Advancing Hydrodynamic Models for Free-Swimming Algae Using a Modified Three-Sphere Approach

The beating flagella of the green alga Chlamydomonas reinhardtii play a vital role in generating propulsion and in facilitating interactions with surrounding fluid and fellow microorganisms. Minimal models, such as the three-sphere model, have been widely used to study various aspects of algal motility, including synchronization of flagellar beating, run-and-tumble behavior, responses to shear flow, and rolling motion. However, detailed investigations of the flow fields generated by these models are limited.

In this study, we systematically explore the time-averaged and time-resolved fluid flows generated by the three-sphere model and compare the predictions with experimental data in both two and three dimensions. Our findings reveal that the standard three-sphere model fails to capture key flow characteristics observed experimentally. To address this, we propose a modified three-sphere model with refined flagellar beating dynamics. By incorporating these modifications, we show significant improvements in the prediction of flow fields. We quantitatively characterize the effect of model parameters on flow structures, including the front stagnation point and side vortices. These results deepen our understanding of microorganism-fluid interactions and offer valuable tools for accurately simulating microswimmer dynamics.