The loss of isotropy due to confinement in kinesin-driven active fluids.*

Kinesin-driven microtubule systems demonstrate complex non-equilibrium dynamics. Here, we focus on the 3D behavior in systems measuring 2 or 4 mm in the horizontal direction, but with varying confinement - ranging from 0.1 to 4 mm -  in the vertical direction. Our results reveal that the active systems maintain small-scale isotropy, independent of the system size or confining boundary location, but lose large-scale isotropy as confinement increases. Meanwhile, the flow observes a transition from sub-diffusion to super-diffusion, initially in the direction perpendicular to the confining boundary and eventually in all three directions. Temporal velocity correlations reflect these transitions, showing faster decay along the perpendicular direction. The size of the large-scale flow structures, characterized by integrating the spatial correlation function, increases with the system size. However, the integral scale saturates at a maximum size of approximately 400 microns - an order of magnitude smaller than the largest system size tested. Such saturation indicates an intrinsic length scale which, along with the small-scale isotropy, demonstrate the multi-scale nature of these kinesin-driven microtubule systems.