Diffusion of interacting particles in a channel with reflection boundary conditions

TL;DR

This study numerically investigates how reflection boundary conditions affect the transport of biased Brownian particles in a symmetric channel, revealing distinct behaviors in mobility and diffusion influenced by boundary type, particle interactions, and energy input.

Contribution

It introduces a detailed numerical analysis of reflection boundary effects on particle transport, highlighting differences from no-flow conditions and the impact of particle interactions.

Findings

Reflection boundary conditions alter transport properties significantly.

Inelastic reflections increase mobility and diffusion at low energy ratios.

Particle interactions decrease mobility but increase diffusion.

Abstract

The diffusive transport of biased Brownian particles in a two-dimensional symmetric channel is investigated numerically considering both the no-flow and the reflection boundary conditions at the channel boundaries. Here, the geometrical confinement leads to entropic barriers which effectively control the transport properties of the particles. We show that compared to no-flow boundary conditions, the transport properties exhibit distinct features in a channel with reflection boundary conditions. For example, the nonlinear mobility exhibits a nonmonotonic behavior as a function of the scaling parameter $f$, which is a ratio of the work done to the particles to available thermal energy. Also, the effective diffusion exhibits a rapidly increasing behavior at higher $f$. The nature of reflection, i.e., elastic or inelastic, also influences the transport properties firmly. We find that inelastic reflections increase both the mobility and the effective diffusion for smaller $f$. In addition, by including the short range interaction force between the Brownian particles, the mobility decreases and the effective diffusion increases for various values of $f$. These findings, which are a signature of the entropic nature of the system, can be useful to understand the transport of small particles or molecules in systems such as microfluidic channels, membrane pores, and molecular sieves.