Developing Three-Dimensional Simulations of Bacteria with Flexible Flagella in Viscous Fluids

Escherichia coli (E. coli) and other similar bacteria move through viscous fluid environments by rotating their flagella. This behavior may be mathematically modeled as a type of fluid-structure interaction wherein the bacterial cell and flagellum are discretized into collections of spherical particles coupled by forces and torques. The flagellar flexibility can be varied using Kirchhoff rod theory and quaternions to resolve both bending and twisting in three dimensions. Our simulations are built upon the MATLAB implementation of the “methods for suspensions of passive and active filaments” in which fluid-structure interactions are accounted for through a direct pairwise evaluation of the Rotne-Prager-Yamakawa (RPY) mobility tensor. By adjusting the flagellar flexibilities, we aim to reproduce experimental observations of E. coli trajectories.