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

Abstract: We present a comprehensive set of numerical simulations of suspensions of slender self-propelled particles. The model is based on a slender body formulation of hydrodynamic interactions coupled to a constraint-based method for resolving steric interactions. Varying the particle size and volume fraction, which are the only free parameters in the model, we observe a transition to collective motion consistent with established stability results. At low particle volume fractions, correlation functions of the fluid velocity and orientational order parameters extend over the entire domain, with the former approaching a universal curve as the particle size goes to zero, consistent with convergence in the mean-field limit. At higher volume fractions, this scaling no longer persists and the correlation functions scale with the particle size, indicating a failure of the dilute mean-field limit. These observations are quantified through analysis and simulation of the dilute mean-field model.

Recommended citation: Bryce Palmer, Scott Weady, Michael O'Brien, Blakesley Burkhart, Michael J. Shelley. "Correlations, mean-field limits, and transition to the concentrated regime in active particle suspensions." Submitted.