Chemoreception and chemotaxis of a three-sphere swimmer

TL;DR

This study investigates the hydrodynamics and chemotactic behavior of a three-sphere swimmer at low Reynolds numbers, revealing the impact of Péclet number on solute flux and the challenges in learning chemotaxis.

Contribution

It combines numerical simulation of coupled hydrodynamics and solute transport with reinforcement learning to analyze chemotaxis and locomotion in a three-sphere swimmer.

Findings

Little gain in solute flux for swimming unless Pe > 10

Learning chemotaxis is more difficult than learning locomotion

Higher Pe increases the difficulty of chemotactic learning

Abstract

The coupled problem of hydrodynamics and solute transport for the Najafi-Golestanian three-sphere swimmer is studied, with the Reynolds number set to zero and P\'eclet numbers (Pe) ranging from 0.06 to 60. The adopted method is the numerical simulation of the problem with a finite element code based upon the FEniCS library. For the swimmer executing the optimal locomotion gait, we report the Sherwood number as a function of Pe in homogeneous fluids and confirm that little gain in solute flux is achieved by swimming unless Pe is significantly larger than 10. We also consider the swimmer as an learning agent moving inside a fluid that has a concentration gradient. The outcomes of Q-learning processes show that learning locomotion (with the displacement as reward) is significantly easier than learning chemotaxis (with the increase of solute flux as reward). The chemotaxis problem, even at low Pe, has a varying environment that renders learning more difficult. Further, the learning difficulty increases severely with the P\'eclet number. The results demonstrate the challenges that natural and artificial swimmers need to overcome to migrate efficiently when exposed to chemical inhomogeneities.