Particle Diffusion Coefficient Research Articles

Experimental and Numerical Study on Scale Effects of Gas Emission from Coal Particles

In order to study the scale effects and formation mechanism of gas emission from coal particles, we conducted gas desorption and diffusion experiments, investigated the variation of particle size and its effect on gas flow, analyzed and discussed the control mechanism and gas diffusion model of coal. Based on the above, we found that the bidisperse diffusion model was suitable to study the size effects of gas emission and further established a simplified numerical method of bidisperse diffusion model and compared it with the experiment results. The results showed that the accumulated gas emission volume and the initial gas emission speed have scale characteristics. The scale effects of gas emission from coal are determined by the multi-scale pore structure of coal. The diffusion coefficient and path of coal particle determined the gas flow process. Through the gas desorption and diffusion experiments, we can find a way to determine the critical diffusion parameters. On the basis of experiments and theoretical analyses performed, the processes of gas emission from coal particles are studied and their mathematical models are put forward. These models can describe the experimental phenomena fairly.

Quantum Diffusion on Molecular Tubes: Universal Scaling of the 1D to 2D Transition.

The transport properties of disordered systems are known to depend critically on dimensionality. We study the diffusion coefficient of a quantum particle confined to a lattice on the surface of a tube, where it scales between the 1D and 2D limits. It is found that the scaling relation is universal and independent of the temperature, disorder, and noise parameters, and the essential order parameter is the ratio between the localization length in 2D and the circumference of the tube. Phenomenological and quantitative expressions for transport properties as functions of disorder and noise are obtained and applied to real systems: In the natural chlorosomes found in light-harvesting bacteria the exciton transfer dynamics is predicted to be in the 2D limit, whereas a family of synthetic molecular aggregates is found to be in the homogeneous limit and is independent of dimensionality.

Effects dust size distribution on transportation of dust grains in a weakly ionized plasma

Transportation of charges, mass and heat of dust particles in a weakly ionized plasma is studied in the present paper. The dependence of electric conductivity, diffusion coefficient and heat conduction coefficient of dust particles on total number density and temperature of dust particles, number density and mass of neutrals, as well as collision cross section area between dust particles and neutrals are given. Effects of dust size distribution on electric conductivity, diffusion coefficient and heat conduction coefficient of dust particles have also been investigated. It is noted that they increase as the mean value of radius of dust particles increases. They increase as difference between maximum and minimum values of dust particles increases when density of the small grains is smaller than that of large grains. However, they decrease as difference between maximum and minimum values of dust particles increases when density of the small grains is larger than that of large grains.

Diffusion properties of active particles with directional reversal

The diffusion properties of self-propelled particles which move at constant speed and, in addition, reverse their direction of motion repeatedly are investigated. The internal dynamics of particles triggering these reversal processes is modeled by a stochastic clock. The velocity correlation function as well as the mean squared displacement is investigated and, furthermore, a general expression for the diffusion coefficient for self-propelled particles with directional reversal is derived. Our analysis reveals the existence of an optimal, finite rotational noise amplitude which maximizes the diffusion coefficient. We comment on the relevance of these results with regard to biological systems and suggest further experiments in this context.

Brownian diffusion of fibers

ABSTRACTMotion of nanoparticles suspended in fluids are dominated by Brownian diffusion—a physical property well understood following the work by Einstein in 1905. While theoretical derivation and experimental measurement of the diffusion coefficients for spherical particles are well developed, such information is lacking for non-spherical particles as the coupled rotational and translational motion hinders a clear description of the overall diffusive outcome. In this study, the Brownian diffusion of elongated nano-fibers is investigated numerically. Motion of the nano-fiber is resolved by solving the system of equations governing its coupled translational and rotational motion. To isolate the Brownian diffusion from other diffusive forces, test fibers are immersed in an unbounded quiescent fluid where only the hydrodynamic drag and Brownian forces are present. The study allows a close look at the Brownian diffusion of nano-fibers with respect to the translation, rotation, coupling, and how the rotation a...

From local to hydrodynamic friction in Brownian motion: A multiparticle collision dynamics simulation study.

