Modeling Fluid Flow of Free-Swimming Algae Using Modified Three-Sphere Models*

Chlamydomonas reinhardtii, a motile species of green algae, rhythmically beats its flagella to transport ambient fluid, generating propulsion for locomotion and facilitating interactions with other microorganisms. A minimal three-sphere model, designed to reflect the basic symmetry and flagella beating mode of C. reinhardtii, has been extensively used to study various aspects of algal swimming dynamics, including flagellar synchronization, run-and-tumble behavior, response to shear flow, and rolling motion. Despite these successes, the detailed flow field generated by this model has not been thoroughly investigated. In this study, we systematically examine both the time-averaged and time-resolved fluid flows of the three-sphere model and compare the model predictions against 2D and 3D experimental measurements. Our results indicate that the current model does not capture the characteristic flow features observed experimentally. To address this, we develop a modified three-sphere model incorporating new beating features and analyze their impact on flow field predictions. This study provides crucial insights into the accurate modeling of hydrodynamics in algal swimming.