Dramatic change of the self-diffusions of colloidal ellipsoids by hydrodynamic interactions in narrow channels

The self-diffusion problem of Brownian particles under the constraint of quasi-one-dimensional(q1 D) channel has raised wide concern.The hydrodynamic interaction(HI) plays an important role in many practical problems and two-body interactions remain dominant under q1D constraint.We measure the diffusion coefficient of individual ellipsoid when two ellipsoidal particles are close to each other by video-microscopy measurement.Meanwhile, we obtain the numerical simulation results of diffusion coefficient using finite element software.We find that the self-diffusion coefficient of the ellipsoid decreases exponentially with the decrease of their mutual distance X when X X_0, where X_0 is the maximum distance of the ellipsoids to maintain their mutual influence, X_0 and the variation rate are related to the aspect ratio p = a/b.The mean squared displacement(MSD) of the ellipsoids indicates that the self-diffusion appears as a crossover region, in which the diffusion coefficient increases as the time increases in the intermediate time regime, which is proven to be caused by the spatial variations affected by the hydrodynamic interactions.These findings indicate that hydrodynamic interaction can significantly affect the self-diffusion behavior of adjacent particles and has important implications to the research of microfluidic problems in blood vessels and bones, drug delivery, and lab-on-chip.     

Dissipative particle dynamics study of velocity autocorrelation function and self-diffusion coefficient in terms of interaction potential strength

This research focuses on numerically investigating the self-diffusion coefficient and velocity autocorrelation function (VACF) of a dissipative particle dynamics (DPD) fluid as a function of the conservative interaction strength. Analytic solutions to VACF and self-diffusion coefficients in DPD were obtained by many researchers in some restricted cases including ideal gases, without the account of conservative force. As departure from the ideal gas conditions are accentuated with increasing the relative proportion of conservative force, it is anticipated that the VACF should gradually deviate from its normally expected exponentially decay. This trend is confirmed through numerical simulations and an expression in terms of the conservative force parameter, density and temperature is proposed for the self-diffusion coefficient. As it concerned the VACF, the equivalent Langevin equation describing Brownian motion of particles with a harmonic potential is adapted to the problem and reveals an exponentially decaying oscillatory pattern influenced by the conservative force parameter, dissipative parameter and temperature. Although the proposed model for obtaining the self-diffusion coefficient with consideration of the conservative force could not be verified due to computational complexities, nonetheless the Arrhenius dependency of the self-diffusion coefficient to temperature and pressure permits to certify our model over a definite range of DPD parameters.     

Memory effects in the diffusion of an interacting polydisperse suspension: II. Hard spheres at low density

We consider the diffusion of a low density suspension of polydisperse hard spheres. In a previous article (I) we have obtained at long wavelength a general expression to first order in density for the memory matrix appropriate to such a system. In the present article we evaluate the memory matrix in closed form using a certain approximations for the hydrodynamic interaction and for the 2-body propagator. We find that memory effects convert the exponential decay of density correlation functions to long time power law decay of the form $\text{t}{}^{\mathrm{<mtext>-</mtext><mtext>5</mtext><mtext>2</mtext>}}$. We consider the so-called long time self-diffusion constant and show that memory effects to first order in density are negligible compared to the first cumulant contribution. Our treatment shows that for hard sphere systems it is essential to treat the short distance hydrodynamic forces accurately.     

Kinetic theory of long time tails in velocity correlation functions in a moderately dense electron gas

The long time tails of the correlation functions that determine the self-diffusion coefficient and the kinetic parts of the shear viscosity and heat conductivity in a one-component plasma are calculated using a systematic kinetic theory. The results are in agreement with those obtained from the phenomenological mode coupling theory. The formal kinetic theory calculations of previous workers, who obtained incomplete long time tail results, are also discussed.     

Non-Gaussian effects in the self-diffusion of a low density hard sphere suspension

We consider self-diffusion in a macroparticle suspension of hard spheres. Using an analytic expression for the memory function of such a suspension, correct to first order in concentration, we obtain the first and second cumulants of the self dynamic structure factor in closed form. The limiting behaviour of the cumulants at short and long times is obtained and we show that non-Gaussian contributions are small at all times. Finally we compare our results with recent experimental measurements and with a Brownian dynamics simulation.     

Study of molecular mobility of fluid in zeolite NaX.

The self-diffusion of n-decane in zeolite NaX was studied by NMR PFG method. The situation when the liquid was only in the crystalline channels was studied in details. The restricted molecular motion of liquid in the crystalline channels was observed. The reasons of the anomalous self-diffusion of n-decane in zeolite bed were stated. The technique of the determination of the genuine self-diffusion coefficient in such porous systems was proposed. The genuine self-diffusion coefficients for system NaX/n-decane were obtained.     

