Chiral transfer of angular momentum

Suppose that viscous fluid is contained in the space between a fixed sphere $S_2$ and an interior sphere $S_1$ which moves with time-periodic velocity ${\bf U}(t)$ and angular velocity ${\bf \Omega}(t)$, with $\left<{\bf U}(t)\right> = \left<{\bf \Omega}(t)\right> = 0$. It is shown that, provided this motion is chiral in character, it can drive a flow that exerts a non-zero torque on $S_2$. Thus angular momentum can be transferred through this mechanism.