The friction and diffusion coefficients of rigid spherical colloidal particles dissolved in a fluid are determined from velocity and force autocorrelation functions by mesoscale hydrodynamic simulations. Colloids with both slip and no-slip boundary conditions are considered, which are embedded in fluids modeled by multiparticle collision dynamics with and without angular momentum conservation. For no-slip boundary conditions, hydrodynamics yields the well-known Stokes law, while for slip boundary conditions the lack of angular momentum conservation leads to a reduction of the hydrodynamic friction coefficient compared to the classical result. The colloid diffusion coefficient is determined by integration of the velocity autocorrelation function, where the numerical result at shorter times is combined with the theoretical hydrodynamic expression for longer times. The suitability of this approach is confirmed by simulations of sedimenting colloids. In general, we find only minor deviations from the Stokes-Einstein relation, which even disappear for larger colloids. Importantly, for colloids with slip boundary conditions, our simulation results contradict the frequently assumed additivity of local and hydrodynamic diffusion coefficients.

Relationship between the fractal structure with the shear complex modulus of montmorillonite suspensions

In this work, we characterized and studied the rheological behavior of montmorillonite suspensions. Our objective was to establish the link between the structure of these suspensions and their rheological behavior.We have characterized these suspensions using several techniques: X-ray scattering to determine their composition and structure, the light scattering to determine the diffusion coefficient of the clay particles and their size. We also measured their densities and their rheological properties in linear and non-linear viscoelasticity.The rheological measurements show that the bentonite particles are structured to form a fractal network. We have determined experimentally the moduli and yield stresses. Using Piau model, we have derived its fractal dimension (D=1.74±0.08). The light scattering measurements allowed us to determine the particles size and the characteristic time of diffusion of the clay particles in the suspension. Finally, knowing the structure of our suspensions and characteristic time, we tried to model their viscoelastic behavior G∗(Ω) using Chambon and Winter model.

Theoretical Method of Calculating Solvent Nonequilibrium Effect on Solute Movement

We formulate a theoretical method for studying the solvent particle dynamics around a moving solute, using time-dependent density functional theory. The theoretical method is applied to the insertion process of a large sphere into a cylindrical vessel immersed in solvent particles. For various velocities of the large sphere, we calculate the nonequilibrium spatial distribution of number density of solvent particles. We find a nonequilibrium effect on the distribution, which is characterized by the total number of solvent particles inside of the vessel. The number is 32.5% larger for a velocity of DS/2dS than for the equilibrium state, where, dS and DS are the diameter and diffusion coefficient of a solvent particle, respectively.

Barium Doped Li2FeSiO4 Cathode Material for Li-Ion Secondary Batteries.

Barium-doped Li2Fe(1-x)Ba(x)SiO4 (x = 0, 0.01) cathode materials were synthesized by the sol-gel and electrospinning processes. The structures of the samples were confirmed by X-ray diffraction and Fourier transform infrared spectroscopy. The sizes and the morphologies of the particles and nanofibers were observed by field emission scanning electron microscopy and atomic force microscopy. The initial discharge capacity of Li2FeSiO4 particles was 28 mAh/g, Li2FeSiO4 nanofibers and barium (Ba)-doped Li2FeSiO4 nanofibers showed the discharge capacities of 78 and 85 mAh/g, respectively. The lithium-ion diffusion coefficients of Li2FeSiO4 particles, Li2FeSiO4 nanofibers and Ba-doped Li2FeSiO4 nanofibers were calculated 5.15 x 10-(16), 3.52 x 10(-16), and 2.27 x 10(-15) cm2/s, respectively. The Ba-doped Li2FeSiO4 cathode material showed the highest lithium-ion diffusion coefficient, and its electrochemical properties were better than that of the pristine material.

Scaling Behavior of Dendritic Nanoparticle Mobility in Semidilute Polymer Solutions

In our studies on particle mobility in polymer solutions, we have investigated and determined self-diffusion coefficients of nanoparticles in semidilute solutions of poly(ethylene glycol) (PEG, Mw = 6, 20, 35, and 100 kDa). Specially designed PEGylated dendrimers with well-defined sizes (dh = 3.4–11.0 nm) and with internal 19F moieties allow for background-free 19F NMR diffusion measurements. This way, we were able to assess the self-diffusion coefficients as a function of particle diameter and length scales (correlation length, tube diameter, polymer radius of gyration) with high resolution. Scaling arguments allowed us to visualize a clear crossover between particles probing a lower apparent viscosity to near macroviscosity when the nanoparticle size is comparable to the PEG polymer coil size. The same arguments are shown to correctly predict particle diffusion coefficients as a function of polymer concentration when the particles are smaller than the polymer coils.

Brownian dynamics of confined rigid bodies.

