 Forced-sphere rotation reflected from a held sphere

For equal distant spheres, a force $\mathbf{F}$ on the second generates a Stokeslet velocity $(I+\mathbf{nn})\mathbf{F}/(8\pi \mu R)$ at the held first sphere. The first sphere needs holding force $-3a(I+\mathbf{nn})\mathbf{F}/(4R)$ by Stokes drag law. Its reflected Stokeslet, combined with Faxén rotation law, gives the displayed spin on the second. This translation constraint produces order $Fa/(\mu R^3)$ rotation; if both centers were freely translating the same force monopole would not be emitted by the first sphere. Longitudinal forcing makes the leading cross product vanish.