Particle Diffusion Coefficient Research Articles

Fast Bayesian inference of optical trap stiffness and particle diffusion

Bayesian inference provides a principled way of estimating the parameters of a stochastic process that is observed discretely in time. The overdamped Brownian motion of a particle confined in an optical trap is generally modelled by the Ornstein-Uhlenbeck process and can be observed directly in experiment. Here we present Bayesian methods for inferring the parameters of this process, the trap stiffness and the particle diffusion coefficient, that use exact likelihoods and sufficient statistics to arrive at simple expressions for the maximum a posteriori estimates. This obviates the need for Monte Carlo sampling and yields methods that are both fast and accurate. We apply these to experimental data and demonstrate their advantage over commonly used non-Bayesian fitting methods.

Symplectic Simulations of Radial Diffusion of Fast Alpha Particles in the Presence of Low-Frequency Modes in Rippled Tokamaks

The symplectic Hamiltonian guiding centre code which enables efficient calculation of charged particle trajectories and diffusion coefficients has been applied to fast ion motion in magnetically perturbed tokamak plasmas. Particularly fusion born alpha particle drift motion, in constant of motion space, is examined in the presence of low mode-number neoclassical tearing mode (NTM) perturbation in a toroidally rippled tokamak. The main focus of this study is to investigate the dependence of the radial diffusion coefficient of energetic ions on the perturbation strength and on the localization of the perturbation. The resonance between bounce motion and toroidal field ripples plays a significant role in this context. The presence of NTMs results in substantial enhancement of radial diffusion coefficient for passing particles. Depending on the strength and localization of the NTM it can cause enhancement or degradation of the radial ripple diffusion coefficient of trapped particles.

Diffusion in systems crowded by active force-dipole molecules.

Experimental studies of systems containing active proteins that undergo conformational changes driven by catalytic chemical reactions have shown that the diffusion coefficients of passive tracer particles and active molecules are larger than the corresponding values when chemical activity is absent. Various mechanisms have been proposed for such behavior, including, among others, force dipole interactions of molecular motors moving on filaments and collective hydrodynamic effects arising from active proteins. Simulations of a multi-component system containing active dumbbell molecules that cycle between open and closed states, a passive tracer particle and solvent molecules are carried out. Consistent with experiments, it is shown that the diffusion coefficients of both passive particles and the dumbbells themselves are enhanced when the dumbbells are active. The dependence of the diffusion enhancement on the volume fraction of dumbbells is determined, and the effects of crowding by active dumbbell molecules are shown to differ from those due to inactive molecules.

Transport, geometrical, and topological properties of stealthy disordered hyperuniform two-phase systems.

Disordered hyperuniform many-particle systems have attracted considerable recent attention, since they behave like crystals in the manner in which they suppress large-scale density fluctuations, and yet also resemble statistically isotropic liquids and glasses with no Bragg peaks. One important class of such systems is the classical ground states of "stealthy potentials." The degree of order of such ground states depends on a tuning parameter χ. Previous studies have shown that these ground-state point configurations can be counterintuitively disordered, infinitely degenerate, and endowed with novel physical properties (e.g., negative thermal expansion behavior). In this paper, we focus on the disordered regime (0 < χ < 1/2) in which there is no long-range order and control the degree of short-range order. We map these stealthy disordered hyperuniform point configurations to two-phase media by circumscribing each point with a possibly overlapping sphere of a common radius a: the "particle" and "void" phases are taken to be the space interior and exterior to the spheres, respectively. The hyperuniformity of such two-phase media depends on the sphere sizes: While it was previously analytically proven that the resulting two-phase media maintain hyperuniformity if spheres do not overlap, here we show numerically that they lose hyperuniformity whenever the spheres overlap. We study certain transport properties of these systems, including the effective diffusion coefficient of point particles diffusing in the void phase as well as static and time-dependent characteristics associated with diffusion-controlled reactions. Besides these effective transport properties, we also investigate several related structural properties, including pore-size functions, quantizer error, an order metric, and percolation thresholds. We show that these transport, geometrical, and topological properties of our two-phase media derived from decorated stealthy ground states are distinctly different from those of equilibrium hard-sphere systems and spatially uncorrelated overlapping spheres. As the extent of short-range order increases, stealthy disordered two-phase media can attain nearly maximal effective diffusion coefficients over a broad range of volume fractions while also maintaining isotropy, and therefore may have practical applications in situations where ease of transport is desirable. We also show that the percolation threshold and the order metric are positively correlated with each other, while both of them are negatively correlated with the quantizer error. In the highly disordered regime (χ → 0), stealthy point-particle configurations are weakly perturbed ideal gases. Nevertheless, reactants of diffusion-controlled reactions decay much faster in our two-phase media than in equilibrium hard-sphere systems of similar degrees of order, and hence indicate that the formation of large holes is strongly suppressed in the former systems.

