A Geometric Criterion for the Optimal Spreading of Active Polymers in Porous Media

TL;DR

This paper introduces a geometric criterion for optimal spreading of active polymers in porous media, revealing how run length and pore geometry influence transport efficiency, with implications for biological and environmental systems.

Contribution

It presents a unifying geometric criterion for optimal spreading of active polymers, linking run length to pore structure and transport efficiency in complex media.

Findings

Effective diffusivity can increase up to 100-fold with reversal dynamics.

Optimal spreading occurs when run length matches the longest pore path.

The criterion applies across diverse pore geometries.

Abstract

We perform Brownian dynamics simulations of active stiff polymers undergoing run-reverse dynamics, and so mimic bacterial swimming, in porous media. In accord with recent experiments of \emph{Escherichia coli}, the polymer dynamics are characterized by trapping phases interrupted by directed hopping motion through the pores. We find that the effective translational diffusivities of run-reverse agents can be enhanced up to two orders in magnitude, compared to their non-reversing counterparts, and exhibit a non-monotonic behavior as a function of the reversal rate, which we rationalize using a coarse-grained model. Furthermore, we discover a geometric criterion for the optimal spreading, which emerges when their run lengths are comparable to the longest straight path available in the porous medium. More significantly, our criterion unifies results for porous media with disparate pore sizes and shapes and thus provides a fundamental principle for optimal transport of microorganisms and cargo-carriers in densely-packed biological and environmental settings.