Temperature anomalies of oscillating diffusion in ac-driven periodic systems.

We investigate an overdamped Brownian motion in symmetric periodic potential switching by Markovian dichotomous noise between two configurations. Second configuration differs from the first one by the half of spatial period displacement when the maxima of a potential profile become the minima and vice versa. We establish a validity of the formula for effective diffusion constant previously obtained in the case of fixed periodic potentials and, thus, reduce the problem to calculation of mean first-passage times (MFPTs). At the same time the MFPT in this formula should be substituted for the semi-sum of MFPTs regarding two initial configurations of potential profile. A set of equations for MFPTs in flipping potentials can be solved for the sawtooth periodic potential. As a result, after cumbersome calculations we obtain the exact complex expression for effective diffusion coefficient of Brownian particles in such a medium which is valid for arbitrary mean frequency of potential switchings. We detect the acceleration of diffusion in comparison with the case of fixed sawtooth potential profile as it was demonstrated for a symmetric periodic potential modulating by external Gaussian white noise.

Collective directional transport of particles in symmetric periodic potentials is studied. An example is given to reveal the directed motion of a single particle in a symmetric periodic potential and subject to an asymmetric ac force with zero mean. It is then shown that the asymmetric coupling can give rise to a directed transport. The transport failure (pinning of the lattice) is related to the phase delocalization (crisis) in the circle map. For symmetric couplings, it is found that a train of plane wave can also lead to a directed transport. The mode-locking steps of the transport velocity is found and analyzed. The collective transport can be well optimized by adjusting parameters in the system.

Defect modes are studied in parity-time (PT) symmetric periodic complex potentials for both positive and negative defects. Such new kinds of linear localized modes may conserve their energy or endure gain or loss upon propagating. The existence domain of the conserved modes would be prolonged by positive defects or shortened by negative defects, and the dissipative modes would appear before the phase transition point of the PT symmetric potential at stronger negative defects.

Applying a temperature gradient to a layer of a binary fluid establishes a diffusive transport mechanism called thermophoresis or Soret effect which separates the two fluid’s components and is measured by the Soret coefficient. Recent investigations carried out on concentrated magnetic fluids showed that the intensity of the Soret effect depends on the concentration of the nanoparticles transported. The present article, therefore, deals with the concentration-dependence of the Soret coefficient using five equally composed magnetic fluids only varying in the concentration of the particles from 2 vol. % to 10 vol. % of magnetic material. The current investigations point out that the determination of the Soret coefficient and especially its dependence on the particles’ concentration is based on the determination of the thermal and particle diffusion coefficient. The article, therefore, presents a theoretical approach for the determination of the thermal diffusion coefficient and adapts a commonly used Ansatz for the particle diffusion coefficient for the present case of concentrated magnetic fluids. It is thereby possible to determine a theoretical Soret coefficient in dependence on an empirical parameter α. The coefficient is compared with the experimental approaches which have been previously used, these will be referred to as “analytical approach” throughout the text. A second comparison is achieved with a hybrid Soret coefficient which fits the experimentally detected separation curves numerically. Within the investigations, the hydrodynamic concentration of the particles is used, assuming a surfactant layer’s thickness of 2 nm per magnetic particle which leads to concentrations between approximately 11 vol. % and 47 vol. %. The diffusion coefficient ranges from 0.6 × 10−11 m2/s to 2.5 × 10−11 m2/s depending on the analytical model used. The theoretical Soret coefficient decreases with increasing particles’ concentration; the experimental values derived from the analytical approach decrease from 0.06 K−1 to 0.01 K−1 for increasing particles’ concentration. The numerically determined coefficient ranges from 0.11 K−1 to 0.022 K−1. The experimental values are smaller than former experimental results suggest (0.16 K−1), which is due to the fact that in former works, only magnetic concentrations had been considered. All three current investigations prove what could also be partly seen in former experiments that the higher the particles’ concentration the weaker is thermophoresis. The particle diffusion coefficient has to be known for the determination of the Soret coefficient. It is carried out a proof of principle in the article showing that the horizontal thermophoresis cell can also be used to determine the rehomogenisation process which takes place after separating the fluid by applying a homogeneous temperature to the fluid. The diffusion coefficients that could be determined experimentally range from 1 × 10−11 m2/s to 6 × 10−11 m2/s.

