= Stresslet reflection between two force-free and forced spheres
Consider two widely separated rigid spheres of equal radius $a$, with separation $R\mathbf n$, in <Stokes flow>. Apply a <force> $6\pi\mu a\mathbf U_0$ to the first <sphere> and let the second be <force-free> and <torque-free>. The second <sphere> samples the <rate-of-strain tensor> of the first <sphere>'s <Stokeslet>, $\mathbf E=3a(\mathbf U_0\cdot\mathbf n)(\mathbf I-3\mathbf n\mathbf n)/(4R^2)$. Its leading disturbance is the <stresslet> of a <sphere in a uniform straining Stokes flow>. Evaluating that disturbance back at the first <sphere> gives
$$
\Delta\mathbf U=-\frac{15}{4}\left(\frac aR\right)^4(\mathbf U_0\cdot\mathbf n)\mathbf n.
$$
The <hydrodynamic mobility matrix> decreases at fixed <force>, consistently with the increase of resistance caused by an additional rigid inclusion.
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