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I show that two-dimensional nematic order in an active fluid film can bestable and long-ranged if exchange of particles and momentum with an ambientthree-dimensional fluid is allowed. Number-conserving films present aninstability, with a fastest-growing mode independent of activity at highactivities or low concentrations. Motility can stabilize long-range polar orderon such immersed surfaces even when the swimmer number in the film isconserved. Active ordering in immersed surfaces is much richer than previouslyexpected, with functional consequences for active transport, and suggests thata broader exploration of parameters in current and future experiments woulddisplay the new features predicted here.

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