The mutual (or collective) diffusion coefficient of Brownian particles treated in most of previous microscopic theories is regarded as defined on the basis of the dynamic structure factor. It is pointed out for cases where both direct and hydrodynamic pair interactions are present between Brownian particles that this diffusion coefficient does not satisfy the generalized Einstein relation which results from conventional irreversible thermodynamics and which should be obeyed by the diffusion coefficient as would be determined by conventional gradient diffusion experiments. This is ascribed to the fact that the diffusion coefficient based on the dynamic structure factor is generally not identical with the conventional diffusion coefficient, i.e., whereas the latter diffusion coefficient describes the collective diffusion of Brownian particles under conditions of uniform temperature and pressure, the former describes that under conditions of uniform temperature and uniform chemical potential of solvent. A correct expression for the conventional diffusion coefficient is derived by taking this difference into account. Both diffusion coefficients are evaluated for the case of hard spheres.

Fluorescence recovery after photobleaching (FRAP) and single particle tracking (SPT) techniques determine the diffusion coefficient from average diffusive motion of high-concentration molecules and from trajectories of low-concentration single molecules, respectively. Lateral diffusion coefficients measured by FRAP and SPT techniques for the same biomolecule on cell membrane have exhibited inconsistent values across laboratories and platforms with larger diffusion coefficient determined by FRAP, but the sources of the inconsistency have not been investigated thoroughly. Here, we designed an image-based FRAP-SPT system and made a direct comparison between FRAP and SPT for diffusion coefficient of submicron particles with known theoretical values derived from Stokes–Einstein equation in aqueous solution. The combined [Formula: see text]FRAP-SPT technique allowed us to measure the diffusion coefficient of the same fluorescent particle by utilizing both techniques in a single platform and to scrutinize inherent errors and artifacts of FRAP. Our results reveal that diffusion coefficient overestimated by FRAP is caused by inaccurate estimation of the bleaching spot size and can be corrected by simple image analysis. Our [Formula: see text]FRAP-SPT technique can be potentially used for not only cellular membrane dynamics but also for quantitative analysis of the spatiotemporal distribution of the solutes in small scale analytical devices.

Magnetorheological properties significantly depend on the regime of aggregate structures. In the case of cubic particles, closely-packed clusters that are significantly different from those for the case of spherical or rod-like particles are formed in the system since magnetic cube-like particles prefer a face-to-face contact with the neighboring particles. Therefore, a cubic particle suspension is expected to exhibit a sufficiently strong magnetorheological effect, which may be investigated by means of Brownian dynamics simulations. However, the translational and rotational diffusion (or friction) coefficients of a cube are not known and indispensable in order to develop this simulation technique. From this background, in the present study, we have analyzed the flow field around a cube in a Stokes flow regime in order to estimate the diffusion (or friction) coefficients of cube-like particles that are required for performing Brownian dynamics simulations of a cubic particle suspension. In the situation of a uniform flow field with a Reynolds number sufficiently smaller than unity, the force acts on the cube only in the flow field direction, and the torque acting on the cube may be regarded as negligible. In the situation of a rotational flow field with a sufficiently low Reynolds number, the torque acts on the cube only in the direction of angular velocity of the rotational flow field, and the force negligibly act on the cube. These characteristics are in significantly similar to those for the case of spheres in a Stokes flow situation. From these results, we may conclude that the diffusion coefficients of cube-like particles can be expressed by introducing a correction factor to those of the spherical particles.

