Coherent Structures and Transitional Behavior of Confined Polar Active Suspensions*

Confined suspensions of self-propelled Brownian particles exhibit distinct behaviors, such as density fluctuations and polarization instabilities. This study explores the three-dimensional transport dynamics of dilute active fluids composed of oblong swimmers, extending earlier work on two-dimensional confined flows. We numerically investigate a thin fluid film confined between no-slip walls with periodic boundaries, where confinement critically shapes the dynamics of active polar suspensions. The Doi-Onsager kinetic theory in a mean-field framework provides moment equations for particle concentration, polarization, and nematic ordering. Two key parameters, the swimming Peclet number (governing confinement) and the propulsion parameter (characterizing activity), define the system’s behavior. Numerical simulations map the swimmer activity and confinement parameter space, revealing equilibrium profiles for concentration, polarization, and nematic ordering. Notably, boundary layers form within the film, resembling one-dimensional traveling waves with finite spatial wavelengths, a coherent feature of the system. Critical transitions from steady unidirectional flow at low propulsion to spatiotemporal chaos, or active turbulence at higher propulsion, are identified. Intermediate propulsion strengths reveal a bifurcation, where coherent boundary layers signal a shift from steady-state to oscillatory behavior. Stability analysis further supports these numerical findings, predicting the onset of finite-wavenumber instabilities. Confinement redistributes concentration, polarization, and nematic ordering across the film thickness, significantly impacting local dynamics. The combined insights from numerical simulations and stability analysis elucidate the structuring and transitions in three-dimensional polar active suspensions, particularly emphasizing the emergence of finite-wavelength boundary layers.