A universal scaling law for active diffusion in complex media

TL;DR

This paper introduces a universal scaling law for active particle diffusion in complex media, validated through experiments and simulations, offering a predictive framework for diverse active systems.

Contribution

It proposes a new dimensionless parameter and a modified scaling relation that unify active diffusion behavior across various media and propulsion mechanisms.

Findings

Universal active diffusion-structure relation established

Scaling law collapses diverse experimental and simulation data

Predictive framework applicable to equilibrium and nonequilibrium regimes

Abstract

Using granular experiments and computer simulations, we investigate the long-time diffusion of active tracers in a broad class of complex media composed of frozen obstacles of diverse structures. By introducing a dimensionless persistence length $Q = v_d \tau_r / d_t$, we propose a modified scaling relation that independently collapses experimental and simulation results across active and passive particles, diverse media, and distinct propulsion mechanisms. Our results reveal a universal active diffusion-structure relation that holds across both equilibrium and nonequilibrium regimes, providing a simple predictive framework for active diffusion in complex environments.