Diffusing probe measurements in Newtonian and elastic solutions

Near-surface Brownian motor with synchronously fluctuating symmetric potential and applied force

Here, we investigate transport of an inertial particle in a symmetric periodic potential and subjected to an external signal, such that mass of the particle is modulated sinusoidally. Our numerical results indicate that the mass modulation can induce abnormal transport in the system, whereas no current appears in the case of constant mass. In the absence of external bias, direction of mean velocity of the particle changes several times as amplitude and frequency of the mass modulation are varied, i.e., a multiple current reversals (CR) phenomenon. The multiple CRs result from temporal symmetry breaking of the system. In the presence of external bias, multiple absolute negative mobilities (ANM) take place in the system. Intrinsic physical mechanisms responsible for the occurrence of the multiple ANMs are analyzed in detail.

Granular mixing with bladed mixers is widely used across various industries. This study employed the Discrete Element Method (DEM) to explore the effects of rake angles (30° (150°), 45° (135°), 60° (120°), and 90°), rotational speeds (25, 50, 75, 100, and 150 rpm), and fill levels (1, 2 and 3) on the flow and mixing efficiency of 2- and 3-bladed impellers. The Lacey mixing index, granular temperature, circumferential velocity, diffusion coefficient, and void percentage were used to evaluate mixer performance. Results showed that for rake angles ≥ 90°, the highest values for the Lacey mixing index, granular temperature, and diffusion coefficient were achieved, although particle circumferential velocity decreased. The mixing efficiency improved significantly with 2-bladed impellers at rake angles of 135° and 150° and 3-bladed impellers at 120° and 135° rake angles. The void percentage increased linearly with rake angle. Rotational speed and fill levels were found to strongly affected the Lacey mixing index, with optimal rotational speeds < 100 rpm. Increasing rotational speed raised particle granular temperature, circumferential velocity, diffusion coefficient, and void percentage. For 3-bladed impellers, performance improved at fill levels where H/h > 1, although granular temperature and diffusion coefficient decreased with increasing fill levels. Granular temperature and diffusion coefficient were found to be reliable indicators of pre-mixing performance. It is recommended to use 3-bladed impellers at H/h > 1 and rotational speeds < 100 rpm, while 2-bladed impellers perform better at lower fill levels.

Giant diffusion, where the diffusion coefficient of a Brownian particle in a periodic potential with an external force is significantly enhanced by the external force, is a nontrivial nonequilibrium phenomenon. We propose a simple stochastic model of giant diffusion, which is based on a biased continuous-time random walk (CTRW) with flight time. By introducing a flight time representing traversal dynamics, we derive the diffusion coefficient using renewal theory and demonstrate its universal peak behavior under various periodic potentials, especially in low-temperature regimes. Giant diffusion is universally observed in the sense that there is a peak of the diffusion coefficient for any tilted periodic potentials and the degree of the diffusivity is greatly enhanced especially for low-temperature regimes. The biased CTRW models with flight times are applied to diffusion under three tilted periodic potentials. Furthermore, the temperature dependence of the maximum diffusion coefficient and the external force that attains the maximum are presented for diffusion under a tilted sawtooth potential.

In this paper the diffusion coefficient for the fast alpha particles produced in a thermonuclear plasma is derived numerically for the case of a magnetic field perturbed by ripple and magnetohydrodynamic (MHD) helical modes. It is found that this diffusion coefficient varies monotonously with the amplitude of the magnetic perturbations and that the transition from the classic to the stochastic regime occurs smoothly. The ripple perturbations as well as the MHD perturbations essentially affect the trapped-particle orbits It is shown that above an MHD perturbation amplitude of some 10[sup [minus]3] of the total magnetic field, severe fast alpha-particle losses must be expected. Parametric studies have shown the dependence of the MHD helical diffusion coefficient on the amplitude of the perturbation, the helical mode number, and the energy of the alpha particles. An analytic expression for the MHD diffusion coefficient, based on these scalings, is proposed.

Ratchet effect in an underdamped periodic potential and its characterisation

Enhancement of current commensurate with mutual noise–noise correlation in a symmetric periodic substrate: The benefits of noise and nonlinearity