= Suppressed spin from a force-free distant sphere
{title2=$\Omega_{\rm self}=O((U/a)(a/R)^7)$}
For a forced sphere and a distant equal <force-free>, <torque-free> sphere, the leading incident <Stokeslet> strain is proportional to $(\mathbf U\cdot\mathbf n)(I-3\mathbf n\mathbf n)$. Its reflected <stresslet> is axisymmetric about the line of centers and has zero <vorticity> on that line. The nominal fifth-order self-spin coefficient therefore vanishes. Finite-size incident-strain corrections and higher force-free scattering multipoles first supply a generic seventh-order <angular velocity>. Purely longitudinal forcing has zero spin exactly by axial symmetry. The leading translation correction is fourth order for a generic orientation, but sixth order for purely transverse forcing. These cancellations matter when using the <method of reflections for Stokes flow> to infer orders from far-field decay alone.
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