Crowding-Enhanced Diffusion: An Exact Theory for Highly Entangled Self-Propelled Stiff Filaments

TL;DR

This paper presents an exact theoretical framework and simulations showing that crowding enhances the diffusion of self-propelled stiff filaments, revealing a counter-intuitive 'crowded is faster' phenomenon.

Contribution

It introduces a scaling theory for effective diffusivity and an exact expression predicting complex dynamics of entangled active filaments across scales.

Findings

Effective diffusivity increases with filament density by over an order of magnitude.

The theory captures short-time diffusion, directed motion, and long-time relaxation.

Crowding can enhance mobility in active filament systems.

Abstract

We study a strongly interacting crowded system of self-propelled stiff filaments by event-driven Brownian dynamics simulations and an analytical theory to elucidate the intricate interplay of crowding and self-propulsion. We find a remarkable increase of the effective diffusivity upon increasing the filament number density by more than one order of magnitude. This counter-intuitive 'crowded is faster' behavior can be rationalized by extending the concept of a confining tube pioneered by Doi and Edwards for highly entangled crowded, passive to active systems. We predict a scaling theory for the effective diffusivity as a function of the P\'eclet number and the filament number density. Subsequently, we show that an exact expression derived for a single self-propelled filament with motility parameters as input can predict the non-trivial spatiotemporal dynamics over the entire range of length and time scales. In particular, our theory captures short-time diffusion, directed swimming motion at intermediate times, and the transition to complete orientational relaxation at long times.