Correlations, mean-field limits, and transition to the concentrated regime in motile particle suspensions

Suspensions of swimming particles exhibit complex collective behaviors driven by hydrodynamic interactions, showing persistent large-scale flows and long-range correlations. While heavily studied, it remains unclear how such structures depend on the system size and swimmer concentration. To address these issues, we simulate very large systems of suspended swimmers across a range of system sizes and volume fractions. For this we use high-performance simulation tools that build on slender body theory and implicit resolution of steric interactions. At low volume fractions and long times, the particle simulations reveal dynamic flow structures and correlation functions that scale with the system size. These results are consistent with a mean-field limit and agree well with a corresponding kinetic theory. At higher concentrations, the system departs from mean-field behavior. Flow structures become cellular, and correlation lengths scale with the particle size. Here, translational motion is suppressed, while rotational dynamics dominate. These findings highlight the limitations of dilute mean-field models and reveal new behaviors in dense active suspensions.