Active polar fluids exhibit spontaneous flow when sufficient active stress is generated by internal molecular mechanisms. This is also referred to as an active Fr\'{ e}edericksz transition. Experiments have revealed the existence of competing in-plane and out-of-plane instabilities in three-dimensional active matter. So far, however, a theoretical model reconciling all observations is missing. In particular, the role of boundary conditions in these instabilities still needs to be explained. Here, we characterize the spontaneous flow transition in a symmetry-preserving three-dimensional active Ericksen-Leslie model, showing that the boundary conditions select the emergent behavior. Using nonlinear numerical solutions and linear perturbation analysis, we explain the mechanism for both in-plane and out-of-plane instabilities under extensile active stress for perpendicular polarity anchoring at the boundary, whereas parallel anchoring only permits in-plane flows under contractile stress or out-of-plane wrinkling under extensile stress.
Categories: cond-mat.soft