Diffusion in time-dependent confined geometries

We study a system consisting of one particle whose Brownian motion is restricted by confining walls with specific temporal dependence. An increase in the time reflects one reduction of diameter in the medium that affects the diffusion process. Therefore, we are interested in how the mobility and effective diffusion coefficient of the particles is modified by changes in the width of the geometry. In this way, we purpose an extension of the actual formalism related to analytical description of the diffusion process in confined geometries to include the effects of temporal change.

Rapid determination of hydrodynamic radii beyond the limits of Taylor dispersion

Taylor dispersion analysis (TDA) is an absolute method for determining the diffusion coefficients, and hence the hydrodynamic radii, of particles by measuring the dispersion in a carrier medium flowing within a capillary. It is applicable under conditions which allow the particles to radially diffuse appreciably across the cross-section of the flow before the measurement and therefore implies long measurement times are required for large particles with small diffusion coefficients. In this paper, a method has been developed by which the diffusion coefficients of large particles can be rapidly estimated from the shapes of the concentration profiles obtained at much earlier measurement times. The method relies on the fact that the shapes of the early-time concentration profiles are dependent on the diffusion coefficient, flow rate and the capillary radius through the dimensionless residence time which, theoretically, is a measure of the amount of radial diffusion undergone by the particles. The amount of radial diffusion for nanospheres of varying sizes was estimated by quantifying the relative change in the shapes of concentration profiles obtained at two points in the flow and a correlation was obtained with the variation of the dimensionless residence time to confirm the theory. This correlation was then tested by applying it to another set of measurements of solutes and solute mixtures of different sizes including a protein. The estimated diffusion coefficients were found to be in good agreement with the expected values. This demonstrates the potential for the method to extend dispersion analysis to regimes well outside the TDA limits to enable the rapid characterization of large particles.

Physical characterization of nanoparticle size and surface modification using particle scattering diffusometry

As the field of colloidal science continues to expand, tools for rapid and accurate physiochemical characterization of colloidal particles will become increasingly important. Here, we present Particle Scattering Diffusometry (PSD), a method that utilizes dark field microscopy and the principles of particle image velocimetry to measure the diffusivity of particles undergoing Brownian motion. PSD measures the diffusion coefficient of particles as small as 30 nm in diameter and is used to characterize changes in particle size and distribution as a function of small, label-free, surface modifications of particles. We demonstrate the rapid sizing of particles using three orders-of-magnitude less sample volume than current standard techniques and use PSD to quantify particle uniformity. Furthermore, PSD is sensitive enough to detect biomolecular surface modifications of nanometer thickness. With these capabilities, PSD can reliably aid in a wide variety of applications, including colloid sizing, particle corona characterization, protein footprinting, and quantifying biomolecule activity.

Transport of magnetic turbulence in supernova remnants

Context. Supernova remnants are known as sources of galactic cosmic rays for their non-thermal emission of radio waves, X-rays, and gamma-rays. However, the observed soft broken power-law spectra are hard to reproduce within standard acceleration theory based on the assumption of Bohm diffusion and steady-state calculations. Aims. We point out that a time-dependent treatment of the acceleration process together with a self-consistent treatment of the scattering turbulence amplification is necessary. Methods. We numerically solve the coupled system of transport equations for cosmic rays and isotropic Alfvenic turbulence. The equations are coupled through the growth rate of turbulence determined by the cosmic-ray gradient and the spatial diffusion coefficient of cosmic rays determined by the energy density of the turbulence. The system is solved on a co-moving expanding grid extending upstream for dozens of shock radii, allowing for the self-consistent study of cosmic-ray diffusion in the vicinity of their acceleration site. The transport equation for cosmic rays is solved in a test-particle approach. Results. We demonstrate that the system is typically not in a steady state. In fact, even after several thousand years of evolution, no equilibrium situation is reached. The resulting time-dependent particle spectra strongly differ from those derived assuming a steady state and Bohm diffusion. Our results indicate that proper accounting for the evolution of the scattering turbulence and hence the particle diffusion coefficient is crucial for the formation of the observed soft spectra. In any case, the need to continuously develop magnetic turbulence upstream of the shock introduces non-linearity in addition to that imposed by cosmic-ray feedback.

