Hydrodynamic analysis of flagellated bacteria swimming near one and between two no-slip plane boundaries

Near a solid boundary, Escherichia coli swims in clockwise circular motion. We provide a hydrodynamic model for this behavior. We show that circular trajectories are natural consequences of force-free and torque-free swimming and the hydrodynamic interactions with the boundary, which also leads to a hydrodynamic trapping of the cells close to the surface. We compare the results of the model with experimental data and obtain reasonable agreement. In particular, the radius of curvature of the trajectory is observed to increase with the length of the bacterium body.

Bacteria swim by rotating flagellar filaments that are several micrometers long, but only about 20 nm in diameter. The filaments can exist in different polymorphic forms, having distinct values of curvature and twist. Rotation rates are on the order of 100 Hz. In the past, the motion of individual filaments has been visualized by dark-field or differential-interference-contrast microscopy, methods hampered by intense scattering from the cell body or shallow depth of field, respectively. We have found a simple procedure for fluorescently labeling cells and filaments that allows recording their motion in real time with an inexpensive video camera and an ordinary fluorescence microscope with mercury-arc or strobed laser illumination. We report our initial findings with cells of Escherichia coli. Tumbles (events that enable swimming cells to alter course) are remarkably varied. Not every filament on a cell needs to change its direction of rotation: different filaments can change directions at different times, and a tumble can result from the change in direction of only one. Polymorphic transformations tend to occur in the sequence normal, semicoiled, curly 1, with changes in the direction of movement of the cell body correlated with transformations to the semicoiled form.