Diffusion Dynamics Of Particles Research Articles

Numerical investigation of a fractional diffusion model on circular comb-inward structure

In this paper, the diffusion dynamics of particles on a circular comb-inward structure with different radial and tangential mobilities are studied. The Scott-Blair time-fractional memory model is exploited to incorporate the trapping process in the diffusion. A new formulation of particle flux is proposed for which the numerical discretization is straightforward. The numerical scheme is based on the second-order L2−1σ formula for time stepping and uses the finite difference method for spatial approximations. The influences of involved parameters on the distribution of particles and the mean-square displacement (MSD) are investigated in detail. According to the model prediction, the diffusion of particles on the ring decreases with the smaller values of the fractional order α. Results also indicate that the radial and tangential mobilities exhibit the opposite effects on the MSD of particles.

Photon ensemble correlation spectroscopy enables decorrelation-rate-limited ultrafast measurement of diffusive particle dynamics.

In contrast to conventional dynamic light scattering (DLS) measurement via a single sampling volume (SV) observation over a long time span, we propose a novel technique named "photon ensemble correlation spectroscopy" for ultrafast characterization of diffusive particle dynamics through decorrelation analysis of complex-valued DLS scattering signals from an ensemble of independent SVs. We confirm that the ensemble analysis provides a decorrelation-rate-limited ultrafast measurement and demonstrates the feasibility of imaging spatially resolved particle dynamics. Moreover, the use of complex-valued signals gives additional superiority in terms of reliability.

Anomalous transport in heterogeneous media

The diffusion dynamics of particles in heterogeneous media is studied using particle-based simulation techniques. A special focus is placed on systems where the transport of particles at long times exhibits anomalies such as subdiffusive or superdiffusive behavior. First, a two-dimensional model system is considered containing gas particles (tracers) that diffuse through a random arrangement of pinned, disk-shaped particles. This system is similar to a classical Lorentz gas. However, different from the original Lorentz model, soft instead of hard interactions are considered and we also discuss the case where the tracer particles interact with each other. We show that the modification from hard to soft interactions strongly affects anomalous-diffusive transport at high obstacle densities. Second, non-linear active micro-rheology in a glass-forming binary Yukawa mixture is investigated, pulling single particles through a deeply supercooled state by applying a constant force. Here, we observe superdiffusion in force direction and analyze its origin. Finally, we consider the Brownian dynamics of a particle which is pulled through a two-dimensional random force field. We discuss the similarities of this model with the Lorentz gas as well as active micro-rheology in glass-forming systems.

Characterization of the diffusive dynamics of particles with time-dependent asymmetric microscopy intensity profiles.

We put forth an algorithm to track isolated micron-size solid and liquid particles that produce time-dependent asymmetric intensity patterns. This method quantifies the displacement of a particle in the image plane from the peak of a spatial cross-correlation function with a reference image. The peak sharpness results in subpixel resolution. We demonstrate the utility of the method for tracking liquid droplets with changing shapes and micron-size particles producing images with exaggerated asymmetry. We compare the accuracy of diffusivity determination with particles of known size by this method to that by common tracking techniques and demonstrate that our algorithm is superior. We address several open questions on the characterization of diffusive behaviors. We show that for particles, diffusing with a root-mean-square displacement of 0.6 pixel widths in the time between two successive recorded frames, more accurate diffusivity determinations result from mean squared displacement (MSD) for lag times up to 5 time intervals and that MSDs determined from non-overlapping displacements do not yield more accurate diffusivities. We discuss the optimal length of image sequences and demonstrate that lower frame rates do not affect the accuracy of the estimated diffusivity.

Modeling Nanoparticle Targeting to a Vascular Surface in Shear Flow Through Diffusive Particle Dynamics.