We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust, space efficient, and easy to accumulate. We construct a system of overdamped Langevin equations in the quaternion representation that accounts for hydrodynamic effects, preserves the unit-norm constraint on the quaternion, and is time reversible with respect to the Gibbs-Boltzmann distribution at equilibrium. We introduce two schemes for temporal integration of the overdamped Langevin equations of motion, one based on the Fixman midpoint method and the other based on a random finite difference approach, both of which ensure that the correct stochastic drift term is captured in a computationally efficient way. We study several examples of rigid colloidal particles diffusing near a no-slip boundary and demonstrate the importance of the choice of tracking point on the measured translational mean square displacement (MSD). We examine the average short-time as well as the long-time quasi-two-dimensional diffusion coefficient of a rigid particle sedimented near a bottom wall due to gravity. For several particle shapes, we find a choice of tracking point that makes the MSD essentially linear with time, allowing us to estimate the long-time diffusion coefficient efficiently using a Monte Carlo method. However, in general, such a special choice of tracking point does not exist, and numerical techniques for simulating long trajectories, such as the ones we introduce here, are necessary to study diffusion on long time scales.

Quantification of sampling uncertainty for molecular dynamics simulation: Time-dependent diffusion coefficient in simple fluids

We analyze two standard methods to compute the diffusion coefficient of a tracer particle in a medium from molecular dynamics (MD) simulation, the velocity autocorrelation function (VACF) method, and the mean-squared displacement (MSD) method. We show that they are equivalent in the sense that they provide the same mean values with the same level of statistical errors. We obtain analytic expressions for the level of the statistical errors present in the time-dependent diffusion coefficient as well as the VACF and the MSD. Under the assumption that the velocity of the tracer particle is a Gaussian process, all results are expressed in terms of the VACF. Hence, the standard errors of all relevant quantities are computable once the VACF is obtained from MD simulation. By using analytic models described by the Langevin equations driven by Gaussian white noise and Poissonian white shot noise, we verify our theoretical error estimates and discuss the non-Gaussianity effect in the error estimates when the Gaussian process approximation does not hold exactly. For validation, we perform MD simulations for the self-diffusion of a Lennard-Jones fluid and the diffusion of a large and massive colloid particle suspended in the fluid. Our theoretical framework is also applicable to mesoscopic simulations, e.g., Langevin dynamics and dissipative particle dynamics.

Structure and dynamics of a layer of sedimented particles.

We investigate experimentally and theoretically thin layers of colloid particles held adjacent to a solid substrate by gravity. Epifluorescence, confocal, and holographic microscopy, combined with Monte Carlo and hydrodynamic simulations, are applied to infer the height distribution function of particles above the surface, and their diffusion coefficient parallel to it. As the particle area fraction is increased, the height distribution becomes bimodal, indicating the formation of a distinct second layer. In our theory, we treat the suspension as a series of weakly coupled quasi-two-dimensional layers in equilibrium with respect to particle exchange. We experimentally, numerically, and theoretically study the changing occupancies of the layers as the area fraction is increased. The decrease of the particle diffusion coefficient with concentration is found to be weakened by the layering. We demonstrate that particle polydispersity strongly affects the properties of the sedimented layer, because of particle size segregation due to gravity.

Simultaneous Electro-Optical Tracking for Nanoparticle Recognition and Counting

We present the first detailed experimental observation and analysis of nanoparticle electrophoresis through a nanochannel obtained with synchronous high-bandwidth electrical and camera recordings. Optically determined particle diffusion coefficients agree with values extracted from fitting electrical transport measurements to distributions from 1D Fokker-Planck diffusion-drift theory. This combined tracking strategy enables optical recognition and electrical characterization of nanoparticles in solution, which can have a broad range of applications in biology and materials science.

Analytical representation of the relations of inertial diffusion transport

A generalized approach has been proposed to describe the diffusive transport of inertial particles at which the known inertialess relations (in particular, between the concentration of particles and the corresponding flux) are supplemented by a factor allowing the calculation of inertial effects in terms of the matrix continued fraction method. The advantage of this approach, which is in the analytical representation of the results, is illustrated by solving the problem of the determination of the effective diffusion coefficient of an inertial particle in a sawtooth potential and the average velocity of the adiabatic inertial ratchet. The character of the nonanalytic behavior of these quantities in the presence of large gradients of the potential has been established.

