The random walk of a low-Reynolds-number swimmer

TL;DR

This study investigates the dispersal behavior of the micro-alga Chlamydomonas Reinhardtii at low Reynolds number, revealing a transition from correlated to standard random walk influenced by flagella motion and drag forces.

Contribution

It provides a detailed analysis of the swimming trajectories of Chlamydomonas Reinhardtii, modeling their movement as a correlated random walk and examining effects of flagella dynamics and drag forces.

Findings

Trajectories are well modeled by a correlated random walk.

Short-term motion shows back-and-forth flagella movement affecting dynamics.

Drag forces alter the characteristics of the random walk.

Abstract

Swimming at a micrometer scale demands particular strategies. Indeed when inertia is negligible as compared to viscous forces (i.e. Reynolds number $Re$ is lower than unity), hydrodynamics equations are reversible in time. To achieve propulsion at low Reynolds number, swimmers must then deform in a way that is not invariant under time reversal. Here, we investigate dispersal properties of self propelled organisms by means of microscopy and cell tracking. Our system of interest is the micro-alga \textit{Chlamydomonas Reinhardtii}, a motile single celled green alga about 10 micrometers in diameter that swims with to two front flagella. In the case of dilute suspensions, we show that tracked trajectories are well modeled by a correlated random walk. This process is based on short time correlations in the direction of movement called persistence. At longer times, correlations are lost and a standard random walk characterizes the trajectories. Moreover, high speed imaging enables us to show how the back-and-forth motion of flagella at very short times affects the statistical description of the dynamics. Finally we show how drag forces modify the characteristics of this particular random walk.