Suppose that viscous fluid is contained in the space between a fixed sphere S2 and an interior sphere S1 which moves with time-periodic velocity U(t) and angular velocity ω(t), with U(t)=ω(t)=0. It is shown that, provided this motion is chiral in character, it can drive a flow that exerts a nonzero torque on S2. Thus angular momentum can be transferred through this mechanism. In the Appendix, it is shown why lubrication theory does not apply to this problem, even in the limit when the spheres make instantaneous contact.
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