Predicting First Traversal Times for Virions and Nanoparticles in Mucus with Slowed Diffusion

Particle-tracking experiments focusing on virions or nanoparticles in mucus have measured mean-square displacements and reported diffusion coefficients that are orders of magnitude smaller than the diffusion coefficients of such particles in water. Accurate description of this subdiffusion is important to properly estimate the likelihood of virions traversing the mucus boundary layer and infecting cells in the epithelium. However, there are several candidate models for diffusion that can fit experimental measurements of mean-square displacements. We show that these models yield very different estimates for the time taken for subdiffusive virions to traverse through a mucus layer. We explain why fits of subdiffusive mean-square displacements to standard diffusion models may be misleading. Relevant to human immunodeficiency virus infection, using computational methods for fractional subdiffusion, we show that subdiffusion in normal acidic mucus provides a more effective barrier against infection than previously thought. By contrast, the neutralization of the mucus by alkaline semen, after sexual intercourse, allows virions to cross the mucus layer and reach the epithelium in a short timeframe. The computed barrier protection from fractional subdiffusion is some orders of magnitude greater than that derived by fitting standard models of diffusion to subdiffusive data.

Magnetic field driven micro-convection in the Hele-Shaw cell: the Brinkman model and its comparison with experiment

The micro-convection caused by the ponderomotive forces of the self-magnetic field in a magnetic fluid is studied here both numerically and experimentally. The theoretical approach based on the general Brinkman model substantially improves the description with respect to the previously proposed Darcy model. The predictions of both models are here compared to finely controlled experiments. The Brinkman model, in contrast to the Darcy model, allows us to describe the formation of mushrooms on the plumes of the micro-convective flow and the width of the fingers. In the Brinkman approach, excellent quantitative agreement is also obtained for the finger velocity dynamics and the velocity maximal values as a function of the magnetic Rayleigh number. The diffusion coefficient of particles of the water-based magnetic colloid determined by the threshold field strength value of the micro-convection is significantly larger than the diffusion coefficient of individual particles. This result is confirmed by independent measurements of the diffusion coefficient at the smearing of the diffusion front.

The influence of different turbulence models on the diffusion coefficients of energetic particles

AbstractWe explore the influence of turbulence on the transport of energetic particles by using test particle simulations. We compute parallel and perpendicular diffusion coefficients for two‐component turbulence, isotropic turbulence, a model based on Goldreich‐Sridhar scaling, noisy reduced magnetohydrodynamic turbulence, and a noisy slab model. We show that diffusion coefficients have a similar rigidity dependence regardless which turbulence model is used, and thus, we conclude that the influence of turbulence on particle transport is not as strong as originally thought. Only fundamental quantities such as particle rigidity and the Kubo number are relevant. In the current paper we also confirm the unified nonlinear transport theory for noisy slab turbulence. To double check the validity and accuracy of our numerical results, we use a second test particle code. We show that both codes provide very similar results confirming the validity of our conclusions.

Diffusion deposition of submicron aerosol particles in screen filters

The deposition of submicron aerosol particles on metal screens has been studied at small Reynolds numbers. The obtained experimental data have been compared with theoretical estimates of the deposition of Brownian particles in a model fibrous filter with allowance for a finite particle size and the existence of a Knudsen boundary layer on a wire surface, with the thickness of the layer being, under normal conditions, comparable with particle sizes. The possibility of using screen diffusion batteries for determining the average diffusion coefficient of submicron particles and as test filters has been discussed.

Dynamic Viscosity of Tetracyanoborate- and Tricyanomethanide-Based Ionic Liquids by Dynamic Light Scattering

Low-viscosity ionic liquids (ILs) based on the anions [B(CN)4]− (tetracyanoborate) and [C(CN)3]− (tricyanomethanide) are currently discussed as alternative working fluids for various applications. The dynamic viscosity of such ILs carrying [1-alkyl-MIM]+ (1-alkyl-3-methylimidazolium) cations was investigated via determination of the translational particle diffusion coefficient by dynamic light scattering (DLS). The long-term stability of suspensions of different particles in the ILs, their particle diameters, and the influence of laser power on the measured particle diffusion coefficient for semitransparent ILs were studied. For temperatures from 283 to 353 K at atmospheric pressure, the dynamic viscosity of the four pure ILs forming stable suspensions was obtained with an uncertainty of less than 5% (k = 2) and agrees with literature. Absorption of CO2 at pressures up to 0.87 MPa induced a distinct decrease in the dynamic viscosity. Differences between the viscosities of the different systems can be explained by varying strength of molecular interactions.