= Forced-sphere rotation reflected from a held sphere
{title2=$\delta\boldsymbol\Omega=\frac{3a}{32\pi\mu R^3}\widehat{\mathbf R}\times\mathbf F$}
For equal distant spheres, a force $\mathbf F$ on the second generates a <Stokeslet> velocity $(I+\mathbf n\mathbf n)\mathbf F/(8\pi\mu R)$ at the held first sphere. The first sphere needs holding force $-3a(I+\mathbf n\mathbf n)\mathbf F/(4R)$ 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.
Back to article page
