Transport of finite size particles in confined narrow channels: Diffusion, coherence, and particle separation

Entropic stochastic resonance of finite-size particles in confined Brownian transport

We demonstrate the existence of entropic stochastic resonance (ESR) of passive Brownian particles with finite size in a double- or triple-circular confined cavity, and compare the similarities and differences of ESR in the double-circular cavity and triple-circular cavity. When the diffusion of Brownian particles is constrained to the double- or triple-circular cavity, the presence of irregular boundaries leads to entropic barriers. The interplay between the entropic barriers, a periodic input signal, the gravity of particles, and intrinsic thermal noise may give rise to a peak in the spectral amplification factor and therefore to the appearance of the ESR phenomenon. It is shown that ESR can occur in both a double-circular cavity and a triple-circular cavity, and by adjusting some parameters of the system, the response of the system can be optimized. The differences are that the spectral amplification factor in a triple-circular cavity is significantly larger than that in a double-circular cavity, and compared with the ESR in a double-circular cavity, the ESR effect in a triple-circular cavity occurs within a wider range of external force parameters. In addition, the strength of ESR also depends on the particle radius, and smaller particles can induce more obvious ESR, indicating that the size effect cannot be safely neglected. The ESR phenomenon usually occurs in small-scale systems where confinement and noise play an important role. Therefore, the mechanism that is found could be used to manipulate and control nanodevices and biomolecules.

Velocity jump process with volume exclusions in a narrow channel

This paper analyzes the impact of collisions in a system of N identical hard-core particles driven according to a velocity jump process. The physical space is essentially a channel in R with a probability of occupants being able to pass each other. The system mimics what nature does, where individuals pass one another in a narrow channel while making incidental contact with those moving in the opposite direction. The passing probability may depend on the particles' size and the channel's width. Starting from the particle level model, we systematically derive a nonlinear transport equation based on an asymptotic expansion. Under low-occupied fractions, numerical solutions of both the kinetic model and the stochastic particle system are compared well during biased and unbiased random velocity changes. Analysis of the subpopulation motility within a large population exhibits the consequences of volume exclusions and channel confinements on the traveling speeds.

Confined diffusion in a random Lorentz gas environment

We study the diffusive behavior of biased Brownian particles in a two dimensional confined geometry filled with the freezing obstacles. The transport properties of these particles are investigated for various values of the obstacle density η and the scaling parameter f, which is the ratio of work done to the particles to available thermal energy. We show that, when the thermal fluctuations dominate over the external force, i.e., small f regime, particles get trapped in the given environment when the system percolates at the critical obstacle density η_{c}≈1.2. However, as f increases, we observe that particle trapping occurs prior to η_{c}. In particular, we find a relation between η and f which provides an estimate of the minimum η up to a critical scaling parameter f_{c} beyond which the Fick-Jacobs description is invalid. Prominent transport features like nonmonotonic behavior of the nonlinear mobility, anomalous diffusion, and greatly enhanced effective diffusion coefficient are explained for various strengths of f and η. Also, it is interesting to observe that particles exhibit different kinds of diffusive behaviors, i.e., subdiffusion, normal diffusion, and superdiffusion. These findings, which are genuine to the confined and random Lorentz gas environment, can be useful to understand the transport of small particles or molecules in systems such as molecular sieves and porous media, which have a complex heterogeneous environment of the freezing obstacles.

Particle separation induced by triangle obstacles in a straight channel

Efficient separation of particles has ever-growing importance in both fundamental research and nanotechnological applications. However, such particles usually suffer from some fluctuations from external surroundings and outside intervention from unknown directions. Here, we numerically investigate the transport of Brownian particles in a straight channel with regular arrays of equilateral triangle obstacles. The particles can be rectified by the triangle obstacles under the action of an oscillating (square wave) force. At the given amplitude and frequency of the oscillating force, the transport is sensitively dependent on the force direction and particle size. In the cases of longitudinal and transversal oscillating force, the particles with different sizes exhibit different transport behaviors. Interestingly, under a constant force in the longitudinal direction, the phenomenon of particle separation is observed, where the particles with different radii will move in different directions. Furthermore, we also study the transport of Brownian particles driven by a tilt oscillating force. By choosing proper force directions, we can observe the gating phenomenon and transport reversal. Under different driving conditions, we can separate particles of different sizes and make them move in opposite directions.

Spontaneous rectification and absolute negative mobility of inertial Brownian particles induced by Gaussian potentials in steady laminar flows

We study the transport of inertial Brownian particles in steady laminar flows in the presence of two-dimensional Gaussian potentials. Through extensive numerical simulations, it is found that the transport is sensitively dependent on the external constant force and the Gaussian potential. Within tailored parameter regimes, the system exhibits a rich variety of transport behaviors. There exists the phenomenon of spontaneous rectification (SR), where the directed transport of particles can occur in the absence of any external driving forces. It is found that SR of the particles can be manipulated by the spatial position of the Gaussian potential. Moreover, when the potential lies at the center of the cellular flow, the system exhibits absolute negative mobility (ANM), i.e., the particles can move in a direction opposite to the constant force. More importantly, the phenomenon of ANM induced by Gaussian potentials is robust in a wide range of system parameters and can be further strengthened with the optimized parameters, which may pave the way to the implementation of related experiments.

