Simulating the swimming motion of a flagellated bacterium in a microstructured bio-fluid

TL;DR

This paper introduces a numerical framework for simulating the swimming of flagellated bacteria in complex biofluids with microstructure and elasto-viscoplastic properties, combining two-fluid modeling with slender-body theory.

Contribution

The authors develop a computational approach that efficiently models bacterial locomotion in microstructured biofluids by decomposing flow components and precomputing hydrodynamic contributions.

Findings

Polymer microstructure significantly influences bacterial motility.

The decomposition method improves computational efficiency in transient simulations.

Flow contributions from motion, flagella, and polymers can be effectively separated.

Abstract

We develop a numerical framework to simulate the locomotion of a flagellated bacterium with a spheroidal head (such as Escherichia coli) in biological fluids like mucus, which are entangled polymer solutions exhibiting elasto-viscoplastic (EVP) rheology and porous microstructure. To account for the scale disparity between the large bacterial head and the slender flagellar bundle, whose thickness is comparable to the pore size, we employ a two-fluid model in which the bundle directly drives the solvent and exchanges momentum with the polymer phase via drag proportional to their relative velocity. The numerical implementation combines a finite-difference discretization of the two-fluid equations with a slender-body theory (SBT) to model flagellar forcing. A key observation is that the coupled mass and momentum equations for these inertialess flows, together with SBT, are linear in the pressure and velocity fields and in the force distribution along the flagellar bundle. By treating the polymer stress as a body force, we decompose the flow field and hydrodynamic moments into three additive contributions: kinematic (motion), flagellar forcing, and polymer stress. This decomposition allows several components of the flow to be precomputed and enables the determination of swimming velocity via a resistivity formulation driven by polymer-induced forces, which greatly improves computational efficiency during transient calculations of the polymer stress and the resulting flow. We validate the method and use it to analyze how polymer microstructure and its interactions with the bacterial head and tail affect motility in complex biofluids.