Unveiling Pattern Formation in Confined Three-Dimensional Active Polar Fluids

Active polar fluids composed of force-generating microswimmers (e.g., pushers) exhibit a rich spectrum of spontaneous flows when confined within narrow channels. Through direct numerical simulations of a continuum model, we identify a sequence of flow regimes—ranging from isotropic diffusion to unidirectional shear flow, traveling-wave states, roller-like vortices, and ultimately chaotic dynamics—as the activity parameter is increased. This activity parameter, a dimensionless measure of the active stress generated by individual swimmers, encapsulates the interplay between dipole strength, fluid viscosity, swimmer velocity, and length scale. A phase diagram is constructed to map the boundaries between these regimes as a function of activity and geometric confinement. Linear stability analysis of the isotropic and unidirectional base states reveals the critical thresholds governing the onset of spontaneous symmetry breaking and pattern formation. Our results highlight how activity-driven rheological responses control flow instabilities in confined active suspensions, with implications for understanding transport in synthetic and biological microscale systems.