Spontaneous flow instabilities of active polar fluids in three dimensions

TL;DR

This paper develops a comprehensive 3D theoretical model for active polar fluids, explaining how boundary conditions influence spontaneous flow instabilities and reconciling experimental observations of in-plane and out-of-plane behaviors.

Contribution

It introduces a symmetry-preserving 3D active Ericksen-Leslie model that explains the role of boundary conditions in flow instabilities of active polar fluids.

Findings

Boundary conditions determine the type of flow instability.

Extensile stress leads to both in-plane and out-of-plane instabilities.

Parallel anchoring restricts flows to in-plane or out-of-plane wrinkling depending on stress.

Abstract

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.