Particle image velocimetry experiments on a macro-scale model for bacterial flagellar bundling

Escherichia coli (E. coli) and other bacteria are propelled through water by several helical flagella, which are rotated by motors embedded at random points on the cell wall. Depending on the handedness and rotation sense, the motion of the flagella induces a flow field that causes them to wrap around each other and form a bundle. Our objective is to understand and model the mechanics of this process. Full-scale flagella are 10 m in length, 20 nm in diameter, and turn at a rate of 100 Hz. To accurately simulate bundling at a more easily observable scale, we built a scale model in which 20-cm-long helices are rotated in 100,000 cp silicone oil (Poly-di-methyl-siloxane). The highly viscous oil ensures an appropriately low Reynolds number. We developed a macro-scale particle image velocimetry (PIV) system to measure the full-field velocity distribution for rotating rigid helices and rotating flexible helices. In the latter case, the helices were made from epoxy-filled plastic tubing to give approximately the same ratio of elastic to viscous stresses as in the full-scale flagella. Comparison between PIV measurements and slender-body calculations shows good agreement for the case of rigid helices. For the flexible helices, we find that the flow field generated by a bundle in the steady state is well approximated by the flow generated by a single rigid helix with twice the filament radius.