Nanoparticles are regarded as promising carriers for targeted drug delivery and imaging probes. A fundamental understanding of the dynamics of polymeric nanoparticle targeting to receptor-coated vascular surfaces is therefore of great importance to enhance the design of nanoparticles toward improving binding ability. Although the effects of particle size and shear flow on the binding of nanoparticles to a vessel wall have been studied at the particulate level, a computational model to investigate the details of the binding process at the molecular level has not been developed. In this research, dissipative particle dynamics simulations are used to study nanoparticles with diameters of several nanometers binding to receptors on vascular surfaces under shear flow. Interestingly, shear flow velocities ranging from 0 to 2000 s−1 had no effect on the attachment process of nanoparticles very close to the capillary wall. Increased binding energy between the ligands and wall caused a corresponding linear increase in bonding ability. Our simulations also indicated that larger nanoparticles and those of rod shape with a higher aspect ratio have better binding ability than those of smaller size or rounder shape.

Entropic particle transport: Higher-order corrections to the Fick-Jacobs diffusion equation

Transport of point-size Brownian particles under the influence of a constant and uniform force field through a planar three-dimensional channel with smoothly varying, axis-symmetric periodic side walls is investigated. Here we employ an asymptotic analysis in the ratio between the difference of the widest and the most narrow constriction divided through the period length of the channel geometry. We demonstrate that the leading-order term is equivalent to the Fick-Jacobs approximation. By use of the higher-order corrections to the probability density we show that in the diffusion-dominated regime the average transport velocity is obtained as the product of the zeroth-order Fick-Jacobs result and the expectation value of the spatially dependent diffusion coefficient D(x), which substitutes the constant diffusion coefficient in the common Fick-Jacobs equation. The analytic findings are corroborated with the precise numerical results of a finite element calculation of the Smoluchowski diffusive particle dynamics occurring in a reflection symmetric sinusoidal-shaped channel.

Path-Length-Resolved Diffusive Particle Dynamics in Spectral-Domain Optical Coherence Tomography

We describe a new method to measure the decorrelation rate of the optical coherence tomography (OCT) magnitude simultaneously in space and time. We measure the decorrelation rate of the OCT magnitude in a Fourier-domain OCT system for a large range of translational diffusion coefficients by varying the sphere diameter. The described method uses the sensitivity advantage of Fourier-domain OCT over time-domain OCT to increase the particle diffusion imaging speed by a factor of 200. By coherent gating, we reduce the contribution of multiple scattering to the detected signal, allowing a quantitative study of diffusive particle dynamics in high concentration samples. We demonstrate that this technique is well suited to image diffusive particle dynamics in samples with a complex geometry as we measure the morphology and diffusive particle dynamics simultaneously with both high spatial and high temporal resolution.

Dynamics in shear flow studied by X-ray Photon Correlation Spectroscopy

X-ray Photon Correlation Spectroscopy was used to measure the diffusive dynamics of colloidal particles in a shear flow. The results presented here show how the intensity autocorrelation functions measure both the diffusive dynamics of the particles and their flow-induced, convective motion. However, in the limit of low flow/shear rates, it is possible to obtain the diffusive component of the dynamics, which makes the method suitable for the study of the dynamical properties of a large class of complex soft-matter and biological fluids. An important benefit of this experimental strategy over more traditional X-ray methods is the minimization of X-ray-induced beam damage. While the method can be applied also for photon correlation spectroscopy in the visible domain, our analysis shows that the experimental conditions under which it is possible to measure the diffusive dynamics are easier to achieve at higher q values (with X-rays).

Ion dynamics in structurally disordered materials: effects of random Coulombic traps

A stochastic lattice gas model is presented pertaining to classical charge transport in doped solid materials. Specifically, we investigate the diffusive dynamics of particles of charge q in an energy-landscape determined by immobile centers of charge — q which are distributed randomly in space. Results from extensive Monte Carlo simulations for tracer diffusion, conductivity and nuclear-spin relaxation are discussed and compared in detail with experiments on ion conduction in alkali-doped network glasses. Emphasis is put on the dependence of transport properties on carrier concentration and on non-exponential, slow relaxational effects which manifest themselves in different experimental spectra.