Transition to Freedericksz-type Spontaneous Flow and Spatiotemporal Chaos in Three-Dimensional Active Fluids

Active fluids display rich behavior from spontaneous flow to turbulent mixing at low Reynolds number. Recent experiments suggest fundamental differences in spontaneous symmetry breaking of a 3D extensile active liquid crystal in comparison to the two dimensional counterpart. We investigate the role of confining boundary conditions on the active length scale of a three-dimensional active polar fluid. Using perturbation theory and linear stability analysis, we find that the nature of the spontaneous flow transition depends on the polarity boundary conditions and on the sign (contractile vs. extensile) of the active stress. We show that perpendicular anchoring of polarity at the confining walls only allows for extensile spontaneous flow, whereas parallel anchoring leads to in-plane spontaneous flow for contractile stress and out-of-plane wrinkling for extensile stress. We confirm these theoretical predictions in direct numerical solutions of the nonlinear 3D active Ericksen-Leslie hydrodynamic model. We further show transitions to traveling waves and spatiotemporal chaos when active stress increases beyond the spontaneous flow regime, confirming the existence of active turbulence in 3D.