A two-sphere model for bacteria swimming near solid surfaces

TL;DR

This paper introduces a simplified two-sphere model to simulate bacteria like E. coli swimming near surfaces, capturing complex behaviors such as circular and straight swimming close to walls.

Contribution

The model incorporates hydrodynamic interactions and force/torque balances to replicate bacteria swimming behaviors near surfaces, providing insights into their dynamics.

Findings

The model reproduces circular and straight swimming behaviors.

The radius of curvature matches experimental observations.

Different initial conditions lead to diverse swimming patterns.

Abstract

We present a simple model for bacteria like \emph{Escherichia coli} swimming near solid surfaces. It consists of two spheres of different radii connected by a dragless rod. The effect of the flagella is taken into account by imposing a force on the tail sphere and opposite torques exerted by the rod over the spheres. The hydrodynamic forces and torques on the spheres are computed by considering separately the interaction of a single sphere with the surface and with the flow produced by the other sphere. Numerically, we solve the linear system which contains the geometrical constraints and the force-free and torque-free conditions. The dynamics of this swimmer near a solid boundary is very rich, showing three different behaviors depending on the initial conditions: (1) swimming in circles in contact with the wall, (2) swimming in circles at a finite distance from the wall, and (3) swimming away from it. Furthermore, the order of magnitude of the radius of curvature for the circular motion is in the range $8-50\,\mu$m, close to values observed experimentally.