Numerical simulation of bundling of helical elastic rods in a viscous fluid

Abstract

We introduce a numerical framework to study the fluid-structure interaction between two helical filaments rotating under low Reynolds number condition, motivated by the propulsion of bacteria using helical flagella. Our numerical framework couples the elasticity of the thin filaments, nonlocal hydrodynamic loading, and the contact between multiple elastic rods. Each of these three ingredients is respectively modeled by the Discrete Elastic Rods method (for a geometrically nonlinear description of soft filaments), Regularized Stokeslet Segments method (for the nonlocal drag force in a viscous fluid), and non-penetration condition between rod segments. Two helical rods rotating side by side attract each other and become closer because of their hydrodynamic interplay in a viscous environment. Depending on the initial distance between the two and their rotational frequency, the two filaments can come in physical contact. Exploiting the efficiency and robustness of the simulator, we perform a systematic parameter sweep to quantify the bundling behavior. The findings may shed light on the physics of the bio-locomotion of microorganisms and inspire the design of novel biomimetic soft robots.