Dispersion of run-and-tumble microswimmers through disordered media

TL;DR

This paper investigates how run-and-tumble microswimmers' diffusion is hindered in disordered porous media, deriving a universal function that describes the effect of obstacle density and swimmer activity on long-term diffusivity.

Contribution

It introduces a universal hindrance function for microswimmer diffusion in disordered media, combining analytical and simulation approaches for dilute and dense obstacle conditions.

Findings

Long-time diffusivity decreases with obstacle density.

Derived an asymptotic expression for dilute media.

Validated the model with stochastic simulations.

Abstract

Understanding the transport properties of microorganisms and self-propelled particles in porous media has important implications for human health as well as microbial ecology. In free space, most microswimmers perform diffusive random walks as a result of the interplay of self-propulsion and orientation decorrelation mechanisms such as run-and-tumble dynamics or rotational diffusion. In an unstructured porous medium, collisions with the microstructure result in a decrease in the effective spatial diffusivity of the particles from its free-space value. Here, we analyze this problem for a simple model system consisting of non-interacting point particles performing run-and-tumble dynamics through a two-dimensional disordered medium composed of a random distribution of circular obstacles, in the absence of Brownian diffusion or hydrodynamic interactions. The particles are assumed to collide with the obstacles as hard spheres and subsequently slide on the obstacle surface with no frictional resistance while maintaining their orientation, until they either escape or tumble. We show that the variations in the long-time diffusivity can be described by a universal dimensionless hindrance function $f(\phi,\mathrm{Pe})$ of the obstacle area fraction $\phi$ and P\'eclet number $\mathrm{Pe}$, or ratio of the swimmer run length to the obstacle size. We analytically derive an asymptotic expression for the hindrance function valid for dilute media ($\mathrm{Pe}\,\phi\ll 1$), and its extension to denser media is obtained using stochastic simulations.