Stable long-range uniaxial order in active fluids at two-dimensional interfaces

I show that two-dimensional nematic order in an active fluid film can be stable and long-ranged if exchange of particles and momentum with an ambient three-dimensional fluid is allowed. Number-conserving films present an instability, with a fastest-growing mode independent of activity at high activities or low concentrations. Motility can stabilize long-range polar order on such immersed surfaces even when the swimmer number in the film is conserved. Active ordering in immersed surfaces is much richer than previously expected, with functional consequences for active transport, and suggests that a broader exploration of parameters in current and future experiments would display the new features predicted here.