Analytical estimates of free brownian diffusion times in corrugated narrow channels

Particle-wall alignment interaction and active Brownian diffusion through narrow channels

We numerically examine the impacts of particle-wall alignment interactions on active species diffusion through a structureless narrow two-dimensional channel. We consider particle-wall interaction to depend on the self-propulsion velocity direction whereby some specific particle's alignments with respect to the boundary walls are stabilized more. Further, the alignment interaction is meaningful as long as particles are close to the confining boundaries. Unbiased diffusion of active particles for various possible stable velocity alignments against the walls has been examined. We show that for the most stable configuration leading to the self-propulsion velocity direction perpendicular to the wall, diffusivity becomes inversely proportional to the square of the alignment interaction torque. On the other hand, when the self-propulsion velocity direction making an acute angle to the channel walls is the most stable configuration, diffusion exponentially grows with strengthening alignment interaction. Hence, particle-wall interaction plays a pivotal role in the transport control of active particles through narrow channels. Moreover, the impacts of the alignment interactions on diffusion largely depend on the particle's self-propulsion properties and its chirality. Our simulation results can potentially be used to understand unbiased diffusion of artificial or living micro/nano-objects (such as virus, bacteria, Janus particles, etc.) though narrow confined structures.

Escape dynamics of a self-propelled nanorod from circular confinements with narrow openings

We perform computer simulations to explore the escape dynamics of a self-propelled (active) nanorod from circular confinements with narrow opening(s). Our results clearly demonstrate how the persistent and directed motion of the nanorod helps it to escape. Such escape events are absent if the nanorod is passive. To quantify the escape dynamics, we compute the radial probability density function (RPDF) and mean first escape time (MFET) and show how the activity is responsible for the bimodality of RPDF, which is clearly absent if the nanorod is passive. Broadening of displacement distributions with activity has also been observed. The computed mean first escape time decreases with activity. In contrast, the fluctuations of the first escape times vary in a non-monotonic way. This results in high values of the coefficient of variation and indicates the presence of multiple timescales in first escape time distributions and multimodality in uniformity index distributions. We hope our study will help in differentiating activity-driven escape dynamics from purely thermal passive diffusion in confinement.

Narrow Pore Crossing of Active Particles under Stochastic Resetting

We propose a two-dimensional model of biochemical activation process, whereby self-propelling particles of finite correlation times are injected at the center of a circular cavity with constant rate equal to the inverse of their lifetime; activation is triggered when one such particle hits a receptor on the cavity boundary, modeled as a narrow pore. We numerically investigated this process by computing the particle mean-first exit times through the cavity pore as a function of the correlation and injection time constants. Due to the breach of the circular symmetry associated with the positioning of the receptor, the exit times may depend on the orientation of the self-propelling velocity at injection. Stochastic resetting appears to favor activation for large particle correlation times, where most of the underlying diffusion process occurs at the cavity boundary.

Escape kinetics of self-propelled particles from a circular cavity

We numerically investigate the mean exit time of an inertial active Brownian particle from a circular cavity with single or multiple exit windows. Our simulation results witness distinct escape mechanisms depending on the relative amplitudes of the thermal length and self-propulsion length compared to the cavity and pore sizes. For exceedingly large self-propulsion lengths, overdamped active particles diffuse on the cavity surface, and rotational dynamics solely governs the exit process. On the other hand, the escape kinetics of a very weakly damped active particle is largely dictated by bouncing effects on the cavity walls irrespective of the amplitude of self-propulsion persistence lengths. We show that the exit rate can be maximized for an optimal self-propulsion persistence length, which depends on the damping strength, self-propulsion velocity, and cavity size. However, the optimal persistence length is insensitive to the opening windows' size, number, and arrangement. Numerical results have been interpreted analytically based on qualitative arguments. The present analysis aims at understanding the transport controlling mechanism of active matter in confined structures.

