Calibrating the method of regularized Stokeslets using macroscopic experimental measurements*

The swimming of microorganisms is typically studied using biological experiments and/or numerical simulations. However, numerical simulations of microorganisms are not often compared to precise measurements because it is difficult to make microscopic measurements of forces and torques in biological experiments. The Trinity Centre Collaboration, instead, uses macroscopic dynamically similar table-top experiments in highly viscous silicone oil to test theories and create a library of forces and torques on simple geometric shapes such as helices, cylinders, and spheres (see Shindell et al. 2021). These geometries can be used to model bacilli and cocci bacteria such as Escherichia coli, Pseudomonas aeruginosa, and Rhodobacter sphaeroides. The forces and torques on the macroscopic models can be measured directly, and the results scaled to biologically relevant sizes. Our recent sphere measurements experimentally verified the theory of Lee and Leal (1980) for the force and torque on a sphere moving near a wall with much greater precision than previously reported. The force and torque data from our experiments and the Lee and Leal theory were used to calibrate the Method of Images for Regularized Stokeslets and the Generalized System of Images for Regularized Stokeslets for use as a noninvasive probe of bacterial swimming dynamics by modeling bacterial motion from microscopic image data. Our optimized computational parameters and a numerical implementation of theory are available via ArXiv (arXiv:2401.16214).