Thermal Fluctuations For a Three-Beads Swimmer

Abstract

We discuss a micro-swimmer model made of three spheres actuated by an internal active time-periodic force, tied by an elastic potential and submitted to hydrodynamic interactions with thermal noise. The dynamical approach we use, replacing the more common kinetic one, unveils the instability of the original model and the need of a confining potential to prevent the evaporation of the swimmer. We investigate the effect of the main parameters of the model, such as the frequency and phase difference of the periodic active force, the stiffness of the confining potential, the length of the swimmer and the temperature and viscosity of the fluid. Our observables of interest are the averages of the swim velocity, of the energy consumption rate, the diffusion coefficient and the swimming precision, which is limited by the energy consumption through the celebrated Thermodynamic Uncertainty Relations. An optimum for velocity and precision is found for an intermediate frequency. Reducing the potential stiffness, the viscosity or the length, is also beneficial for the swimming performance, but these parameters are limited by the consistency of the model. Analytical approximation for many of the interesting observables is obtained for small deformations of the swimmer. We also discuss the efficiency of the swimmer in terms of its maximum precision and of the hydrodynamic, or Lighthill, criterion, and how they are connected.