Enhanced motility in a binary mixture of active nano/microswimmers

It is often desirable to enhance the motility of active nano- or microscale swimmers such as, e.g., self-propelled Janus particles as agents of chemical reactions or weak sperm cells for better chances of successful fertilization. Here we tackle this problem based on the idea that motility can be transferred from a more active guest species to a less active host species. We performed numerical simulations of motility transfer in two typical cases, namely for interacting particles with a weak inertia effect, by analyzing their velocity distributions, and for interacting overdamped particles, by studying their effusion rate. In both cases, we detected motility transfer with a motility enhancement of the host species of up to a factor of four. This technique of motility enhancement can find applications in chemistry, biology and medicine.

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.

Relation between the porosity and tortuosity of a membrane formed by disconnected irregular pores and the spatial diffusion coefficient of the Fick-Jacobs model

In this work, we provide a theoretical relationship between the spatial-dependent diffusion coefficient derived in the Fick-Jacobs (FJ) approximation and the macroscopic diffusion coefficient of a membrane that depends on the porosity, tortuosity, and the constriction factors. Based on simple mass conservation arguments under equilibrium as well as in nonequilibrium conditions, we generalize previous expressions for the effective diffusion coefficient of an irregular pore, originally obtained by Festa and d'Agliano for horizontal and periodic pores, and then extended by Bradley for tortuous periodic pores, to the case of pores with arbitrary geometry. Through a formal definition of the constrictivity factor in terms of the geometry of the pore, our results provide very clear physical interpretation of experimental measurements since they link the local properties of the flow with macroscopic quantities of experimental relevance in the design and optimization of porous materials. The macroscopic diffusion coefficient as well as the spatiotemporal evolution of the concentration profiles inside a pore have been recently measured by using pulse field gradient NMR techniques. The advantage of using the FJ approach is that the spatiotemporal concentration profile inside a pore of irregular geometry is directly related to the pore's shape and, therefore, that the macroscopic diffusion coefficient can be obtained by comparing the spatiotemporal concentration profiles from such experiments with those of the theoretical model. Hence, the present study is relevant for the understanding of the transport properties of porous materials where the shape and arrangement of pores can be controlled at will.

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.

Drift in Diffusion Gradients

The longstanding problem of Brownian transport in a heterogeneous quasi one-dimensional medium with space-dependent self-diffusion coefficient is addressed in the overdamped (zero mass) limit. A satisfactory mesoscopic description is obtained in the Langevin equation formalism by introducing an appropriate drift term, which depends on the system macroscopic observables, namely the diffuser concentration and current. The drift term is related to the microscopic properties of the medium. The paradoxical existence of a finite drift at zero current suggests the possibility of designing a Maxwell demon operating between two equilibrium reservoirs at the same temperature.

When is the next extending of Fick-Jacobs equation necessary?

Applicability of the effective one-dimensional equations, such as Fick-Jacobs equation and its extensions, describing diffusion of particles in 2D or 3D channels with varying cross section A(x) along the longitudinal coordinate x, is studied. The leading nonstationary correction to Zwanzig-Reguera-Rubí equation [R. Zwanzig, J. Phys. Chem. 96, 3926 (1992); D. Reguera and J. M. Rubí, Phys. Rev. E 64, 061106 (2001)] is derived and tested on the exactly solvable model, diffusion in a 2D linear cone. The effects of such correction are demonstrated and discussed on elementary nonstationary processes, a time dependent perturbation of the stationary flow and calculation of the mean first passage time.

Current control in a two-dimensional channel with nonstraight midline and varying width

Transport of overdamped Brownian particles in a two-dimensional channel with nonstraight midline and narrow varying width is investigated in the presence of an asymmetric unbiased external force. In the adiabatic limit, we obtain the analytical expression of the directed current. It is found that the current is manipulated by changing the phase shift between the top and bottom walls of the channel. As the phase shift is increased from 0 to π, the variation of the channel width decreases and the current also decreases. Remarkably, the current is always zero when the phase shift is equal to π, where the entropic barrier disappears. In addition, the temporal asymmetric parameter of the unbiased force not only determines the direction of the current but also affects its amplitude.