# Direct Measurement of the Flow Field around Swimming Microorganisms

Entry by Leon Furchtgott, APP 225 Fall 2010.

Knut Drescher, Raymond E. Goldstein, Nicolas Michel, Marco Polin, and Idan Tuval. "Direct Measurement of the Flow Field Around Swimming Microorganisms". Physical Review Letters 105, 168101 (2010)

## Summary

Swimming microorganisms create flows that influence their mutual interactions and modify the rheology of their suspensions. These flows have been studied theoretically but have not been measured. In this paper, the authors take measurements of the flow field around swimming Volvox carteri and Chlamydomonas reinhardtii, two alga species. They find that flows around V. carteri have strong Stokeslet contribution whereas C. reinhardtii is best modeled as a stresslet but in the near field as 3 off-centered Stokeslets.

## Background

Microorganisms are present in fluids in every part of the biosphere. Much of the behavior of microorganims such as bacteria and protozoa takes place at low Reynolds number and in large collective groups. Advances in imaging techniques have allowed for careful study of the motion of flagella that have been pinned down but there is much less known about the behavior of freely swimming microorganisms. This paper presents the first of such measurements.

## Results

Shown in Figure 1 is the flow field of a freely swimming V. cateri in the laboratory frame. The authors made such measurements using a technique called particle image velocimetry, which consists of tracking the motion of small passive tracer beads suspended in a fluid. The authors recorded the motions of small tracer particles and using this information determined the instantaneous velocities and the flow field at each time point.

In the low-Reynolds-number regime, the flow disturbance driven by the motion of a body depends linearly upon the stresses exerted by the body on the fluid, and typically decays very slowly with the distance r from the body center. These flow disturbances can be described as linear superpositions of fundamental solutions of the Stokes equations, which decay as inverse powers of r. The first such solution, coined the “Stokeslet,” arises from the net force on the fluid, and has a velocity field that decays like <math>1/r</math> in three dimensions. At the next level, the “stresslet” flow, which is induced by the first force moment exerted by the particle on the fluid, decays more rapidly like <math>1/r^2</math>. Higher-order solutions include the “source doublet” and “force quadrupole,” with velocities decaying as <math>1/r^3</math>. Linear combinations of these basic solutions can yield various flows with complex and qualitatively different near-field and far-field behaviors.

Until this work, it was assumed that the flow around a swimming microorganism could be described by a stresslet coming from a balance between thrust and drag forces acting on the microorganism. But the authors find that for V. carteri (200 microns), the flow field can be modeled as a Stokeslet with only a second-order correction stresslet (Figure 2).

For C. reinhardtii (5 microns), the flow field can be described as a stresslet, but only for far distances. Closer to the organism, the field is more complex and can be modeled as a superposition of 3 Stokeslets.

## Discussion/Connection to Soft Matter

These flow field measurements are very important for studying interactions between swimming organisms or between swimming organisms and boundaries. The paper illustrates some of the theoretical and experimental complexities of low-Reynolds number regimes.