Force and torque on a rotating helical flagellum near a boundary

As a free swimming bacterium approaches a boundary, both the propulsive force and torque on its helical flagellum increase rapidly. Though a constrained helical swimmer pumps the fluid, a similar increase in force and torque occur near a boundary (Das et al. 2018). We use scaled macroscopic experiments to measure this functional dependence of the the force and torque as a constrained rotating helical flagellum approaches a boundary. We keep the Reynolds number in the experiments much less than unity to model bacterial fluid dynamics. These Reynolds-number-scaled experiments are compared with numerical simulations that use the method of images for regularized Stokeslets (Ainley et al. 2008). The computations find a similar functional dependence of force and torque on boundary distance. We also compare the results to biological measurements that use total internal reflection fluorescence microscopy to simultaneously measure the distance to the boundary and the dynamics of the bacteria. We show that all of the data can be collapsed onto a single curve by non-dimensionalizing the force, torque and boundary distance appropriately.