长时间内密度的自然衰减研究了粒子输运,给出了一种简单的研究弹丸注入后粒子输运的方法。计算表明,分子束和弹丸注入改善了等离子体的粒子输运特性。将计算结果与实验测量进行了比较。     

Microscopic derivation of non-Markovian thermalization of a Brownian particle

In this paper, the first microscopic approach to Brownian motion is developed in the case where the mass density of the suspending bath is of the same order of magnitude as that of the Brownian (B) particle. Starting from an extended Boltzmann equation, which describes correctly the interaction with the fluid, we derive systematically via multiple-time-scale analysis a reduced equation controlling the thermalization of the B particle, i.e., the relaxation toward the Maxwell distribution in velocity space. In contradistinction to the Fokker-Planck equation, the derived new evolution equation is nonlocal both in time and in velocity space, owing to correlated recollision events between the fluid and particle B. In the long-time limit, it describes a non-Markovian generalized Ornstein-Uhlenbeck process. However, in spite of this complex dynamical behavior, the Stokes-Einstein law relating the friction and diffusion coefficients is shown to remain valid. A microscopic expression for the friction coefficient is derived, which acquires the form of the Stokes law in the limit where the meanfree path in the gas is small compared to the radius of particle B.Knowing the interest of Matthieu Ernst in the subtle and fundamental problems of kinetic theory, we have the pleasure to dedicate this study to him.     

Effect of Soret diffusion on lean hydrogen/air flames at normal and elevated pressure and temperature

The influence of Soret diffusion on lean premixed flames propagating in hydrogen/air mixtures is numerically investigated with a detailed chemical and transport models at normal and elevated pressure and temperature. The Soret diffusion influence on the one-dimensional (1D) flame mass burning rate and two-dimensional (2D) flame propagating characteristics is analysed, revealing a strong dependency on flame stretch rate, pressure and temperature. For 1D flames, at normal pressure and temperature, with an increase of Karlovitz number from 0 to 0.4, the mass burning rate is first reduced and then enhanced by Soret diffusion of H₂ while it is reduced by Soret diffusion of H. The influence of Soret diffusion of H₂ is enhanced by pressure and reduced by temperature. On the contrary, the influence of Soret diffusion of H is reduced by pressure and enhanced by temperature. For 2D flames, at normal pressure and temperature, during the early phase of flame evolution, flames with Soret diffusion display more curved flame cells. Pressure enhances this effect, while temperature reduces it. The influence of Soret diffusion of H₂ on the global consumption speed is enhanced at elevated pressure. The influence of Soret diffusion of H on the global consumption speed is enhanced at elevated temperature. The flame evolution is more affected by Soret diffusion in the early phase of propagation than in the long run due to the local enrichment of H₂ caused by flame curvature effects. The present study provides new insights into the Soret diffusion effect on the characteristics of lean hydrogen/air flames at conditions that are relevant to practical applications, e.g. gas engines and turbines.     

Soret effect in interacting micellar solutions

We show that electrostatic effects have a dramatic influence on thermal diffusion of charged micelles. In the dilute regime, the Soret coefficient strongly decreases with the solution ionic strength, and scales as the square of the Debye-Hückel length. Yet, collective effects yield a reversed scenario even at fairly low surfactant concentration. We find that single-particle behavior can be explained using an interfacial tension mechanism proposed by Ruckenstein, which also fairly accounts for collective effects and opens the way to a general picture of thermal diffusion in disperse systems.     

Approach to a Stationary State in an External Field

We study relaxation towards a stationary out-of-equilibrium state by analyzing a one-dimensional stochastic process followed by a particle accelerated by an external field and propagating through a thermal bath. The effect of collisions is described within one-dimensional formulation of Boltzmann’s kinetic theory. We present analytical solutions for the Maxwell gas and for the very hard particle model. The exponentially fast relaxation of the velocity distribution towards the stationary form is demonstrated. In the reference frame moving with constant drift velocity the hydrodynamic diffusive mode is shown to govern the distribution in the position space. We show that the exact value of the diffusion coefficient for any value of the field is correctly predicted by the Green-Kubo autocorrelation formula generalized to the stationary state.     

Effects of Soret diffusion on the laminar flame speed and Markstein length of syngas/air mixtures

The effects of Soret diffusion on premixed syngas/air flames at normal and elevated temperatures and pressures are investigated numerically including detailed chemistry and transport. The emphasis is placed on assessing and interpreting the influence of Soret diffusion on the unstretched and stretched laminar flame speed and Markstein length of syngas/air mixtures. The laminar flame speed and Markstein length are obtained by simulating the unstretched planar flame and positively-stretched spherical flame, respectively. The results indicate that at atmospheric pressure the laminar flame speed of syngas/air is mainly reduced by Soret diffusion of H radical while the influence of H₂ Soret diffusion is negligible. This is due to the facts that the main reaction zone and the Soret diffusion for H radical (H₂) are strongly (weakly) coupled, and that Soret diffusion reduces the H concentration in the reaction zone. Because of the enhancement in the Soret diffusion flux of H radical, the influence of Soret diffusion on the laminar burning flux increases with the initial temperature and pressure. Unlike the results at atmospheric pressure, at elevated pressures the laminar flame speed is shown to be affected by the Soret diffusion of H₂ as well as H radical. For stretched spherical flame, it is shown that the Soret diffusion of both H and H₂ should be included so that the stretched flame speed can be accurately predicted. Similar to the laminar flame speed, the Markstein length is also reduced by Soret diffusion. However, the reduction is found to be mainly caused by Soret diffusion of H₂ rather than that of H radical. Moreover, the influence of Soret diffusion on the Markstein length is demonstrated to decrease with the initial temperature and pressure.     

Clustering of the low-inertia particle number density field in random divergence-free hydrodynamic flows

We consider the diffusion of the low-inertia particle number density field in random divergence-free hydrodynamic flows. The principal feature of this diffusion is the divergence of the particle velocity field, which results in clustering of the particle number density field. This phenomenon is coherent, occurs with a unit probability, and must show up in almost all realizations of the process dynamics. We calculate the statistical parameters that characterize clustering in three-dimensional and two-dimensional random fluid flows and in a rapidly rotating two-dimensional random flow. In the former case, the vortex component of the random divergence-free flow generates a vortex component of the low-inertia particle velocity field, which generates a potential component of the velocity field through advection. By contrast, in the case of rapid rotation, a potential component of the velocity field is generated directly by the vortex component of the random divergence-free flow (linear problem).     

Self-diffusion in granular gases: Green-Kubo versus Chapman-Enskog

We study the diffusion of tracers (self-diffusion) in a homogeneously cooling gas of dissipative particles, using the Green-Kubo relation and the Chapman-Enskog approach. The dissipative particle collisions are described by the coefficient of restitution epsilon which for realistic material properties depends on the impact velocity. First, we consider self-diffusion using a constant coefficient of restitution, epsilon=const, as frequently used to simplify the analysis. Second, self-diffusion is studied for a simplified (stepwise) dependence of epsilon on the impact velocity. Finally, diffusion is considered for gases of realistic viscoelastic particles. We find that for epsilon=const both methods lead to the same result for the self-diffusion coefficient. For the case of impact-velocity dependent coefficients of restitution, the Green-Kubo method is, however, either restrictive or too complicated for practical application, therefore we compute the diffusion coefficient using the Chapman-Enskog method. We conclude that in application to granular gases, the Chapman-Enskog approach is preferable for deriving kinetic coefficients.