Effect of particle size oscillations on drift and diffusion along a periodically corrugated channel

We study diffusive transport of a particle in a channel with periodically varying cross-section, occurring when the size of the particle periodically switches between two values. In such a situation, the entropy potential, which accounts for the area accessible for diffusion particle, varies both spatially (along the channel axis) and temporally. This underlies the complex interplay between different timescales of the system and leads to novel dynamic regimes. The most notable observations are: emergence of directed motion (in case of asymmetric channel) and resonant diffusion, both controlled by the switching frequency. Resonantlike behaviors of the drift velocity and the effective diffusion coefficient are shown and discussed. Based on heuristic arguments, an approximate analytical treatment of the transport process is proposed. As a comparison with the results obtained from Brownian dynamics simulations indicates, this approach provides a satisfactory way to handle the problem analytically.

Tracer diffusion in crowded narrow channels

We summarise different results on the diffusion of a tracer particle in lattice gases of hard-core particles with stochastic dynamics, which are confined to narrow channels-single-files, comb-like structures and quasi-one-dimensional channels with the width equal to several particle diameters. We show that in such geometries a surprisingly rich, sometimes even counter-intuitive, behaviour emerges, which is absent in unbounded systems. This is well-documented for the anomalous diffusion in single-files. Less known is the anomalous dynamics of a tracer particle in crowded branching single-files-comb-like structures, where several kinds of anomalous regimes take place. In narrow channels, which are broader than single-files, one encounters a wealth of anomalous behaviours in the case where the tracer particle is subject to a regular external bias: here, one observes an anomaly in the temporal evolution of the tracer particle velocity, super-diffusive at transient stages, and ultimately a giant diffusive broadening of fluctuations in the position of the tracer particle, as well as spectacular multi-tracer effects of self-clogging of narrow channels. Interactions between a biased tracer particle and a confined crowded environment also produce peculiar patterns in the out-of-equilibrium distribution of the environment particles, very different from the ones appearing in unbounded systems. For moderately dense systems, a surprising effect of a negative differential mobility takes place, such that the velocity of a biased tracer particle can be a non-monotonic function of the force. In some parameter ranges, both the velocity and the diffusion coefficient of a biased tracer particle can be non-monotonic functions of the density. We also survey different results obtained for a tracer particle diffusion in unbounded systems, which will permit a reader to have an exhaustively broad picture of the tracer diffusion in crowded environments.

Spatial heterogeneity can facilitate the target search of self-propelled particles

A numerical investigation of the target search dynamics of self-propelled particles (SPPs) in heterogeneous environments is presented in this work. We show that the spatial heterogeneity has a dramatic effect on the target search dynamics of SPPs. The relative magnitude of the self-propulsion length l_p and the radius of the circular domain R_c determines how the mean search time of SPPs τ depends on the area fraction of fixed obstacles ϕ_ob. For l_p < R_c, the target search process is diffusion-dominated so that a monotonic increase in τ with increasing ϕ_ob is observed. For l_p > R_c, τ is shown to be a non-monotonic convex function as a function of ϕ_ob due to the interplay of the distribution-dominated and diffusion-dominated dynamic regimes. Furthermore, at fixed ϕ_ob, τ shows a minimum upon increasing the self-propulsion velocity v₀ of a SPP of a slow rotational diffusion when it searches for a target at low ϕ_ob, while it decreases monotonically at high ϕ_ob. The present work highlights that the introduction of spatial heterogeneity causes rich dynamic behaviors of a SPP searching for a target, and deepens our understanding of the transport of active matter in heterogeneous media.

Landauer's blow-torch effect in systems with entropic potential

We consider local heating of a part of a two-dimensional bilobal enclosure of a varying cross section confining a system of overdamped Brownian particles. Since varying cross section in higher dimension results in an entropic potential in lower dimension, local heating alters the relative stability of the entropic states. We show that this blow-torch effect modifies the entropic potential in a significant way so that the resultant effective entropic potential carries both the features of variation of width of the confinement and variation of temperature along the direction of transport. The reduced probability distribution along the direction of transport calculated by full numerical simulations in two dimensions agrees well with our analytical findings. The extent of population transfer in the steady state quantified in terms of the integrated probability of residence of the particles in either of the two lobes exhibits interesting variation with the mean position of the heated region. Our study reveals that heating around two particular zones of a given lobe maximizes population transfer to the other.

The influence of a phase shift between the top and bottom walls on the Brownian transport of self-propelled particles

Transport of noninteracting self-propelled particles is numerically investigated in a two-dimensional horizontally asymmetrical channel with nonstraight midline which can be controlled by the phase shift between the top and bottom walls. From numerical simulations, we found that self-propelled particles can be rectified by the self-propelled velocity. The direction of the average velocity is determined by the horizontally asymmetrical parameter of the channel. The average velocity is very sensitive to the phase shift and its behaviors can be manipulated by changing the phase shift. As the phase shift is increased, the average velocity decreases and its peak position moves (to right or left). Remarkably, the average velocity is zero when the phase shift is in the interval [ 3π/5, 4π/5]. The small phase shift may facilitate the rectification process for the large horizontal asymmetry of the channel.

Brownian transport of finite size particles in a periodic channel coexisting with an energetic potential

Transport of particles with different sizes moving in a two-dimensional periodic channel is studied in the presence of an unbiased external force and a periodic energetic potential. While particles are going through entropic barrier resulting from the geometric restraints, the transport is also influenced by the energetic potential. For the case of an unbiased external force, the competition between the energetic potential and entropic barrier leads to different transport direction of particles, which sensitively depends on the particles radius. Particles move to the left when smaller than a critical radius and larger than another critical radius, whereas particles move to the right in the range of two critical radii. Therefore, the results we have presented can contribute further to the invention of machines for particle separation.