Measured effect of boundary distance on flagellar motor torque

Darnton et al. (2007) used resistive force theory to derive experimental measurements of the torque generated by bacterial motors in free swimming Escherichia coli. Recent reports have found similar torque values using both boundary element methods and slender body theory to model flagella swimming near a boundary (Das et al. 2018). Such numerical methods have also been used to model constrained bacteria swimming near a boundary, where their flagella act as micropumps (Dauparas et al., 2018). We use scaled macroscopic experiments to directly measure the torque on constrained, pumping flagella as a function of boundary distance. The helical flagella have a diameter ≈12 mm and are immersed in a fluid with viscosity 10⁵ times that of water to ensure the Reynolds number in the experiments is much less than unity, just as in the bacterial experiments. We compare our nondimensionalized values to the numerical data and find good agreement, particularly in the dependence of motor torque on boundary distance. We also report a similar functional dependence of propulsive force measurements as a function of boundary distance.