Calibrating the method of images for regularized Stokeslets using dynamically similar experiments

Many bacteria use a helical flagellum for propulsion and when bacteria approach a boundary, the forces and torques exerted by the fluid increase rapidly. The method of images for regularized Stokeslets (MIRS) is often used to model such bacterial swimming near a boundary. The method includes both discretization and regularization parameters, but there is no theory that predicts the appropriate regularization parameter for a given surface discretization of a solid object. The choice has generally been made without precise connection to real-world experiments. Thus, we used dynamically similar macroscopic experiments to calibrate MIRS for our model of a bacterium, which has a cylindrical body and a helical flagellum. We have measured the torque on constrained rotating cylinders and constrained rotating helices at various distances from a solid boundary. We have thereby verified, for the first time, the theory of Jeffrey and Onishi (1981) for the torque on a rotating cylinder near a plane wall. We then used theory and the experiments to determine optimal discretization and regularization parameters for MIRS for these two geometries. The average mean-square error between our experiments and simulations is less than 5%. Our technique allows us to extract accurate predictions of forces and torques from our model of a swimming bacterium to assess various efficiency measures as a function of boundary distance and body/flagellum geometry, as presented in Shindell et al., Fluids (2021), and discussed in the same session by Orrin Shindell.