Granular gas of viscoelastic particles in a homogeneous cooling state

Kinetic properties of a granular gas of viscoelastic particles in a homogeneous cooling state are studied analytically and numerically. We employ the most recent expression for the velocity-dependent restitution coefficient for colliding viscoelastic particles, which allows us to describe systems with large inelasticity. In contrast to previous studies, the third coefficient a₃ of the Sonine polynomials expansion of the velocity distribution function is taken into account. We observe a complicated evolution of this coefficient. Moreover, we find that a₃ is always of the same order of magnitude as the leading second Sonine coefficient a₂; this contradicts the existing hypothesis that the subsequent Sonine coefficients a₂,a₃…, are of an ascending order of a small parameter, characterizing particles inelasticity. We analyze evolution of the high-energy tail of the velocity distribution function. In particular, we study the time dependence of the tail amplitude and of the threshold velocity, which demarcates the main part of the velocity distribution and the high-energy part. We also study evolution of the self-diffusion coefficient D and explore the impact of the third Sonine coefficient on the self-diffusion. Our analytical predictions for the third Sonine coefficient, threshold velocity and the self-diffusion coefficient are in a good agreement with the numerical finding.     

Molecular collisions and self-diffusion in liquids

The velocity autocorrelation function and coefficient of self-diffusion are derived for a hard-sphere fluid. An earlier quasi-lattice model of self-diffusion in liquids is re-examined and a less restrictive expression for the self-diffusion coefficient is derived. The coefficient of self-diffusion of a light or heavy isotope in the normal liquid is considered both for hard spheres and in the quasi-lattice approximation. An experiment is proposed to clarify the nature of the isotope effect in self-diffusion.     

Self-diffusion and sedimentation of tracer spheres in (semi)dilute dispersions of rigid colloidal rods

Long-time self-diffusion and sedimentation of fluorescent tracer spheres in electrostatically stabilized dispersions of rigid colloidal host rods have been measured in situ with fluorescence recovery after photobleaching, and gravitational and ultracentrifugal sedimentation. The dynamics of silica tracer spheres of 39 and 370 nm radius was monitored in dispersions of host rods with aspect ratios 9.6 and 25.7 at various rod volume fractions. The translational and rotational diffusion coefficient of the host rods was obtained independently with dynamic light scattering and birefringence decay measurements. Our results indicate that sedimentation and long-time self-diffusion are determined by the same friction factor. Furthermore we find that, as long as the host rods are relatively mobile, tracer sphere sedimentation and long-time self-diffusion are governed by the macroscopic solution viscosity, regardless of the tracer and host rod size. However, when the host rods are immobilized, due to rod entanglements at higher volume fractions, tracer sphere dynamics depends strongly on the tracer size relative to the pore size of the host rod network. The large tracers are completely trapped in the network whereas the small tracer spheres remain mobile. Current models for tracer sphere motion in rod assemblies do not satisfactorily explain the complete dynamic regime covered by our experimental model system because the effect of host rod mobility is not properly taken into account.     

Concentration-dependent self-diffusion of adsorbates in mesoporous materials

The pulsed-field gradient NMR method has been applied to study self-diffusion of liquids in mesoporous materials with different pore sizes and morphologies as a function of pore loading. It is found that the effective diffusivities of adsorbate molecules in mesopores at partial loadings are related to two mechanisms, the Knudsen diffusion through the gaseous phase in the pore space and the diffusion within the layer of molecules adsorbed on the pore walls. The relative contributions of these modes, which are determined by the details of the interphase equilibrium, change with variation of the pore loading, leading to a complex behavior of the effective self-diffusion coefficient. The impact of the pore size and the adsorbate-surface interaction on self-diffusion is elucidated. Possible reasons for an experimentally obtained hysteresis in the diffusivities measured on adsorption and desorption in mesopores are discussed.     

1H NMR study of water relaxation and self-diffusion in human serum albumin aqueous solutions

Summary Water proton spin-lattice relaxation and self-diffusion in aqueous solutions of human serum albumin have been studied by¹H NMR as a function of the protein concentration. Spin-lattice relaxation data, which display a nonlinear behaviour with the protein concentration, could be fitted with a two-phase model taking into account the experimentally determined hydration (?bound?) water values. Despite a similar trend is registered for the water self-diffusion coefficient, such a model has been found unable to explain the related experimental data taken as a function of the biomolecule concentration. On the other hand, the solute-induced proton self-diffusion decrease could be satisfactorily interpreted by postulating an enhanced probability of hydrogen-bond formation occurring within the ?vicinal? water surrounding the biomolecules for several hydration shells. The consistency within the two models is discussed in connection with the magnetic interactions occurring within the solute-solvent systems.     

