Swimming with an Image

The hydrodynamic interactions of a swimming bacterium with a neighboring surface can cause it to swim in circles. For example, when E. coli is above a solid surface it had been observed to swim in a clockwise direction. By contrast we observe that, when swimming near a liquid-air interface, the sense of rotation is reversed. We quantitatively account for this through the hydrodynamic interaction of the bacterium with its own mirror image swimming on the opposite side of a perfect-slip boundary. The strength of the coupling is reduced for longer cells, where the torque is spread over a larger length, resulting in longer bacteria swimming in larger circles. We confirm this through precise video measurements of bacterial trajectories and orientations.

Figure 1

(a) Thresholded bacteria image and corresponding covariance ellipsoid. (b) Superposition of frames showing the trajectory of a single cell swimming above a liquid-gas interface. The time interval between frames is 0.16 s. For most of the trajectory the cell axis (black line) is tilted away from the local trajectory tangent. (c) Schematic representation of the main parameters extracted from each trajectory.

Figure 2

Cell length ($L$) dependence of swimming velocity ($U$), average curvature radius ($R$) of trajectories, and average tilt angle ($\theta$) of body axis from local trajectory tangent line. Gray circles are raw data, white circles are binned data, and solid black lines represent theoretical predictions when considering a nearby swimming image.

Figure 3

Side, rear, and top views of the swimming bacterium and corresponding image bacterium on the opposite side of the interface. Solid green and dotted red arrows in rear and top views represent the flows produced by the rotating images of, respectively, the flagellar bundle and the body.