Active nemato-hydrodynamics in toroidal microchannels

We investigate flow driven by activity in nematic and polar fluids confined in a toroidal geometry. Using a perturbative expansion in the activity strength, we obtain closed form analytic solutions for the activity-driven flow. A distinguishing feature of this system is that there is no critical threshold which the activity needs to overcome in order to initiate the flow; rather, the flow is a consequence of the combination of activity and curved geometry at any non-zero activity, however small.