缔合流体在高温高压下的自扩散系数研究

在统计力学理论基础上,本文提出了一个考虑氢键对自扩散系数影响的方程．这个方程为非氢键贡献部分与氢键贡献部分之积,其中自扩散系数的非氢键部分由Ｌｅｎｎａｒｄ－Ｊｏｎｅｓ链模型求得,而一个分子中的平均氢键数随温度和密度的变化关系使用统计缔合流体理论得到。链节之间的相互作用能量参数由粘度的关联式获得,其它四个参数则由扩散系数的实验数据获得。对７个典型的缔合流体在相当宽的温度压力范围内计算的平均相对百分误差为５．９８％。     

Electric field dynamics at charged point in two component plasma

The autocorrelation function for the velocity and for the electric microfield of an impurity ion in a Two Ionic Component Plasma (TICP) is considered. A simple model is constructed for this purpose that preserves the exact short time dynamics and the long time global constraint of a given self-diffusion coefficient. The memory function and then the collision effects associated with the correlation function for the self-diffusion are expressed in terms of an effective two body interaction via a screened effective potential. The basic approximation used in our approach is the disconnected one that refers to the collision operator. A comparison of the prediction of this model for the self-diffusion and for the autocorrelation functions with the results of the molecular dynamics simulation developed in our laboratory (PIIM) shows an acceptable agreement over a wide range of plasma coupling, impurity ion charge and concentration.Received: 11 August 2003, Published online: 19 February 2004PACS: 52.20.Dq Particle orbits - 52.65.Cc Particle orbit and trajectory - 47.40.Nm Shock wave interactions and shock effects - 05.20.-y Classical statistical mechanics     

Water self-diffusion in Chlorella sp. studied by pulse field gradient NMR

The water self-diffusion behavior in chlorella water suspension was investigated by pulsed field gradient NMR technique. Three types of water was determined, which differs according to the self-diffusion coefficients; bulk water, extracellular and intracellular water. Intracellular and extracellular water self-diffusion were restricted, and the sizes of restriction regions were 3.4 microm and 17 microm, respectively. The water molecular exchange process between these three diffusion regions was investigated. The residence time and exchange rate constant for chlorella cells were obtained. The cell wall permeability determined from the rate constant as 3 x 10(-6) m/s agreed with the permeability 10(-6) m/s obtained from time dependence of intracellular water self-diffusion coefficient. The structural cluster model of chlorella cell is estimated to describe the extracellular water self-diffusion in chlorella water suspension.     

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.     

Investigation of a new mean temperature-dependent potential energy function for methane and its use for the prediction of transport properties

In this work an improved mean potential energy function for the interaction of an isolated pair of methane is obtained, from which the non-equilibrium properties of methane at zero pressure limit are calculated, accurately. The potential energy function of 21 different fixed orientations of (CH₄)₂ dimer has been obtained via the coupled cluster method. In order to obtain a mean potential energy function, the Boltzmann-average of the obtained potentials of the selected fixed orientations has been used. Unlike the full potential energy surface with the angle-dependent, the parameters of the mean potential are found to be temperature-dependent. The mean potential energy function is fitted well by an analytical expression at different temperatures. The mean absolute percentage deviation of analytical expression compare to the calculated value is about 0.6%. In studying a system with a great number of configurations, calculation of the potential energy function for all configurations is an impossible task; in the proposed model, 21 important fixed orientations have been selected. Introduction of a new approach for calculating the potential energy in methane and investigation of the temperature dependence of mean potential energy are the most important claims of this work. The mean potential function is used to calculate the viscosity, self-diffusion coefficient, and thermal conductivity at the zero pressure limit. The mean absolute percentage deviation in the calculated viscosity, self-diffusion coefficient and thermal conductivity is 3.1, 2.4, and 5.3%, respectively. Also, the second virial coefficient has been calculated for some temperatures.     

One-dimensional time-dependent distributions

A new derivation of two important one-dimensional time-dependent distributions for an infinite system of hard rods is presented. This derivation is simpler than previous derivations and it provides a direct physical interpretation of the individual terms in the final expressions. A new, more unusual distribution is also presented and discussed. Finally, an exact expression for the diffusion of a Brownian particle is obtained and compared with the exact expression for the self-diffusion coefficient.     

The motion of light interstitials in metals: Recent experiments

Recent theoretical considerations suggest, that at low temperatures the transport properties of light interstitials in metals are dominated by the interaction with the conduction electrons. After briefly surveying the state of the theory, experimental examples for the low and high temperature cases are presented. We begin with the low T regime and display first neutron scattering experiments on H trapped at O-impurities in Nb where a coherent tunneling state is observed. Its dependence on temperature and its properties in normal and superconducting Nb are discussed. Thereafter muon diffusion results in Al are examined. In Al, muon diffusion is observed via diffusion limited trapping and local properties of the impurity as well as long range diffusion are playing a role. Using a large variety of impurities it was possible to evaluate the diffusion coefficient over a large T-range. Muon motion in Al at accessible temperatures falls entirely in the hopping regime and constitutes an example for the high T regime of the theory.     

The effect of dynamical screening on self-diffusion in a dense magnetized plasma

The coefficient of self-diffusion along an external magnetic field in a dense plasma is evaluated with the use of a kinetic equation that takes dynamical screening effects into account. It is found that the self-diffusion coefficient diminishes monotonously as the magnetic field strength increases. Qualitatively the present calculation corroborates a result obtained recently in a cruder approximation in which only static screening effects are considered.