= Fore-aft symmetry of a sedimenting-sphere encounter
{title2=$Y(X)=Y(-X)$}
For a smooth passing encounter of a force-driven <sphere> with a fixed <sphere>, isotropy and reflection symmetry imply $\mathbf U=[m_\perp(R)I+(m_\parallel(R)-m_\perp(R))\mathbf n\mathbf n]\mathbf F$. Along a <force> axis $X$, $U_X$ is even and the transverse <velocity> is odd in $X$. Uniqueness then makes the trajectory fore-aft symmetric and restores the incoming impact parameter downstream. This consequence of <kinematic reversibility of Stokes flow> remains valid with <lubrication resistance>, provided the particles remain smooth, noncontacting and subject only to the stated <forces>. Surface roughness and contact can invalidate these assumptions.
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