  Small organisms (e.g., bacteria) and artificial microswimmers move due to a
combination of active swimming and passive Brownian motion. Considering a
simplified linear three-sphere swimmer, we study how the swimmer size regulates
the interplay between self-driven and diffusive behavior at low Reynolds
number. Starting from the Kirkwood-Smoluchowski equation and its corresponding
Langevin equation, we derive formulas for the orientation correlation time, the
mean velocity and the mean square displacement in three space dimensions. The
validity of the analytical results is illustrated through numerical
simulations. Tuning the swimmer parameters to values that are typical of
bacteria, we find three characteristic regimes: (i) Brownian motion at small
times, (ii) quasi-ballistic behavior at intermediate time scales, and (iii)
quasi-diffusive behavior at large times due to noise-induced orientation
flipping. Our analytical results can be useful for a better quantitative
understanding of optimal foraging strategies in bacterial systems, and they can
help to construct more efficient artificial microswimmers in fluctuating
fluids.
