Fumiaki NakaiGranular rheology 日本語

Rod diffusion · Markov process

More Obstacles Can Make a Long Rod Diffuse Faster

Main claim

For a sufficiently slender rod, translational diffusivity can rise as fixed obstacles become denser even in a Markovian model without a tube-like kinetic constraint. More obstacles do not always slow a long particle down; they can suppress rotation in a way that helps its centre move farther.

Rod-shaped particle moving through fixed point obstacles
A rod-shaped particle moving through fixed obstacles.

Problem

Particles normally diffuse more slowly as obstacles become denser, yet long rods can show the opposite trend over an intermediate density range. Earlier explanations invoked a tube-like kinetic constraint that preserves motion along the rod axis. We asked whether that memory-like constraint is truly necessary or whether simpler collision kinetics are sufficient.

Approach

We simulated one hard spherocylinder moving ballistically among spatially fixed point obstacles. A kinetic Monte Carlo scheme sampled statistically independent collisions, deliberately making the dynamics Markovian and removing a persistent tube. Rod length and obstacle density were varied, and scaling arguments connected translational diffusion to collision frequency and angular velocity.

What we found

For sufficiently long rods, the translational diffusion coefficient first decreases, then increases, and finally decreases again as obstacle density rises. The upturn appears above an aspect-ratio threshold of about 24 even though successive collisions are uncorrelated. Denser obstacles suppress rotation, allowing axial motion to persist long enough to enhance centre-of-mass transport before rod thickness eventually limits it.

Why it matters

The result shows that a tube-like kinetic constraint is not a necessary explanation for enhanced rod diffusion. It isolates a simpler mechanism based on shape, rotation, and collision frequency, helping separate generic single-particle kinetics from collective or memory effects in transport through crowded media.

Keywords

rod diffusion, anisotropic particle, Markov process, kinetic Monte Carlo, obstacle density.

Paper

Fumiaki Nakai, Martin Kröger, Takato Ishida, Takashi Uneyama, Yuya Doi, Yuichi Masubuchi, “Increase in rod diffusivity emerges even in Markovian nature,” Physical Review E 107, 044604 (2023).