Two-dimensional long-range uniaxial order in three-dimensional active fluids

Abstract

Elongated active units cannot spontaneously break rotation symmetry in bulk fluids to form nematic or polar phases. This has led to the image of active suspensions as spontaneously evolving, spatiotemporally chaotic fluids. Here, in contrast, I show that bulk active fluids have stable active nematic and polar states at fluid–fluid or fluid–air interfaces. The active flow-mediated long-range interactions that destroy the ordered phase in bulk lead to long-range order at the interface. Thus, active fluids have a surface ordering transition and form states with quiescent, ordered surfaces and chaotic bulk. I further consider active units that are constrained to live at an interface to examine the minimal conditions for the existence of two-dimensional order in bulk three-dimensional fluids. In this case, immotile units do not order, but motile particles still form a long-range-ordered polar phase. This prediction of stable, uniaxial, active phases in bulk fluids may have functional consequences for active transport. Bulk active fluids are unstable because activity destroys long-range ordering. Now, a model of 3D active liquids shows that stable states can form at fluid–fluid surfaces.