= Vertical bound pair in the point-force sedimentation model
{title2=$r_*=-3D/(2\delta),\quad\lambda_r=-\delta/r_*,\quad\lambda_\theta=\delta/(2r_*)$}
If $\delta D<0$, the <leading interaction of two sedimenting spheres> has a formal vertical <equilibrium> at $r_*=-3D/(2\delta)$. Choose labels with $\delta>0,D<0$ and put <sphere> one above <sphere> two. On that invariant vertical line, $\dot r=-\delta+\delta r_*/r$, so both sides approach $r_*$ and the radial <eigenvalue> is $-\delta/r_*$. A small tilt instead grows at rate $\delta/(2r_*)$: the full configuration-space <equilibrium> is a saddle, not an attracting node. A physically valid far-field bound pair requires $r_*\gg a_1+a_2$, or $|D|\gg(a_1+a_2)|\delta|$. Reversing both driving <forces> reverses the <vector> field, interchanging radial attraction and repulsion, consistent with <kinematic reversibility of Stokes flow>.
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