Effective and efficient modeling of the hydrodynamics for bacterial flagella

The hydrodynamic interactions among bacterial cell bodies, flagella, and surrounding boundaries are crucial for understanding bacterial motility in complex environments. In this study, we demonstrate that each slender flagellum can be modeled as a series of spheres and the interactions between these spheres can be accurately characterized using a resistance matrix. This approach allows us to effectively and efficiently evaluate the propulsive effects of the flagella. Notably, our investigation into bacterial motility near a colloidal sphere reveals significant discrepancies between results derived from the twin multipole moment and those obtained through resistive force theory. Consequently, neglecting the hydrodynamic interactions among cell bodies, flagella, and colloidal spheres may lead to substantial inaccuracies. Our model simplifies bacteria into a series of spheres, making it well-suited for examining bacterial motility near spherical boundaries and the nonlinear deformation dynamics of elastic flagella.