Adsorption characteristics of Direct Red 23 from aqueous solution by biochar

Biochar, produced by the pyrolysis of pig manure at 800°C, was characterized and investigated as an adsorbent for the removal of Direct Red 23 from aqueous solution. The adsorption kinetics was best described by a modified Freundlich model and intra-particle diffusion models. The value of the apparent adsorption constant k (modified Freundlich model) decreased from 0.133 to 0.076L/(g·min1/m), when the amount of biochar increased from 1 to 8g/L. Values of effective particle diffusion coefficient (Dp) and liquid film diffusion coefficient (Df) were calculated to further determine the rate-limiting step of the adsorption process. The value of activation energy 5.558kcal/mol indicates that the adsorption is a physical process controlled by film diffusion and the adsorption process is endothermic. When pH<pHZPC (8.71),the surface of biochar is positively charged; the positive charge promoted the anionic dyes attracted onto the biochar by electrostatic force; and a hydrogen band was formed with the protonated OH functional groups on the active sites. The adsorption equilibrium study indicates that the adsorption was in a multilayer mode, and the maximum adsorption capacity was 2.19×10−5mol/g, at pH2.20 and temperature 25°C. Considering the widely availability and high removal efficiency, biochar is deserved further investigations for applications in more hazardous substances removal.

Simulations of energetic particles interacting with nonlinear anisotropic dynamical turbulence

We investigate test-particle diffusion in dynamical turbulence based on a numerical approach presented before. For the turbulence we employ the nonlinear anisotropic dynamical turbulence model which takes into account wave propagation effects as well as damping effects. We compute numerically diffusion coefficients of energetic particles along and across the mean magnetic field. We focus on turbulence and particle parameters which should be relevant for the solar system and compare our findings with different interplanetary observations. We vary different parameters such as the dissipation range spectral index, the ratio of the turbulence bendover scales, and the magnetic field strength in order to explore the relevance of the different parameters. We show that the bendover scales as well as the magnetic field ratio have a strong influence on diffusion coefficients whereas the influence of the dissipation range spectral index is weak. The best agreement with solar wind observations can be found for equal bendover scales and a magnetic field ratio of $\delta$B/B0 = 0.75.

Optimizing experimental parameters for tracking of diffusing particles.

We describe how a single-particle tracking experiment should be designed in order for its recorded trajectories to contain the most information about a tracked particle's diffusion coefficient. The precision of estimators for the diffusion coefficient is affected by motion blur, limited photon statistics, and the length of recorded time series. We demonstrate for a particle undergoing free diffusion that precision is negligibly affected by motion blur in typical experiments, while optimizing photon counts and the number of recorded frames is the key to precision. Building on these results, we describe for a wide range of experimental scenarios how to choose experimental parameters in order to optimize the precision. Generally, one should choose quantity over quality: experiments should be designed to maximize the number of frames recorded in a time series, even if this means lower information content in individual frames.

Single-File Escape of Colloidal Particles from Microfluidic Channels.

Single-file diffusion is a ubiquitous physical process exploited by living and synthetic systems to exchange molecules with their environment. It is paramount to quantify the escape time needed for single files of particles to exit from constraining synthetic channels and biological pores. This quantity depends on complex cooperative effects, whose predominance can only be established through a strict comparison between theory and experiments. By using colloidal particles, optical manipulation, microfluidics, digital microscopy, and theoretical analysis we uncover the self-similar character of the escape process and provide closed-formula evaluations of the escape time. We find that the escape time scales inversely with the diffusion coefficient of the last particle to leave the channel. Importantly, we find that at the investigated microscale, bias forces as tiny as 10^{-15} N determine the magnitude of the escape time by drastically reducing interparticle collisions. Our findings provide crucial guidelines to optimize the design of micro- and nanodevices for a variety of applications including drug delivery, particle filtering, and transport in geometrical constrictions.

3D raster image correlation spectroscopy based on ultra-continuous laser STED system

Stimulated emission depletion is a kind of super resolution imaging technology widely used in biomedical fields, which improves far-field optical resolution to less than 100nm. In this paper, 3D raster image correlation spectroscopy which is based on ultra-continuous laser STED system is introduced. The optimized system will be discussed from the aspects of precise collinear alignment, pulse time delay and central intensity of STED spot. Experiments show that the resolution is about 60nm. The laser reduces the effects of photobleaching and dark state. Moreover, the combination of STED and 3D raster image correlation spectroscopy can extend applications of STED into molecular dynamics. Simplified but rigorous fitting equations were rewritten according to the benefits from the laser. Diffusion coefficients of particles in different situations are obtained.

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.