Refining Minimal Flagellar Models to Capture Flow Fields of Free-Swimming Algae

The ability of Chlamydomonas reinhardtii to navigate and stir its surrounding fluid through coordinated flagellar beating is fundamental to many biological and ecological processes. The three-sphere model, a reduced-order representation of the algal body and flagella, has successfully captured essential swimming kinematics and phase dynamics. However, its ability to predict detailed flow fields remains largely unexplored. In this study, we conduct a comprehensive comparison between time-averaged and time-resolved flow fields generated by the classical three-sphere model and experimental measurements. To address key discrepancies such as the location of the front stagnation point and the structure of side vortices, we evaluate the effects of flagellar orbit shapes, analyzing their impact on both the flow field and swimming kinetics. A quantitative analysis is also performed to reveal how changes in flagellar sphere size between the power and recovery strokes influence the stagnation point and the angular orientation of side vortices, as well as swimming velocity and efficiency. By examining the influence of geometric and dynamical parameters on both near- and far-field hydrodynamics, we show that minimal microswimmer models can be tuned for enhanced physical realism. Our findings provide valuable insights for accurate and computationally efficient simulations of microorganism-fluid interactions, advancing the hydrodynamics of three-sphere microswimmers with potential applications in studying alga-alga interactions and collective behaviors.