= Squirmer reflection from a held sphere
For a <two-mode tensorial squirmer flow> of radius $a$ and a passive equal <sphere> held at $X=Re$, with $a/R\ll1$, let $s=e\cdot Be$. <Faxén's first law> gives holding <force> $F_h=-9\pi\mu a^3s e/R^2+O(\mu a^4|A|/R^3+\mu a^5\|B\|/R^4)$. Its reflected <Stokeslet> changes swimming <velocity> by $-9a^3s e/(4R^3)$. Since this leading <force> is radial, its <vorticity> at the swimmer vanishes. The next holding <force>, generated by the <potential dipole>, yields rotation $a^4 A\times X/(4R^6)$. Terms from the passive <sphere>'s finite radius, reflected <stresslet> and <rotlet> are needed at higher order. These formulas assume fixed slip and no externally applied swimmer <force> or <torque>.
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