Strong coupling between the director field and fluid flow in microtubule-based active nematics

Active nematics are bioinspired fluids with local orientational order that exhibit chaotic dynamics and self-mixing.  We consider here a well-studied laboratory example consisting of a two-dimensional (2D) layer of microtubule bundles crosslinked by kinesin molecular motors and driven by adenosine triphosphate (ATP).  In the usual nematohydrodynamic model of this system, the rotation of the director field need not perfectly follow the fluid, even in highly ordered regions away from topological defects.  Similarly, the velocity of the topological defects need not match the local fluid velocity; defects can move either more slowly or quickly than the surrounding fluid.  However, recent work showing that +1/2  defects "stir" microtubule-based active nematics suggests that there is a strong correlation between the defect velocity and the local fluid velocity.  Furthermore, the relatively long length of the microtubule bundles within the active nematic suggests that steric interactions prevent the director field from rotating without a corresponding deformation of the surrounding patch of material.  We thus explore here the limit of strong coupling between the fluid flow and the director field, whereby the directors evolve as though they are passive rods within the material and topological defects move as though they are passive tracers within the fluid.  We present direct experimental evidence on the correlation between these velocities and we derive a nematic transport equation for this system.